Research ArticleIntegrated Yard Space Allocation and Yard Crane DeploymentProblem in Resource-Limited Container Terminals

Caimao Tan1 and Junliang He2

1Scientific Research Academy Shanghai Maritime University No 1550 Haigang Ave Shanghai 201306 China2Engineering Research Center of Container Supply Chain Technology Ministry of EducationShanghai Maritime University Shanghai 201306 China

Correspondence should be addressed to Junliang He soldierlianglian163com

Received 16 August 2016 Revised 12 September 2016 Accepted 19 September 2016

Academic Editor Lu Zhen

Copyright copy 2016 C Tan and J He This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Yard storage space and yard crane equipment are the core resources in the container terminal yard area This paper studies theintegrated yard space allocation (outbound container space) and yard crane deployment problem in resource-limited containerterminals where yard space and yard cranes are extremely scarce Two corresponding counterstrategies are introduced respectivelyand the integrated problem is solved as mixed integer programming The model this paper formulated considers the containervolume fluctuation of the service line and the objective is a trade-off between yard sharing space and terminal operation costIn numerical experiments this paper tries to reveal the management meaning in practical operation of container terminal andprovides decision support for terminal managers therefore a series of scenarios are presented to analyze the relations among theyard sharing space the number of yard cranes the size of yard subblock and the cost of terminal operation

1 Introduction

With the rapid development of global economy as a centerof interregional trade international container transportationhas experienced rapid growth Container transportation hasbeen developing for nearly 30 years and its throughput kepta sustained increase except for the world economic crisis in2009 Global container throughput witnesses a new record678 million TEUs in 2014 and according to the forecast byDrewry it will be greater than 840 million TEUs in 2018

The sustained growth of the container market puts for-ward a higher requirement for the operation efficiency ofcontainer terminal However the overall berth productionefficiency is not in pace with the trend of shipping maxi-mization according to the Drewry report in 2014 One of themain reasons is the container terminal operational bottleneckmoving from the seaside to the yard area and therefore theoperational efficiency in the yard area becomes increasinglysignificant to the container terminals [1 2]

The storage yard management is complex in practice andinvolves two interrelated decision problems (1) the storagespace allocation problem which is to determine the storage

locations for incoming containers and (2) the yard crane(YC) deployment problem which is to decide the numberof YCs working in each block and their movements betweenblocks [3] Generally speaking yard space allocation consid-ers the containers storage requirement and operating timewindows of the service line and the workload requirementof YCs is that the yard crane deployment must be involved

Yard managers usually solve the two decision problemssequentially in such a way that space allocation is determinedfirst and the resulting workload is used to deploy theYC accordingly However this planning procedure ignoresconsidering the impact of a yard space allocation plan onthe operational efficiency of YC and this impact will begreat in some case In practice the storage allocation plandetermines the distribution of YC workload over the entireyard and affects YCdeployment decisions In some situationsthe YC workload varies greatly between consecutive periods(working shifts) or the YC workload concentrates in certainareas (blocks or yard rows) because of inappropriate spaceallocation (YC deployment is not considered) and this maylead to unnecessary movement of YCs orand even trafficcongestion in the yard Consequently it is necessary to

Hindawi Publishing CorporationScientific ProgrammingVolume 2016 Article ID 6421943 12 pageshttpdxdoiorg10115520166421943

2 Scientific Programming

integrate these two related problems as a system so thatthe yard space allocation and yard crane deployment can beproperly coordinated

Another emerging issue is that there are still many con-tainer terminals confronted with the resource-limited prob-lem such as Shanghai Yangshan port or Ningbo-Zhoushanport although there are many other terminals facing asevere overcapacity situation and the limited resources inthe yard area mainly concern the yard storage resource andYC equipment resource Take Ningbo Port Beilun PhaseIV Container Terminal as an example its throughput hasreached 5 million TEUs in 2014 while the designed annualthroughput is only 2 million TEUs The yard storage spaceand YC equipment resources are extremely scarce thereforethe yard stacking utilization has risen to more than 90during handling peak period and there are only 4 fixedYCs in each row in the yard while they should be serving 6blocks Consequently there is a continued need to study theoptimization of yard operation especially for the resource-limited container terminals

This paper aims to solve resource-limited predicament inthe yard area and thereby improve the operational efficiencyin the terminal Considering that the bottleneck of containerport has moved from the quay side to the yard area the oper-ation optimization in the yard area is regarded as the point ofpenetration This paper integrated yard space allocation andyard crane deployment problem hence an integrated modelis formulated and two corresponding counterstrategies (thespace sharing strategy and yard crane interzone movementstrategy) are introduced These two strategies are used tosolve yard storage space resource and yard crane equipmentresource scarce problem respectively The authors focuson the integrated yard space allocation and yard cranedeployment in the tactical level and the major contributionsare provided as follows

(1) An integrated mathematical optimization model isformulated which provides a comprehensive viewof yard space allocation and yard crane deploymentproblem the objective function of the model is atrade-off between yard space utilization and yardoperation cost

(2) Two factors impacting the operational efficiency ofstorage yard are introduced and these factors playa significant role in the practical container terminaloperation but have seldom been presented in existingliteratures Meanwhile the container volume fluctua-tion of the service line is also under consideration

(3) A detailed scenario analysis among the yard sharingspace the number of YCs the size of yard subblockand the operation cost of container terminal is pre-sented which can provide a precise relative referenceto container terminal manager

The remainder of this paper is organized as followsSection 2 reviews the related researches Section 3 elaboratesthe description for the yard space allocation problem andyard crane deployment problem as well as a mathematicalmodel formulation in Section 4 Numerical examples are

given in Section 5 and a brief conclusion remark is presentedin the concluding section

2 Literature Review

Container terminal operation management is an extremelycomplex conundrumbecause toomany elements are involvedin the system Up to the present there are numerous studieson the container port operations [4ndash6] such as quay craneallocation and inner truck routing in the seaside yard spaceallocation and yard crane scheduling in the landside Fora comprehensive overview we refer readers to the reviewworks given by Vis and De Koster [7] Steenken et al [8]and Stahlbock and Voszlig [9] In this section a brief review ofstudies highly related to container terminal operation in theyard area is provided

21 Yard Space Allocation Generally speaking storage spaceallocation can be analyzed at various levels according to thestorage space unit considered yard section yard block yardsubblock yard bay and individual slot [3]This paper followsup the space sharing strategy [10] between neighbor storageunits based on yard template generation therefore the papersconsidering yard space allocation in subblock level will beintroduced minutely in this subsection

Lee et al [11] used the consignment strategy to storeincoming export and transshipment containers at dedicatedlocations according to the destination vessel helping toreduce the reshuffling level to a negligible level this strategyhas initiated a new line of yard space allocation problem Hanet al [12] extended their research to optimize the yard tem-plate and the yard storage allocation problem simultaneouslythe yard storage space is reserved for each specific vessel inthis paper Jiang et al [10] put forwarded the concept of spacesharing strategy between neighbor subblocks so the containeryard can improve land utilization based on this creativeand meaningful concept a two-space sharing method wasalso proposed to improve the space utilization of a certainyard template Jiang et al [13] considered a flexible spacesharing strategy compared with the previous fixed spacesharing pattern A yard template determined the allocationof spaces in the container terminal yard while fluctuation ofdemand for freight transportation brings challenge to yardtemplate generation Zhen [14] proposed a yard templateplanning considering random numbers of containers thatwill be loaded onto vessels that visit the port periodicallySimilar to Han et al [12] the traffic congestions problem inthe yard area is also considered However there are still someimportant factors which have received inadequate attentionbut should not be overlooked in practical terminal yardspace management Part of those factors is the proportionalmatching of quay operation queue and YC loading point of theservice line

22 Yard Crane Deployment With the yard space allocationplan determined the information of grounding and retrievalactivities in all blocks can be available for planning the yardcrane deployment [3] Compared with yard crane scheduling

Scientific Programming 3

problem the yard crane deployment emphasizes the macroconfigure level Zhang et al [15] addressed crane deploymentproblem with the workload of each block in each period wasgiven and try to find the optimal times and routes of yardcranemovements among yard blocks so that the total delayedworkload in the yard is minimum With the same objectiveChung et al [16] and Linn et al [17] formulated yard cranedeployment problem as a mixed integer linear program theyloosen the restrictions in Zhang et al [15] that each blockshould include not more than two cranes and the maximumnumber of transfers in or out of a block is limited In theabove-mentioned researches the type of the yard crane isa single E-RTG (electric yard crane) system Cao et al [18]focused on the deployment problem of double-rail-mountedgantry yard crane system which has been applied in WesternAutomated Container Terminals An integer programmingmodel was formulated as well as a greedy heuristic algorithma simulated annealing algorithm and a combined yard cranescheduling heuristic were designed to solve the proposedproblem

23 Integrated Management The integration of the yardspace allocation and yard crane deployment problem is alsoregarded by many researchers [10ndash12 19ndash21] due to therelationships between these two problems K H Kim andH B Kim [19] discussed a method to determine the optimalamount of storage space and the optimal number of transferYCs for handling import containers The cost model consistsof the space cost the investment cost of transfer cranes andthe operating cost of transfer cranes and trucks However thismodel cannot give a detailed storage location for containersor group of containers Lee et al [11] Han et al [12] andJiang et al [10] considered yard space allocation and relevantworkload assignment problem and the yard crane resourcerequirement was also included yet the yard crane interblockmovement is not allowed Lee et al [20] addressed theintegrated problem for bay allocation and yard crane schedul-ing in transshipment container terminal and allocated bayresource to fleet containers in a more efficient way Receivingoperation and retrieving operation in the storage yardswere considered simultaneously to achieve a more efficientoperation of the yard crane while bay allocation focused on ablock vision rather than yard overall prospect Won et al [21]proposed an integrated decision-making framework for theyard planning that simultaneously considers storage spaceyard crane and traffic area in the container terminal

The integrated yard space allocation and yard cranedeployment problem studied in this paper follows up thework of Jin et al [3] Instead of dealing with detaileddaily subblock space allocation and yard crane deploymentproblem at the operational level this paper addresses thetactical planning level In addition the subject of this studyis these container terminals where yard space and yardcrane resources are extremely limited the yard space sharingstrategy and yard crane interzone movement strategy areapplied consequently Different from Jin et al [3] this papersimultaneously considers the space allocation and yard cranedeployment in the yard area and not only the operation costbut also the yard storage space utilization is considered

3 Problem Description

Before we elaborate the yard space allocation and yard cranedeployment problem there are some concepts existing in thetext that must be explained

(i) Service Line The service line is service object of thecontainer terminal in a sense a service liner is aset of many voyages with the same departure anddestination Different from Line the line is a generalconcept while the service line is a specific conceptand the object is the container terminal

(ii) Quay Operation Queue The quay operation queue isthe number of quays that service a specified serviceline (loading and unloading operation) simultane-ously The quay operation queue of a service lineis usually determined by the vessel size containervolumes (loading and unloading operation) and theservice line priority level Generally speaking thehigher the priority level of service line the greater thenumber of quay operation queues that the service linehas

(iii) YC Loading Point The YC loading point is the num-ber of YCs servicing a certain service line (loadingoperation) simultaneously Because of the differentoperation efficiency of quay and yard crane thereis a proper matching proportion between the quayoperation queue and YC loading point for a serviceline and it is optimal matching that 1 quay operationqueue deploys 2 or 3 YC loading points

Remarkably for a service line there is at most one YCloading point in one block even if it has two ormore subblocksassigned in one block because of the limitation of YCs Asshowed in Figure 1 there are two service lines service line 1uses vessel Awith 800 TEUs outbound containers and serviceline 2 uses vessel B with 3000 TEUs outbound containersBoth service lines have deployed 4 quay operation queuesAs we can see service line 1 only has 800 TEUs outboundcontainers to be loaded (about 6 subblocks volumes) butbecause line 1 deployed 4 quay operation queues 8 yard YCloading points are needed at least so 8 subblocks locatedin 8 different blocks are assigned to line 1 consequentlyMeanwhile although service line 2 has 3000 TEUs (20subblocks volumes) it only deployed 4 quay operation queues12 yard YC loading points could be fulfilled at most and 20subblocks concentrated which are located in 12 blocks areassigned to service line 2 accordingly

31 Storage Space Allocation The storage space allocationdetermines the container yard stacking position in the sub-block for each service line of the terminal The allocationplan will normally not change once it is determined sincevast shipping companies service lines are relatively stableHowever there has been a realistic problem that it is difficultto calculate the accurate subblocks that each service lineshould be assigned because of the uncertainty of maritimemarket Therefore the volume of outbound containers fluc-tuates frequently If the yard storage space (subblocks) is

4 Scientific Programming

1 loading point for vessel A 1 loading point for vessel B

Subblock 150 TEUs

800 TEUs outbound containersService line 1 vessel A

3000 TEUs outbound containersService line 2 vessel B

S1 S2 S3 S4 S5

S21 S22 S23 S24 S25

S41 S42 S43 S44 S45

S61 S62 S63 S64 S65

S6 S7 S8 S9 S10

S26 S27 S28 S29 S30

S46 S47 S48 S49 S50

S66 S67 S68 S69 S70

S31 S32 S33 S4 S35

S11 S12 S13 S14 S15

S51 S52 S53 S54 S55

S71 S72 S73 S74 S75

S36 S37 S38 S39 S40

S16 S17 S18 S19 S20

S56 S57 S58 S59 S60

S76 S77 S77 S78 S78

Berth

Zone

QC operation queue

(Row)

Figure 1 A typical yard space configuration of container terminal

assigned according to the service line minimal demand it islikely to face storage space shortage for a busy voyage On thecontrary the terminal yard space will not be sufficient

For the container terminal with a static yard template[11 12] all the subblocks in each block have a fixed spacecapacity whichmeans each service line needs to be assigned alarge enough yard storage space to satisfy containers stackingdemand at the peak time To take advantage of the benefitof consignment strategy and increase the yard storage spaceutilization Jiang et al [10] proposed a space sharing strategywhich allows some certain space to be shared betweenneighbor subblocks For a detailed sharing space strategydescription we refer readers to the work given by Jiang et al[10]

In general for a resource-limited container terminal themain concern is the utilization of yard storage in the processof yard space allocation Accordingly the objective couldbe concentrated on the total sharing space between yardneighbor subblocks Constraints that should be consideredwhen allocating storage space mainly include the following

(i) The storage capacity allocated to each service lineshould be sufficient so that it could meet the stackingdemand

(ii) For each service line in order to achieve a high oper-ational efficiency as far as possible the proportion ofquay operation queue and YC loading point would bein the reasonable range

(iii) The YC loading point in the block must be wellcontrolled at any time period otherwise traffic con-gestion can be expected

32 Yard Crane Deployment The yard crane deploymentproblem is to designate and schedule YCs route accordingto the workload requirement in the yard area Many relevantresearches usually focus on the deployment problem betweenyard blocks in the same zone that only the yard craneintrazone movement is considered This is a commendablestrategywhen the terminal yard crane resources are adequate

However there may be a situation that only four YCs arein one zone with 5 or 6 blocks in some container terminals Inthis case 4 YCs should service 5 or 6 blocks the YCs have tomove among different block zones Therefore the yard craneinterzone movement is enabled in this terminal to satisfyoperational requirements In this study we concentrated onthe yard crane interzonemovement rather than the intrazonemovement because the former operation time cost and fuelconsumption cost are much higher than the latter Figure 2shows a diagram of E-RTG interzone movement process Fora detailed yard cranemovement patterns description we referreaders to the works given by Linn et al [17] and Zhang et al[15]

For yard crane deployment the objective is to optimizeworkload distribution of each yard rowduring all the periodsTherefore the optimization objective in this paper is tominimize YCs operation cost when deploying yard craneConstraint that should be considered is to ensure the number

Scientific Programming 5

1

2

3

Electric cables

Figure 2 E-RTG interzone movement process

of YCs deployed in each row can satisfy the containerhandling requirement

4 Mathematic Model

In this section the integrated yard space allocation and yardcrane deployment mathematical model for resource-limitedcontainer terminal is formulatedThe authors raised themaincharacteristics of resource-limited container terminal storagespace allocation and yard crane deployment problem andthen presented the relevant counterstrategies accordingly Foryard space strained problem the space sharing strategy isapplied which has been proposed by Jiang et al [10] and asfor yard crane equipment shortage the yard crane interzonemovement is enabled

41 Assumptions The following assumptions are made in theintegrated model

(1) The yard storage space can satisfy the minimumservice line outbound containers stacking demandand the YCs are sufficient to guarantee the basichandling requirement

(2) The service lines berthing position are given andfixed hence once the service line containers areassigned to the subblocks the minimal inner trucktransportation distances are determined

(3) A subblock can be reserved for only one service lineexcept for part of the storage space which may beshared with its neighbor assigned service lines andwill not change once the storage plan is determined

(4) The YC can only shift to one yard zone in one periodit means that once the yard crane moved from onezone to another then it should be staying in the zonebefore the next planning period is begun

42 Mathematic Formulation This model aims to deal withthe yard space allocation problem and yard crane deploymentproblem at the tactical level and provides the following

results (1) yard storage space allocation plan for outboundcontainers of all the service lines which considers thecontainer volumes quay operation queues YC loading pointsand handling conflicts of service lines in the storage yard(2) yard crane deployment profile including the yard craneassignment plan in the initial period and subsequent yardcrane moving scheme

Sets

119879 set of time periods 119879 = 1 2 119873119879119861 set of yard blocks 119861 = 1 2 119873119861119878 set of yard subblocks 119878 = 1 2 119873119878119878119899119894 set of neighbor subblocks of subblock 119894 isin 119878 119878119899119894 isin 119878119878119904119902 set of subblocks belonging to block 119902 isin 119861 119878119904119902 isin 119878119877 set of yard rows (zone) in the terminal yard 119877 =1 2 119873119877119861119903 set of blocks belonging to row 119903 isin 119877 119861119903 isin 119861119871 set of service lines of terminal 119871 = 1 2 119873119871119884 set of YCs 119884 = 1 2 119873119884

Parameters

119888min119898 minimal outbound containers of service line 119898 isin 119871

(TEUs)119888max119898 maximal outbound containers of service line 119898 isin 119871

(TEUs)119901119898 quay operation queues of service line119898 isin 119871

120583min minimal YC loading points that one quay operationqueue demands

120583max maximal YC loading points that one quay operationqueue can satisfy

119905119904119898 time period to start handling of service line119898 isin 119871119905119890119898 time period to end handling of service line119898 isin 119871ℎ119898119905 handling parameter of service line119898 isin 119871 equal to 1 if119905 isin [119905119904119898 119905119890119898] otherwise equal to 0

6 Scientific Programming

V119904 maximal space capacity of each subblock (TEUs)

V119887 maximal space capacity of each yard block (TEUs)

120575119887 maximal YCs enabled operating in one yard block120575119903 maximal YCs enabled operating in one block row

120596119898119899 yard space sharing space when subblocks of serviceline 119898 isin 119871 and service line 119899 isin 119871 are neighbored (inthis paper120596119898119899 isin 0 1 it is usually determined by thecontainer buildup pattern of two service lines [14])

120579 fixed capacity of one sharing space (TEUs)119889119905119894119898 inner truck moving distance (loading and unloading)

if service line119898 isin 119871 is assigned to subblock 119894 isin 119878 (km)1198891198881199031199031015840 yard cranemovement distance between row 119903 isin 119877 and

row 1199031015840 isin 119877 (km)120593 inner truck transportation cost (yenkmTEU)120590 fixed time consumption of yard crane interzone

movement (h)120587 yard crane time cost (yenh)120588 yard crane movement cost (yenm)

1205821199031199031015840 yard crane interzone movement cost between row 119903 isin119877 and row 1199031015840 isin 119877 119903 = 1199031015840 (yen) where 1205821199031199031015840 = 120590120587 + 1198891198881199031199031015840120588if 119903 = 1199031015840 1205821199031199031015840 = 0

120576 a small and positive constant

Decision Variables

119909119894119898 isin 0 1 1 if subblock 119894 isin 119878was assigned to serviceline119898 isin 119871 0 otherwise1199101199031199031015840119905 isin 119873 YCs moving from row 119903 isin 119877 to row 1199031015840 isin 119877at the end of time period 119905 isin 119879 (and 1199101199041199030 is initial YCsof row 119903 isin 119877 in the beginning of the period)119911119898119902 isin 0 1 the number of YC loading points ofservice line119898 isin 119871 in block 119902 isin 119861119908119889119903119905 isin 119873 minimal yard crane requirement of row 119903 isin119877 in time period 119905 isin 119879119908119886119903119905 isin 119873 the number of YCs assigned to row 119903 isin 119877 intime period 119905 isin 119879

Objective Function

maximize 1198911 = sum119894isin119878

sum119895isin119878119899119894

sum119898119899isin119871

119909119894119898119909119895119899120596119898119899120579 (1)

minimize 1198912 = 1198911199052 + 1198911198882 (2)

1198911199052 = sum119894isin119904

sum119898isin119871

119909119894119898119889119905119894119898120593V119904 (3)

1198911198882 = sum119903isin119877

sum1199031015840isin119877

sum119905isin119879

11991011990311990310158401199051205821199031199031015840 (4)

The mathematical model proposed in this section is amultiobjective optimal model hence the authors transferredit into a single-objective problem by the method of weightedallocation Define 120572 as the coefficient of yard storage space

in the process of terminal operation management and usecoefficient 120572 to combine the two objectives Furthermorebecause the dimensions of two objectives are different thusnondimensional processing is needed Note that 119891max

1 and119891min1 are the independent maximal and minimal value of 1198911

respectively 119891max2 and 119891min

2 are the independent maximaland minimal value of 1198912 Therefore the integrated objectivefunction can be expressed as follows

max 119891 = 120572 (1198911 minus 119891min1 )

(119891max1 minus 119891min

1 ) +(1 minus 120572) (119891max

2 minus 1198912)(119891max2 minus 119891min

2 ) (5)

In formula (5) the coefficient 120572 could be set as0 01 10 with a step size of 01 This step could beadjusted manually according to problem size and terminaloperatorrsquos preference By changing the value of 120572 differentsets of solutions can be obtained In other words when 120572is smaller the solutions are more space-utilizing On thecontrary with the increase of 120572 the solutions are more cost-saving

Constraints

sum119898isin119871

119909119894119898 le 1 forall119894 isin 119878 (6)

sum119894isin119904

119909119894119898 ge lceil119888min119898

V119904rceil forall119898 isin 119871 (7)

sum119894isin119904

119909119894119898 le lceil119888max119898

V119904rceil forall119898 isin 119871 (8)

sum119894isin119878

sum119898isin119871

119909119894119898 = 119873119878 (9)

119911119898119902 le sum119894isin119878119904119902

119909119894119898forall119898 isin 119871 119902 isin 119861

(10)

119911119898119902 ge sum119894isin119878119904119902

119909119894119898120576

forall119898 isin 119871 119902 isin 119861(11)

sum119902isin119861

119911119898119902 ge 120583min119901119898 forall119898 isin 119871 (12)

sum119902isin119861

119911119898119902 le 120583max119901119898 forall119898 isin 119871 (13)

lceil119888max119898

V119904rceil ge 120583min119901119898 forall119898 isin 119871 (14)

sum119898isin119871

119911119898119902ℎ119898119905 le 120575119887 forall119902 isin 119861 119905 isin 119879 (15)

119908119889119903119905 = sum119898isin119871

sum119902isin119861119903

119911119898119902ℎ119898119905forall119903 isin 119877 119905 isin 119879

(16)

Scientific Programming 7

119908119889119903119905 le 120575119887 forall119903 isin 119877 119905 isin 119879 (17)

sum119898isin119871

119909119894119898ℎ119898119905 + 120576sum119895isin119878119899119894

sum119898isin119871

119909119895119898ℎ119898119905 le 1 forall119894 isin 119878 119905 isin 119879 (18)

sum119903isin119877

1199101199041199030 = 119873119884 (19)

sum1199031015840isin119877

1199101199031199031015840119905 = 1199101199041199030 forall119903 isin 119877 119905 = 1 (20)

sum1199031015840isin119877

1199101199031199031015840119905 = sum1199031015840isin119877

1199101199031015840119903(119905minus1)forall119903 isin 119877 2 le 119905 le 119873119879 minus 1

(21)

1199101199041199030 = sum1199031015840isin119877

1199101199031015840119903119905forall119903 isin 119877 119905 = 119873119879

(22)

119908119886119903119905 = 1199101199041199030 forall119903 isin 119877 119905 = 1 (23)

119908119886119903119905 = sum1199031015840isin119877

1199101199031015840119903(119905minus1)forall119903 isin 119877 119905 isin 119879 119905 = 1

(24)

119908119886119903119905 ge 119908119889119903119905 forall119903 isin 119877 119905 isin 119879 (25)

119908119886119903119905 le 120575119903 forall119903 isin 119877 119905 isin 119879 (26)

119909119894119898 isin 0 1 forall119894 isin 119878 119898 isin 119871 (27)

1199101199041199030 isin 119873 forall119903 isin 119877 (28)

1199101199031199031015840119905 isin 119873forall119903 1199031015840 isin 119877 119905 isin 119879 (29)

119911119902119898 isin 0 1forall119898 isin 119871 119902 isin 119861 (30)

119908119886119903119905 119908119889119903119905 isin 119873 forall119903 isin 119877 119905 isin 119879 (31)

The constraints of the mathematical model are composedof three parts the yard space allocation constraints theyard crane deployment constraints and the variables rangeconstraints

Equations (6) to (18) are the constraints of the first partwhich defines the rules of yard space allocation Equation (6)states that each subblock should be reserved for at most oneservice line during the entire planning horizon Equations (7)and (8) state that the subblocks assigned to the service linemust satisfy the outbound containers storage demand of theservice line Considering the service line outbound containervolumes are not generally fixed and the yard storage spaceis extremely limited the loosened constraints are presentedEquation (9) ensures that all the subblocks should be assignedto a service line Equations (10) and (11) are the calculationequations of service line YC loading points in a block equalto 1 if there is at least one subblock reserved for the service

line but otherwise equal to 0 Equations (12) to (14) state therelationship between the service line quay operation queuein the seaside and the YC loading point in the yard areaEquation (15) ensures themaximal handling YCs in the blockEquations (16) and (17) restrict the maximal handling YCsin the yard row Equation (18) states that when one of thesubblocks is in loading state the other neighbor subblocksare unavailable for service line that should be handled at thesame time

Equations (19) to (26) are the constraints of the secondpart which defines the rules of yard crane deploymentEquation (19) guarantees that the summation of initial YCsdeployment in each row is equal to the number of YCsEquations (20) to (22) ensure the YCs resource flow balancein the process of YCs interzone movement in each period ofplanning horizon Equations (23) and (24) are the calculationequations of YCs in each yard row Equations (25) and (26)ensure that the YCs operating in the row should satisfy theoperational demand and not exceed the maximal YCs boundin the row at the same time

Finally the domains of variables defined by (27) to (31)are the constraints of the third part

Linear Transformation As formula (1) is a nonlinear functiona linear transformation operation is applied After lineartransformation formula (1) is equal to

max 1198911 = sum119894isin119878

sum119895isin119878119899119894

sum119898119899isin119871

120601119894119895119898119899120596119898119899120579120601119894119895119898119899 le 119909119894119898 forall119894 isin 119878 119895 isin 119878119899119894 119898 119899 isin 119871120601119894119895119898119899 le 119909119895119899 forall119894 isin 119878 119895 isin 119878119899119894 119898 119899 isin 119871120601119894119895119898119899 ge 119909119894119898 + 119909119895119899 minus 1

forall119894 isin 119878 119895 isin 119878119899119894 119898 119899 isin 119871120601119894119895119898119899 isin 0 1 forall119894 isin 119878 119895 isin 119878119899119894 119898 119899 isin 119871

(32)

5 Numerical Experiment

To evaluate the effectiveness of the proposed model aseries of experiments with different scales are conductedSection 51 introduces the parameters used for generating theexperiments Section 52 analyzes the trade-off between yardstorage space resource utilization and yard operation costSection 53 researches the effects of YCs on yard storage spaceand operational cost Section 54 explores the influence ofsubblock volume on the yard management The integratedmodel in this paper is solved by ILOG CPLEX 124 and all ofthe computation experiments are conducted on aworkstationwith Inter Xeon CPU with 64GHz RAM

51 Instances At present many of the container line arrivalpatterns are weekly arrival In other words the voyage ofservice line arrives at the terminal once a weekTherefore theplanning horizon of this experiment is 1 week and each dayis split into 3 periods of 8 hours in consideration of practicalworking shift in the container terminal The experiment in

8 Scientific Programming

Table 1 Configuration parameters of container terminal yard

Class 119873119871(periods)

119873119861(blocks)

119873119878(subblocks)

119873119877(rows)

119873119884(YCs)

Class S 6 8 32 2 6Class M 8 16 64 4 12Class L 10 24 96 6 18

Table 2 Configuration parameters of yard crane and intertruck

Parameters 120583min 120583max 120575119887 120575119903 120593 120588 120590 120587Value 2 3 2 6 15 24 05 200

this paper considers three different storage yard scales (smallmedium and large) more precisely the instances with 6 to10 service lines 6 to 18 YCs and 8 to 24 blocks resulting inclasses 6 times 8 times 6 (class S) 8 times 16 times 12 (class M) and 10 times 24 times18 (class L) are tested (Table 1)

For all the classes the authors assume that the capacityof each block is 800 TEUs and the subblock capacity (V119887) is200 TEUs Meanwhile the maximal sharing space capacityof each subblock is equal to 20 TEUs (10 V119887) The yardcrane handling parameters and intertruck transportationparameters are shown in Table 2

For each class three scenarios of service line loadingrequirement are tested denoted by W1 W2 and W3 Theloading requirement is determined by the service line quayoperation queues (input data 119901119898 isin 119873 which are generatedwith discrete uniform distributions DU[2 3] DU[3 4] andDU[4 5] resp) the name of the instance indicates the levelof the loading requirement low requirement (W1) generalrequirement (W2) and high requirement (W3)

52 Yard Space Resource Analysis Based on space sharingstrategy the yard storage space utilization is increased owingto the sharing storage space between neighbor subblocks Asshowed in Table 3 the optimal yard operation cost equal to99990 yen and 800TEUsrsquo extra storage space (sharing space) arecreated (119886 = 0 cost-saving pattern) if space sharing strategyis applied in the yard Obviously this strategy can relieveterminal yard space scarce situation to a certain extent

Meanwhile when coefficient 119886 takes 1 it means thatthis model considers yard space allocation problem (space-utilizing pattern) firstly and then the yard crane deploymentproblem (cost-saving pattern) it is the nonintegrated patternin this situation Accordingly with the value of 119886 decreasingthe yard crane deployment is integrated with the yard spaceallocation problem gradually

Furthermore Figures 3 4 5 and 6 show the rela-tionships between yard storage space and yard operationcost of different instances scales As we can see with theincreasing of coefficient 119886 the yard sharing space increasedsynchronously as well as the yard operation cost Hence thereis no ultimate solution with the maximum space sharingand the minimum operation cost Which one should bechosen from these nondominated solutions is determined bythe terminal operators according to the terminal reality If

720 750 810780 840

105000

95000

115000

125000

135000

145000

870 900

a = 0

a = 02

a = 04

a = 06

a = 08

a = 1

Sharing space (TEUs)

Tran

spor

tatio

n co

st (yen

)

Figure 3 Relationships between yard space and operation cost ofsmall-scale experiments

1100 1200 14001300 1500

235000

220000

250000

265000

280000

295000

1600 1700

a = 0

a = 02

a = 04

a = 06

a = 08

a = 1

Sharing space (TEUs)

Tran

spor

tatio

n co

st (yen

)

Figure 4 Relationships between yard space and operation cost ofmedium-scale experiments

1950 2050 22502150 2350

395000

375000

415000

435000

455000

475000

2450 2550

a = 0

a = 02

a = 04

a = 06

a = 08

a = 1

Sharing space (TEUs)

Tran

spor

tatio

n co

st (yen

)

Figure 5 Relationships between yard space and operation cost oflarge-scale experiments

Scientific Programming 9

Table 3 Results of instances with different coefficient values

Instances119886 = 1 119886 = 08 119886 = 06 119886 = 04 119886 = 02 119886 = 01198911

(TEUs)1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

S W1 880 128800 880 110880 840 108900 800 103820 800 99990 800 99990S W2 880 129380 840 119960 840 110880 800 107910 760 102960 760 99990S W3 880 133340 840 127640 800 118800 760 108900 720 102960 680 99990M W1 1680 293150 1600 268500 1480 241600 1360 228830 1240 222450 1160 221760M W2 1600 286480 1560 261460 1440 239900 1320 228670 1240 224960 1160 221950M W3 1560 282360 1520 264300 1440 241860 1320 230100 1200 225960 1120 222140L W1 2480 468460 2400 432570 2360 403120 2200 387550 2120 380350 2080 376180L W2 2480 467820 2400 432800 2320 405670 2160 387610 2120 380640 2040 377050L W3 2400 468680 2360 433130 2280 405880 2160 388060 2080 381020 2000 378120

Table 4 Results of instances with different YCs

Instances119873119884119873119877 = 3 119873119884119873119877 = 35 119873119884119873119877 = 4 119873119884119873119877 = 45 119873119884119873119877 = 51198911

(TEUs)1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

S1 W1 960 99990 980 98040 980 97160 1000 96500 1000 96320S1 W2 960 99990 960 98630 980 97640 980 96500 1000 96320S1 W3 960 99990 960 99160 980 98420 980 97930 1000 96950M1 W1 1680 221760 1700 217730 1780 214200 1820 211770 1820 210040M1 W2 1600 221950 1640 218780 1700 215980 1760 213530 1760 211690M1 W3 1580 222140 1620 219420 1680 216560 1700 213840 1760 211870L1 W1 2480 376180 2540 367550 2580 360430 2640 354660 2640 351530L1 W2 2480 377050 2520 368580 2540 361910 2580 354960 2600 351600L1 W3 2420 378120 2460 368990 2500 362320 2540 355740 2600 352690

Δf1

Δf2

Sharing space (TEUs)

Tran

spor

tatio

n co

st (yen

)

tan 1205792 =Δf2Δf1

1205791

1205792

1205793

Figure 6 Relationships between yard space and operation cost

the container terminal yard storage is extremely scarce thatcould infect yard operation the operators should create morestorage space and the space-utilizing oriented strategy maybe adopted that is 119886 should take a bigger value otherwisethe cost saving should be the primary selection It is worthnoting that the marginal cost of yard sharing space (tan 120579)grows nonlinearly with the increase of coefficient 11988653 Yard Crane Resource Analysis In this section the effectsof total YCs on yard storage space utilization and yardoperation cost are tested We changed the number of YCs in

95000

96000

97000

98000

99000

100000

101000

940

950

960

970

980

990

1000

1010

Sharing space (TEUs)Transportation cost (yen)

NYN

R=3

NYN

R=45

NYN

R=4

NYN

R=5

NYN

R=35

Figure 7 Yard crane influence of small-scale experiments

the yard and the other parameters are unchanged For thisgroup of experiments consider the yard sharing space andyard operation cost separately so the coefficient 119886 is equal to1 and 0 respectively in the calculation of yard sharing spaceand yard operation cost The detailed results are shown inTable 4

Figures 7 8 and 9 show the effects of YCs on yard sharingspace and yard operation cost intuitively From these figures

10 Scientific Programming

Table 5 Results of instances with different subblock volume

Instances119873119878119873119861 = 3 119873119878119873119861 = 4 119873119878119873119861 = 5 119873119878119873119861 = 61198911

(TEUs)1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

S2 W1 756 106550 880 99990 960 95680 mdash mdashS2 W2 756 106550 880 99990 960 96280 mdash mdashS2 W3 756 106550 880 99990 960 99200 mdash mdashM2 W1 1404 231680 1680 221760 1888 217440 1950 210870M2 W2 1404 231760 1600 221950 1856 215210 mdash mdashM2 W3 1350 235930 1560 222140 1824 218130 mdash mdashL2 W1 2214 394550 2480 376180 2720 366960 2938 359620L2 W2 2214 396640 2480 377050 2688 371090 mdash mdashL2 W3 2160 398150 2400 378120 2656 373210 mdash mdash

208000

210000

212000

214000

216000

218000

224000

222000

220000

1550

1600

1650

1700

1750

1800

Sharing space (TEUs)Transportation cost (yen)

NYN

R=3

NYN

R=45

NYN

R=4

NYN

R=5

NYN

R=35

Figure 8 Yard crane influence of medium-scale experiments

we can find that the sharing space gradually becomes biggerwith the average YCs number in each zone increasing but theyard operation cost has an opposite situation

For the increasing of yard sharing space the mainreason could be that the added YCs relieved the YC loadingpoint constraint and then created more flexible service linespairings among subblocks but this effect is slight only about4

However generally speaking the increase of YCs shoulddecrease the yard operation cost considerably because it canavoid yard crane interzone movement as far as possible Butthese results shown in the figures could not express thisphenomenon obviously there is still only 6 cost decreaseA significant cause of this phenomenon is that the operationcost we considered is on the situation that the objectivefunction is cost-saving pattern (the coefficient 120572 equal to 0)so the yard operation cost we compared has been optimizedIt means that the amount of YCs interzone movements hasbeen decreased to an optimal level and this phenomenoncould be directly identified by Table 3 in Section 51

54 Subblock Volume Analysis The authors are also inter-ested in how the volume of subblock infects the yard space

335000340000345000350000355000360000365000370000375000380000

2350

2400

2450

2500

2550

2600

2650

Sharing space (TEUs)Transportation cost (yen)

NYN

R=3

NYN

R=45

NYN

R=4

NYN

R=5

NYN

R=35

Figure 9 Yard crane influence of large-scale experiments

utilization and yard operation cost In this subsection thenumber of subblocks in each block is divided into 3 4 5and 6 thus the volume of each subblock is equal to 270 200160 and 130 TEUs respectively and the other parameters areunchanged Similar to Section 53 the coefficient 119886 is equal to1 and 0 respectively in the calculation of yard sharing spaceand yard operation cost The detailed results are shown inTable 5

As showed in Figures 10 11 and 12 with the volumeof subblock decreasing and the subblocks in the yard blockincreasing gradually that the pairing of service lines becamemore flexible Consequently the space sharing opportunityincreased and the yard operation cost decreased as wellHowever with the decreasing of yard subblocks volume theyard crane service range is limited and such trends willlimit the increase of the yard crane resource demand in theyard When the number of subblocks in the block reaches acertain value the whole container terminal yard area cannotrun normally Accordingly the volume of yard subblock alsoplays an important role in yard management If the value istoo large the sharing space opportunity will decrease andoperation cost will increase However if the value is too smallthe whole system operation pattern will be broken up

Scientific Programming 11

9000092000940009600098000

100000102000104000106000108000

60065070075080085090095010001050

Sharing space (TEUs)Transportation cost (yen)

NSNB=3

NSNB=6

NSNB=5

NSNB=4

Figure 10 Yard subblock size influence of small-scale experiments

1200

1300

1400

1500

1600

1700

1800

1900

2000

200000

205000

210000

215000

220000

225000

230000

235000

Sharing space (TEUs)Transportation cost (yen)

NSNB=3

NSNB=6

NSNB=5

NSNB=4

Figure 11 Yard subblock size influence of medium-scale experi-ments

6 Conclusions

Motivated by the requirement to relieve the operationdilemma for resource-limited container terminal this paperaddressed the integrated yard space allocation and yard cranedeployment problem Two corresponding counterstrategiesare introduced and then an integrated mathematical modelis formulated to solve the problem Numerical experimentsverified the correctness and accuracy of the proposed modelThis study found that space sharing strategy can increase yardspace utilization and yard crane interzone movement strategycan effectively relieve the shortage of YCs In addition aninteresting phenomenon is discovered that there exists atrade-off between yard space utilization and yard operationcost and the volume of yard subblock also plays a significantrole in container port yard management

340000

350000

360000

370000

380000

390000

400000

2000

2200

2400

2600

2800

2900

2100

2300

2500

2700

Sharing space (TEUs)Transportation cost (yen)

NSNB=3

NSNB=6

NSNB=5

NSNB=4

Figure 12 Yard subblock size influence of large-scale experiments

This research can be extended in many relative areas Inthis paper the service line working windows and yard craneefficiency are determined However these parameters mayfluctuate with the factors associated with natural factors andthe equipment operators in reality Therefore the applicationof uncertainty factors in the integratedmanagement problemis a valuable research direction in the future

Competing Interests

The authors declare that they have no competing interests

Authorsrsquo Contributions

All authors contributed equally and significantly to writingthis article

Acknowledgments

This work is sponsored by National Natural Science Founda-tion ofChina (71602114) ldquoChenguangProgramrdquo supported byShanghai Education Development Foundation and ShanghaiMunicipal Education Commission (14CG48) Shanghai Sail-ing Program (14YF1411200) Doctoral Fund of theMinistry ofEducation (20133121110001) Shanghai Municipal EducationCommission Project (14YZ112) Shanghai Science amp Tech-nology Committee Research Project (15590501700) Shang-hai Maritime University Doctoral Innovation Fund Project(2015ycx063) and Shanghai Maritime University DoctoralExcellent Thesis Training Program (2015BXLP006)

References

[1] D Chang Z H JiangW Yan and J He ldquoIntegrating berth allo-cation and quay crane assignmentsrdquo Transportation Research

12 Scientific Programming

Part E LogisticsampTransportation Review vol 46 no 6 pp 975ndash990 2010

[2] J L He D F Chang W J Mi and W Yan ldquoA hybrid parallelgenetic algorithm for yard crane schedulingrdquo TransportationResearch Part E Logistics and Transportation Review vol 46no 1 pp 136ndash155 2010

[3] J G Jin D Lee and J X Cao ldquoStorage yard management inmaritime container terminalsrdquo Transportation Science 2014

[4] C-H Chen and W Yan ldquoEngineering informatics in portoperations and logisticsrdquoAdvanced Engineering Informatics vol25 no 3 pp 401ndash402 2011

[5] C-H Chen L P Khoo Y T Chong and X F Yin ldquoKnowledgediscovery using genetic algorithm for maritime situationalawarenessrdquo Expert Systems with Applications vol 41 no 6 pp2742ndash2753 2014

[6] J He Y Huang and D Chang ldquoSimulation-based heuristicmethod for container supply chain network optimizationrdquoAdvanced Engineering Informatics vol 29 no 3 pp 339ndash3542015

[7] I F A Vis and R De Koster ldquoTransshipment of containersat a container terminal an overviewrdquo European Journal ofOperational Research vol 147 no 1 pp 1ndash16 2003

[8] D Steenken S Voszlig and R Stahlbock ldquoContainer terminaloperation and operations researchmdasha classification and litera-ture reviewrdquo OR Spectrum vol 26 no 1 pp 3ndash49 2004

[9] R Stahlbock and S Voszlig ldquoOperations research at containerterminals a literature updaterdquo Operations Research-Spektrumvol 30 no 1 pp 1ndash52 2008

[10] X Jiang L H Lee E P Chew Y Han and K C Tan ldquoAcontainer yard storage strategy for improving land utilizationand operation efficiency in a transshipment hub portrdquoEuropeanJournal of Operational Research vol 221 no 1 pp 64ndash73 2012

[11] L H Lee E P Chew K C Tan and Y Han ldquoAn optimizationmodel for storage yardmanagement in transshipment hubsrdquoORSpectrum vol 28 no 4 pp 539ndash561 2006

[12] Y Han L H Lee E P Chew and K Tan ldquoA yard storagestrategy forminimizing traffic congestion in amarine containertransshipment hubrdquo OR Spectrum Quantitative Approaches inManagement vol 30 no 4 pp 697ndash720 2008

[13] X Jiang E P Chew L H Lee and K C Tan ldquoFlexible space-sharing strategy for storage yard management in a transship-ment hub portrdquo OR Spectrum vol 35 no 2 pp 417ndash439 2013

[14] L Zhen ldquoContainer yard template planning under uncertainmaritimemarketrdquo Transportation Research Part E Logistics andTransportation Review vol 69 pp 199ndash217 2014

[15] C Zhang Y-W Wan J Liu and R J Linn ldquoDynamiccrane deployment in container storage yardsrdquo TransportationResearch Part B Methodological vol 36 no 6 pp 537ndash5552002

[16] R K Chung C-L Li andW Lin ldquoInterblock crane deploymentin container terminalsrdquoTransportation Science vol 36 no 1 pp79ndash93 2002

[17] R Linn J-Y Liu Y-W Wan C Q Zhang and K G MurtyldquoRubber tired gantry crane deployment for container yardoperationrdquo Computers amp Industrial Engineering vol 45 no 3pp 429ndash442 2003

[18] Z Cao D-H Lee and Q Meng ldquoDeployment strategies ofdouble-rail-mounted gantry crane systems for loading out-bound containers in container terminalsrdquo International Journalof Production Economics vol 115 no 1 pp 221ndash228 2008

[19] K H Kim and H B Kim ldquoThe optimal sizing of the storagespace and handling facilities for import containersrdquoTransporta-tion Research Part B Methodological vol 36 no 9 pp 821ndash8352002

[20] D-H Lee J G Jin and J H Chen ldquoIntegrated bay allocationand yard crane scheduling problem for transshipment contain-ersrdquo Transportation Research Record vol 2222 no 8 pp 63ndash712011

[21] S H Won X Zhang and K H Kim ldquoWorkload-based yard-planning system in container terminalsrdquo Journal of IntelligentManufacturing vol 23 no 6 pp 2193ndash2206 2012

Submit your manuscripts athttpwwwhindawicom

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Advances in

Computer EngineeringAdvances in

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2 Scientific Programming

integrate these two related problems as a system so thatthe yard space allocation and yard crane deployment can beproperly coordinated

Another emerging issue is that there are still many con-tainer terminals confronted with the resource-limited prob-lem such as Shanghai Yangshan port or Ningbo-Zhoushanport although there are many other terminals facing asevere overcapacity situation and the limited resources inthe yard area mainly concern the yard storage resource andYC equipment resource Take Ningbo Port Beilun PhaseIV Container Terminal as an example its throughput hasreached 5 million TEUs in 2014 while the designed annualthroughput is only 2 million TEUs The yard storage spaceand YC equipment resources are extremely scarce thereforethe yard stacking utilization has risen to more than 90during handling peak period and there are only 4 fixedYCs in each row in the yard while they should be serving 6blocks Consequently there is a continued need to study theoptimization of yard operation especially for the resource-limited container terminals

This paper aims to solve resource-limited predicament inthe yard area and thereby improve the operational efficiencyin the terminal Considering that the bottleneck of containerport has moved from the quay side to the yard area the oper-ation optimization in the yard area is regarded as the point ofpenetration This paper integrated yard space allocation andyard crane deployment problem hence an integrated modelis formulated and two corresponding counterstrategies (thespace sharing strategy and yard crane interzone movementstrategy) are introduced These two strategies are used tosolve yard storage space resource and yard crane equipmentresource scarce problem respectively The authors focuson the integrated yard space allocation and yard cranedeployment in the tactical level and the major contributionsare provided as follows

(1) An integrated mathematical optimization model isformulated which provides a comprehensive viewof yard space allocation and yard crane deploymentproblem the objective function of the model is atrade-off between yard space utilization and yardoperation cost

(2) Two factors impacting the operational efficiency ofstorage yard are introduced and these factors playa significant role in the practical container terminaloperation but have seldom been presented in existingliteratures Meanwhile the container volume fluctua-tion of the service line is also under consideration

(3) A detailed scenario analysis among the yard sharingspace the number of YCs the size of yard subblockand the operation cost of container terminal is pre-sented which can provide a precise relative referenceto container terminal manager

The remainder of this paper is organized as followsSection 2 reviews the related researches Section 3 elaboratesthe description for the yard space allocation problem andyard crane deployment problem as well as a mathematicalmodel formulation in Section 4 Numerical examples are

given in Section 5 and a brief conclusion remark is presentedin the concluding section

2 Literature Review

Container terminal operation management is an extremelycomplex conundrumbecause toomany elements are involvedin the system Up to the present there are numerous studieson the container port operations [4ndash6] such as quay craneallocation and inner truck routing in the seaside yard spaceallocation and yard crane scheduling in the landside Fora comprehensive overview we refer readers to the reviewworks given by Vis and De Koster [7] Steenken et al [8]and Stahlbock and Voszlig [9] In this section a brief review ofstudies highly related to container terminal operation in theyard area is provided

21 Yard Space Allocation Generally speaking storage spaceallocation can be analyzed at various levels according to thestorage space unit considered yard section yard block yardsubblock yard bay and individual slot [3]This paper followsup the space sharing strategy [10] between neighbor storageunits based on yard template generation therefore the papersconsidering yard space allocation in subblock level will beintroduced minutely in this subsection

Lee et al [11] used the consignment strategy to storeincoming export and transshipment containers at dedicatedlocations according to the destination vessel helping toreduce the reshuffling level to a negligible level this strategyhas initiated a new line of yard space allocation problem Hanet al [12] extended their research to optimize the yard tem-plate and the yard storage allocation problem simultaneouslythe yard storage space is reserved for each specific vessel inthis paper Jiang et al [10] put forwarded the concept of spacesharing strategy between neighbor subblocks so the containeryard can improve land utilization based on this creativeand meaningful concept a two-space sharing method wasalso proposed to improve the space utilization of a certainyard template Jiang et al [13] considered a flexible spacesharing strategy compared with the previous fixed spacesharing pattern A yard template determined the allocationof spaces in the container terminal yard while fluctuation ofdemand for freight transportation brings challenge to yardtemplate generation Zhen [14] proposed a yard templateplanning considering random numbers of containers thatwill be loaded onto vessels that visit the port periodicallySimilar to Han et al [12] the traffic congestions problem inthe yard area is also considered However there are still someimportant factors which have received inadequate attentionbut should not be overlooked in practical terminal yardspace management Part of those factors is the proportionalmatching of quay operation queue and YC loading point of theservice line

22 Yard Crane Deployment With the yard space allocationplan determined the information of grounding and retrievalactivities in all blocks can be available for planning the yardcrane deployment [3] Compared with yard crane scheduling

Scientific Programming 3

problem the yard crane deployment emphasizes the macroconfigure level Zhang et al [15] addressed crane deploymentproblem with the workload of each block in each period wasgiven and try to find the optimal times and routes of yardcranemovements among yard blocks so that the total delayedworkload in the yard is minimum With the same objectiveChung et al [16] and Linn et al [17] formulated yard cranedeployment problem as a mixed integer linear program theyloosen the restrictions in Zhang et al [15] that each blockshould include not more than two cranes and the maximumnumber of transfers in or out of a block is limited In theabove-mentioned researches the type of the yard crane isa single E-RTG (electric yard crane) system Cao et al [18]focused on the deployment problem of double-rail-mountedgantry yard crane system which has been applied in WesternAutomated Container Terminals An integer programmingmodel was formulated as well as a greedy heuristic algorithma simulated annealing algorithm and a combined yard cranescheduling heuristic were designed to solve the proposedproblem

23 Integrated Management The integration of the yardspace allocation and yard crane deployment problem is alsoregarded by many researchers [10ndash12 19ndash21] due to therelationships between these two problems K H Kim andH B Kim [19] discussed a method to determine the optimalamount of storage space and the optimal number of transferYCs for handling import containers The cost model consistsof the space cost the investment cost of transfer cranes andthe operating cost of transfer cranes and trucks However thismodel cannot give a detailed storage location for containersor group of containers Lee et al [11] Han et al [12] andJiang et al [10] considered yard space allocation and relevantworkload assignment problem and the yard crane resourcerequirement was also included yet the yard crane interblockmovement is not allowed Lee et al [20] addressed theintegrated problem for bay allocation and yard crane schedul-ing in transshipment container terminal and allocated bayresource to fleet containers in a more efficient way Receivingoperation and retrieving operation in the storage yardswere considered simultaneously to achieve a more efficientoperation of the yard crane while bay allocation focused on ablock vision rather than yard overall prospect Won et al [21]proposed an integrated decision-making framework for theyard planning that simultaneously considers storage spaceyard crane and traffic area in the container terminal

The integrated yard space allocation and yard cranedeployment problem studied in this paper follows up thework of Jin et al [3] Instead of dealing with detaileddaily subblock space allocation and yard crane deploymentproblem at the operational level this paper addresses thetactical planning level In addition the subject of this studyis these container terminals where yard space and yardcrane resources are extremely limited the yard space sharingstrategy and yard crane interzone movement strategy areapplied consequently Different from Jin et al [3] this papersimultaneously considers the space allocation and yard cranedeployment in the yard area and not only the operation costbut also the yard storage space utilization is considered

3 Problem Description

Before we elaborate the yard space allocation and yard cranedeployment problem there are some concepts existing in thetext that must be explained

(i) Service Line The service line is service object of thecontainer terminal in a sense a service liner is aset of many voyages with the same departure anddestination Different from Line the line is a generalconcept while the service line is a specific conceptand the object is the container terminal

(ii) Quay Operation Queue The quay operation queue isthe number of quays that service a specified serviceline (loading and unloading operation) simultane-ously The quay operation queue of a service lineis usually determined by the vessel size containervolumes (loading and unloading operation) and theservice line priority level Generally speaking thehigher the priority level of service line the greater thenumber of quay operation queues that the service linehas

(iii) YC Loading Point The YC loading point is the num-ber of YCs servicing a certain service line (loadingoperation) simultaneously Because of the differentoperation efficiency of quay and yard crane thereis a proper matching proportion between the quayoperation queue and YC loading point for a serviceline and it is optimal matching that 1 quay operationqueue deploys 2 or 3 YC loading points

Remarkably for a service line there is at most one YCloading point in one block even if it has two ormore subblocksassigned in one block because of the limitation of YCs Asshowed in Figure 1 there are two service lines service line 1uses vessel Awith 800 TEUs outbound containers and serviceline 2 uses vessel B with 3000 TEUs outbound containersBoth service lines have deployed 4 quay operation queuesAs we can see service line 1 only has 800 TEUs outboundcontainers to be loaded (about 6 subblocks volumes) butbecause line 1 deployed 4 quay operation queues 8 yard YCloading points are needed at least so 8 subblocks locatedin 8 different blocks are assigned to line 1 consequentlyMeanwhile although service line 2 has 3000 TEUs (20subblocks volumes) it only deployed 4 quay operation queues12 yard YC loading points could be fulfilled at most and 20subblocks concentrated which are located in 12 blocks areassigned to service line 2 accordingly

31 Storage Space Allocation The storage space allocationdetermines the container yard stacking position in the sub-block for each service line of the terminal The allocationplan will normally not change once it is determined sincevast shipping companies service lines are relatively stableHowever there has been a realistic problem that it is difficultto calculate the accurate subblocks that each service lineshould be assigned because of the uncertainty of maritimemarket Therefore the volume of outbound containers fluc-tuates frequently If the yard storage space (subblocks) is

4 Scientific Programming

1 loading point for vessel A 1 loading point for vessel B

Subblock 150 TEUs

800 TEUs outbound containersService line 1 vessel A

3000 TEUs outbound containersService line 2 vessel B

S1 S2 S3 S4 S5

S21 S22 S23 S24 S25

S41 S42 S43 S44 S45

S61 S62 S63 S64 S65

S6 S7 S8 S9 S10

S26 S27 S28 S29 S30

S46 S47 S48 S49 S50

S66 S67 S68 S69 S70

S31 S32 S33 S4 S35

S11 S12 S13 S14 S15

S51 S52 S53 S54 S55

S71 S72 S73 S74 S75

S36 S37 S38 S39 S40

S16 S17 S18 S19 S20

S56 S57 S58 S59 S60

S76 S77 S77 S78 S78

Berth

Zone

QC operation queue

(Row)

Figure 1 A typical yard space configuration of container terminal

assigned according to the service line minimal demand it islikely to face storage space shortage for a busy voyage On thecontrary the terminal yard space will not be sufficient

For the container terminal with a static yard template[11 12] all the subblocks in each block have a fixed spacecapacity whichmeans each service line needs to be assigned alarge enough yard storage space to satisfy containers stackingdemand at the peak time To take advantage of the benefitof consignment strategy and increase the yard storage spaceutilization Jiang et al [10] proposed a space sharing strategywhich allows some certain space to be shared betweenneighbor subblocks For a detailed sharing space strategydescription we refer readers to the work given by Jiang et al[10]

In general for a resource-limited container terminal themain concern is the utilization of yard storage in the processof yard space allocation Accordingly the objective couldbe concentrated on the total sharing space between yardneighbor subblocks Constraints that should be consideredwhen allocating storage space mainly include the following

(i) The storage capacity allocated to each service lineshould be sufficient so that it could meet the stackingdemand

(ii) For each service line in order to achieve a high oper-ational efficiency as far as possible the proportion ofquay operation queue and YC loading point would bein the reasonable range

(iii) The YC loading point in the block must be wellcontrolled at any time period otherwise traffic con-gestion can be expected

32 Yard Crane Deployment The yard crane deploymentproblem is to designate and schedule YCs route accordingto the workload requirement in the yard area Many relevantresearches usually focus on the deployment problem betweenyard blocks in the same zone that only the yard craneintrazone movement is considered This is a commendablestrategywhen the terminal yard crane resources are adequate

However there may be a situation that only four YCs arein one zone with 5 or 6 blocks in some container terminals Inthis case 4 YCs should service 5 or 6 blocks the YCs have tomove among different block zones Therefore the yard craneinterzone movement is enabled in this terminal to satisfyoperational requirements In this study we concentrated onthe yard crane interzonemovement rather than the intrazonemovement because the former operation time cost and fuelconsumption cost are much higher than the latter Figure 2shows a diagram of E-RTG interzone movement process Fora detailed yard cranemovement patterns description we referreaders to the works given by Linn et al [17] and Zhang et al[15]

For yard crane deployment the objective is to optimizeworkload distribution of each yard rowduring all the periodsTherefore the optimization objective in this paper is tominimize YCs operation cost when deploying yard craneConstraint that should be considered is to ensure the number

Scientific Programming 5

1

2

3

Electric cables

Figure 2 E-RTG interzone movement process

of YCs deployed in each row can satisfy the containerhandling requirement

4 Mathematic Model

In this section the integrated yard space allocation and yardcrane deployment mathematical model for resource-limitedcontainer terminal is formulatedThe authors raised themaincharacteristics of resource-limited container terminal storagespace allocation and yard crane deployment problem andthen presented the relevant counterstrategies accordingly Foryard space strained problem the space sharing strategy isapplied which has been proposed by Jiang et al [10] and asfor yard crane equipment shortage the yard crane interzonemovement is enabled

41 Assumptions The following assumptions are made in theintegrated model

(1) The yard storage space can satisfy the minimumservice line outbound containers stacking demandand the YCs are sufficient to guarantee the basichandling requirement

(2) The service lines berthing position are given andfixed hence once the service line containers areassigned to the subblocks the minimal inner trucktransportation distances are determined

(3) A subblock can be reserved for only one service lineexcept for part of the storage space which may beshared with its neighbor assigned service lines andwill not change once the storage plan is determined

(4) The YC can only shift to one yard zone in one periodit means that once the yard crane moved from onezone to another then it should be staying in the zonebefore the next planning period is begun

42 Mathematic Formulation This model aims to deal withthe yard space allocation problem and yard crane deploymentproblem at the tactical level and provides the following

results (1) yard storage space allocation plan for outboundcontainers of all the service lines which considers thecontainer volumes quay operation queues YC loading pointsand handling conflicts of service lines in the storage yard(2) yard crane deployment profile including the yard craneassignment plan in the initial period and subsequent yardcrane moving scheme

Sets

119879 set of time periods 119879 = 1 2 119873119879119861 set of yard blocks 119861 = 1 2 119873119861119878 set of yard subblocks 119878 = 1 2 119873119878119878119899119894 set of neighbor subblocks of subblock 119894 isin 119878 119878119899119894 isin 119878119878119904119902 set of subblocks belonging to block 119902 isin 119861 119878119904119902 isin 119878119877 set of yard rows (zone) in the terminal yard 119877 =1 2 119873119877119861119903 set of blocks belonging to row 119903 isin 119877 119861119903 isin 119861119871 set of service lines of terminal 119871 = 1 2 119873119871119884 set of YCs 119884 = 1 2 119873119884

Parameters

119888min119898 minimal outbound containers of service line 119898 isin 119871

(TEUs)119888max119898 maximal outbound containers of service line 119898 isin 119871

(TEUs)119901119898 quay operation queues of service line119898 isin 119871

120583min minimal YC loading points that one quay operationqueue demands

120583max maximal YC loading points that one quay operationqueue can satisfy

119905119904119898 time period to start handling of service line119898 isin 119871119905119890119898 time period to end handling of service line119898 isin 119871ℎ119898119905 handling parameter of service line119898 isin 119871 equal to 1 if119905 isin [119905119904119898 119905119890119898] otherwise equal to 0

6 Scientific Programming

V119904 maximal space capacity of each subblock (TEUs)

V119887 maximal space capacity of each yard block (TEUs)

120575119887 maximal YCs enabled operating in one yard block120575119903 maximal YCs enabled operating in one block row

120596119898119899 yard space sharing space when subblocks of serviceline 119898 isin 119871 and service line 119899 isin 119871 are neighbored (inthis paper120596119898119899 isin 0 1 it is usually determined by thecontainer buildup pattern of two service lines [14])

120579 fixed capacity of one sharing space (TEUs)119889119905119894119898 inner truck moving distance (loading and unloading)

if service line119898 isin 119871 is assigned to subblock 119894 isin 119878 (km)1198891198881199031199031015840 yard cranemovement distance between row 119903 isin 119877 and

row 1199031015840 isin 119877 (km)120593 inner truck transportation cost (yenkmTEU)120590 fixed time consumption of yard crane interzone

movement (h)120587 yard crane time cost (yenh)120588 yard crane movement cost (yenm)

1205821199031199031015840 yard crane interzone movement cost between row 119903 isin119877 and row 1199031015840 isin 119877 119903 = 1199031015840 (yen) where 1205821199031199031015840 = 120590120587 + 1198891198881199031199031015840120588if 119903 = 1199031015840 1205821199031199031015840 = 0

120576 a small and positive constant

Decision Variables

119909119894119898 isin 0 1 1 if subblock 119894 isin 119878was assigned to serviceline119898 isin 119871 0 otherwise1199101199031199031015840119905 isin 119873 YCs moving from row 119903 isin 119877 to row 1199031015840 isin 119877at the end of time period 119905 isin 119879 (and 1199101199041199030 is initial YCsof row 119903 isin 119877 in the beginning of the period)119911119898119902 isin 0 1 the number of YC loading points ofservice line119898 isin 119871 in block 119902 isin 119861119908119889119903119905 isin 119873 minimal yard crane requirement of row 119903 isin119877 in time period 119905 isin 119879119908119886119903119905 isin 119873 the number of YCs assigned to row 119903 isin 119877 intime period 119905 isin 119879

Objective Function

maximize 1198911 = sum119894isin119878

sum119895isin119878119899119894

sum119898119899isin119871

119909119894119898119909119895119899120596119898119899120579 (1)

minimize 1198912 = 1198911199052 + 1198911198882 (2)

1198911199052 = sum119894isin119904

sum119898isin119871

119909119894119898119889119905119894119898120593V119904 (3)

1198911198882 = sum119903isin119877

sum1199031015840isin119877

sum119905isin119879

11991011990311990310158401199051205821199031199031015840 (4)

The mathematical model proposed in this section is amultiobjective optimal model hence the authors transferredit into a single-objective problem by the method of weightedallocation Define 120572 as the coefficient of yard storage space

in the process of terminal operation management and usecoefficient 120572 to combine the two objectives Furthermorebecause the dimensions of two objectives are different thusnondimensional processing is needed Note that 119891max

1 and119891min1 are the independent maximal and minimal value of 1198911

respectively 119891max2 and 119891min

2 are the independent maximaland minimal value of 1198912 Therefore the integrated objectivefunction can be expressed as follows

max 119891 = 120572 (1198911 minus 119891min1 )

(119891max1 minus 119891min

1 ) +(1 minus 120572) (119891max

2 minus 1198912)(119891max2 minus 119891min

2 ) (5)

In formula (5) the coefficient 120572 could be set as0 01 10 with a step size of 01 This step could beadjusted manually according to problem size and terminaloperatorrsquos preference By changing the value of 120572 differentsets of solutions can be obtained In other words when 120572is smaller the solutions are more space-utilizing On thecontrary with the increase of 120572 the solutions are more cost-saving

Constraints

sum119898isin119871

119909119894119898 le 1 forall119894 isin 119878 (6)

sum119894isin119904

119909119894119898 ge lceil119888min119898

V119904rceil forall119898 isin 119871 (7)

sum119894isin119904

119909119894119898 le lceil119888max119898

V119904rceil forall119898 isin 119871 (8)

sum119894isin119878

sum119898isin119871

119909119894119898 = 119873119878 (9)

119911119898119902 le sum119894isin119878119904119902

119909119894119898forall119898 isin 119871 119902 isin 119861

(10)

119911119898119902 ge sum119894isin119878119904119902

119909119894119898120576

forall119898 isin 119871 119902 isin 119861(11)

sum119902isin119861

119911119898119902 ge 120583min119901119898 forall119898 isin 119871 (12)

sum119902isin119861

119911119898119902 le 120583max119901119898 forall119898 isin 119871 (13)

lceil119888max119898

V119904rceil ge 120583min119901119898 forall119898 isin 119871 (14)

sum119898isin119871

119911119898119902ℎ119898119905 le 120575119887 forall119902 isin 119861 119905 isin 119879 (15)

119908119889119903119905 = sum119898isin119871

sum119902isin119861119903

119911119898119902ℎ119898119905forall119903 isin 119877 119905 isin 119879

(16)

Scientific Programming 7

119908119889119903119905 le 120575119887 forall119903 isin 119877 119905 isin 119879 (17)

sum119898isin119871

119909119894119898ℎ119898119905 + 120576sum119895isin119878119899119894

sum119898isin119871

119909119895119898ℎ119898119905 le 1 forall119894 isin 119878 119905 isin 119879 (18)

sum119903isin119877

1199101199041199030 = 119873119884 (19)

sum1199031015840isin119877

1199101199031199031015840119905 = 1199101199041199030 forall119903 isin 119877 119905 = 1 (20)

sum1199031015840isin119877

1199101199031199031015840119905 = sum1199031015840isin119877

1199101199031015840119903(119905minus1)forall119903 isin 119877 2 le 119905 le 119873119879 minus 1

(21)

1199101199041199030 = sum1199031015840isin119877

1199101199031015840119903119905forall119903 isin 119877 119905 = 119873119879

(22)

119908119886119903119905 = 1199101199041199030 forall119903 isin 119877 119905 = 1 (23)

119908119886119903119905 = sum1199031015840isin119877

1199101199031015840119903(119905minus1)forall119903 isin 119877 119905 isin 119879 119905 = 1

(24)

119908119886119903119905 ge 119908119889119903119905 forall119903 isin 119877 119905 isin 119879 (25)

119908119886119903119905 le 120575119903 forall119903 isin 119877 119905 isin 119879 (26)

119909119894119898 isin 0 1 forall119894 isin 119878 119898 isin 119871 (27)

1199101199041199030 isin 119873 forall119903 isin 119877 (28)

1199101199031199031015840119905 isin 119873forall119903 1199031015840 isin 119877 119905 isin 119879 (29)

119911119902119898 isin 0 1forall119898 isin 119871 119902 isin 119861 (30)

119908119886119903119905 119908119889119903119905 isin 119873 forall119903 isin 119877 119905 isin 119879 (31)

The constraints of the mathematical model are composedof three parts the yard space allocation constraints theyard crane deployment constraints and the variables rangeconstraints

Equations (6) to (18) are the constraints of the first partwhich defines the rules of yard space allocation Equation (6)states that each subblock should be reserved for at most oneservice line during the entire planning horizon Equations (7)and (8) state that the subblocks assigned to the service linemust satisfy the outbound containers storage demand of theservice line Considering the service line outbound containervolumes are not generally fixed and the yard storage spaceis extremely limited the loosened constraints are presentedEquation (9) ensures that all the subblocks should be assignedto a service line Equations (10) and (11) are the calculationequations of service line YC loading points in a block equalto 1 if there is at least one subblock reserved for the service

line but otherwise equal to 0 Equations (12) to (14) state therelationship between the service line quay operation queuein the seaside and the YC loading point in the yard areaEquation (15) ensures themaximal handling YCs in the blockEquations (16) and (17) restrict the maximal handling YCsin the yard row Equation (18) states that when one of thesubblocks is in loading state the other neighbor subblocksare unavailable for service line that should be handled at thesame time

Equations (19) to (26) are the constraints of the secondpart which defines the rules of yard crane deploymentEquation (19) guarantees that the summation of initial YCsdeployment in each row is equal to the number of YCsEquations (20) to (22) ensure the YCs resource flow balancein the process of YCs interzone movement in each period ofplanning horizon Equations (23) and (24) are the calculationequations of YCs in each yard row Equations (25) and (26)ensure that the YCs operating in the row should satisfy theoperational demand and not exceed the maximal YCs boundin the row at the same time

Finally the domains of variables defined by (27) to (31)are the constraints of the third part

Linear Transformation As formula (1) is a nonlinear functiona linear transformation operation is applied After lineartransformation formula (1) is equal to

max 1198911 = sum119894isin119878

sum119895isin119878119899119894

sum119898119899isin119871

120601119894119895119898119899120596119898119899120579120601119894119895119898119899 le 119909119894119898 forall119894 isin 119878 119895 isin 119878119899119894 119898 119899 isin 119871120601119894119895119898119899 le 119909119895119899 forall119894 isin 119878 119895 isin 119878119899119894 119898 119899 isin 119871120601119894119895119898119899 ge 119909119894119898 + 119909119895119899 minus 1

forall119894 isin 119878 119895 isin 119878119899119894 119898 119899 isin 119871120601119894119895119898119899 isin 0 1 forall119894 isin 119878 119895 isin 119878119899119894 119898 119899 isin 119871

(32)

5 Numerical Experiment

To evaluate the effectiveness of the proposed model aseries of experiments with different scales are conductedSection 51 introduces the parameters used for generating theexperiments Section 52 analyzes the trade-off between yardstorage space resource utilization and yard operation costSection 53 researches the effects of YCs on yard storage spaceand operational cost Section 54 explores the influence ofsubblock volume on the yard management The integratedmodel in this paper is solved by ILOG CPLEX 124 and all ofthe computation experiments are conducted on aworkstationwith Inter Xeon CPU with 64GHz RAM

51 Instances At present many of the container line arrivalpatterns are weekly arrival In other words the voyage ofservice line arrives at the terminal once a weekTherefore theplanning horizon of this experiment is 1 week and each dayis split into 3 periods of 8 hours in consideration of practicalworking shift in the container terminal The experiment in

8 Scientific Programming

Table 1 Configuration parameters of container terminal yard

Class 119873119871(periods)

119873119861(blocks)

119873119878(subblocks)

119873119877(rows)

119873119884(YCs)

Class S 6 8 32 2 6Class M 8 16 64 4 12Class L 10 24 96 6 18

Table 2 Configuration parameters of yard crane and intertruck

Parameters 120583min 120583max 120575119887 120575119903 120593 120588 120590 120587Value 2 3 2 6 15 24 05 200

this paper considers three different storage yard scales (smallmedium and large) more precisely the instances with 6 to10 service lines 6 to 18 YCs and 8 to 24 blocks resulting inclasses 6 times 8 times 6 (class S) 8 times 16 times 12 (class M) and 10 times 24 times18 (class L) are tested (Table 1)

For all the classes the authors assume that the capacityof each block is 800 TEUs and the subblock capacity (V119887) is200 TEUs Meanwhile the maximal sharing space capacityof each subblock is equal to 20 TEUs (10 V119887) The yardcrane handling parameters and intertruck transportationparameters are shown in Table 2

For each class three scenarios of service line loadingrequirement are tested denoted by W1 W2 and W3 Theloading requirement is determined by the service line quayoperation queues (input data 119901119898 isin 119873 which are generatedwith discrete uniform distributions DU[2 3] DU[3 4] andDU[4 5] resp) the name of the instance indicates the levelof the loading requirement low requirement (W1) generalrequirement (W2) and high requirement (W3)

52 Yard Space Resource Analysis Based on space sharingstrategy the yard storage space utilization is increased owingto the sharing storage space between neighbor subblocks Asshowed in Table 3 the optimal yard operation cost equal to99990 yen and 800TEUsrsquo extra storage space (sharing space) arecreated (119886 = 0 cost-saving pattern) if space sharing strategyis applied in the yard Obviously this strategy can relieveterminal yard space scarce situation to a certain extent

Meanwhile when coefficient 119886 takes 1 it means thatthis model considers yard space allocation problem (space-utilizing pattern) firstly and then the yard crane deploymentproblem (cost-saving pattern) it is the nonintegrated patternin this situation Accordingly with the value of 119886 decreasingthe yard crane deployment is integrated with the yard spaceallocation problem gradually

Furthermore Figures 3 4 5 and 6 show the rela-tionships between yard storage space and yard operationcost of different instances scales As we can see with theincreasing of coefficient 119886 the yard sharing space increasedsynchronously as well as the yard operation cost Hence thereis no ultimate solution with the maximum space sharingand the minimum operation cost Which one should bechosen from these nondominated solutions is determined bythe terminal operators according to the terminal reality If

720 750 810780 840

105000

95000

115000

125000

135000

145000

870 900

a = 0

a = 02

a = 04

a = 06

a = 08

a = 1

Sharing space (TEUs)

Tran

spor

tatio

n co

st (yen

)

Figure 3 Relationships between yard space and operation cost ofsmall-scale experiments

1100 1200 14001300 1500

235000

220000

250000

265000

280000

295000

1600 1700

a = 0

a = 02

a = 04

a = 06

a = 08

a = 1

Sharing space (TEUs)

Tran

spor

tatio

n co

st (yen

)

Figure 4 Relationships between yard space and operation cost ofmedium-scale experiments

1950 2050 22502150 2350

395000

375000

415000

435000

455000

475000

2450 2550

a = 0

a = 02

a = 04

a = 06

a = 08

a = 1

Sharing space (TEUs)

Tran

spor

tatio

n co

st (yen

)

Figure 5 Relationships between yard space and operation cost oflarge-scale experiments

Scientific Programming 9

Table 3 Results of instances with different coefficient values

Instances119886 = 1 119886 = 08 119886 = 06 119886 = 04 119886 = 02 119886 = 01198911

(TEUs)1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

S W1 880 128800 880 110880 840 108900 800 103820 800 99990 800 99990S W2 880 129380 840 119960 840 110880 800 107910 760 102960 760 99990S W3 880 133340 840 127640 800 118800 760 108900 720 102960 680 99990M W1 1680 293150 1600 268500 1480 241600 1360 228830 1240 222450 1160 221760M W2 1600 286480 1560 261460 1440 239900 1320 228670 1240 224960 1160 221950M W3 1560 282360 1520 264300 1440 241860 1320 230100 1200 225960 1120 222140L W1 2480 468460 2400 432570 2360 403120 2200 387550 2120 380350 2080 376180L W2 2480 467820 2400 432800 2320 405670 2160 387610 2120 380640 2040 377050L W3 2400 468680 2360 433130 2280 405880 2160 388060 2080 381020 2000 378120

Table 4 Results of instances with different YCs

Instances119873119884119873119877 = 3 119873119884119873119877 = 35 119873119884119873119877 = 4 119873119884119873119877 = 45 119873119884119873119877 = 51198911

(TEUs)1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

S1 W1 960 99990 980 98040 980 97160 1000 96500 1000 96320S1 W2 960 99990 960 98630 980 97640 980 96500 1000 96320S1 W3 960 99990 960 99160 980 98420 980 97930 1000 96950M1 W1 1680 221760 1700 217730 1780 214200 1820 211770 1820 210040M1 W2 1600 221950 1640 218780 1700 215980 1760 213530 1760 211690M1 W3 1580 222140 1620 219420 1680 216560 1700 213840 1760 211870L1 W1 2480 376180 2540 367550 2580 360430 2640 354660 2640 351530L1 W2 2480 377050 2520 368580 2540 361910 2580 354960 2600 351600L1 W3 2420 378120 2460 368990 2500 362320 2540 355740 2600 352690

Δf1

Δf2

Sharing space (TEUs)

Tran

spor

tatio

n co

st (yen

)

tan 1205792 =Δf2Δf1

1205791

1205792

1205793

Figure 6 Relationships between yard space and operation cost

the container terminal yard storage is extremely scarce thatcould infect yard operation the operators should create morestorage space and the space-utilizing oriented strategy maybe adopted that is 119886 should take a bigger value otherwisethe cost saving should be the primary selection It is worthnoting that the marginal cost of yard sharing space (tan 120579)grows nonlinearly with the increase of coefficient 11988653 Yard Crane Resource Analysis In this section the effectsof total YCs on yard storage space utilization and yardoperation cost are tested We changed the number of YCs in

95000

96000

97000

98000

99000

100000

101000

940

950

960

970

980

990

1000

1010

Sharing space (TEUs)Transportation cost (yen)

NYN

R=3

NYN

R=45

NYN

R=4

NYN

R=5

NYN

R=35

Figure 7 Yard crane influence of small-scale experiments

the yard and the other parameters are unchanged For thisgroup of experiments consider the yard sharing space andyard operation cost separately so the coefficient 119886 is equal to1 and 0 respectively in the calculation of yard sharing spaceand yard operation cost The detailed results are shown inTable 4

Figures 7 8 and 9 show the effects of YCs on yard sharingspace and yard operation cost intuitively From these figures

10 Scientific Programming

Table 5 Results of instances with different subblock volume

Instances119873119878119873119861 = 3 119873119878119873119861 = 4 119873119878119873119861 = 5 119873119878119873119861 = 61198911

(TEUs)1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

S2 W1 756 106550 880 99990 960 95680 mdash mdashS2 W2 756 106550 880 99990 960 96280 mdash mdashS2 W3 756 106550 880 99990 960 99200 mdash mdashM2 W1 1404 231680 1680 221760 1888 217440 1950 210870M2 W2 1404 231760 1600 221950 1856 215210 mdash mdashM2 W3 1350 235930 1560 222140 1824 218130 mdash mdashL2 W1 2214 394550 2480 376180 2720 366960 2938 359620L2 W2 2214 396640 2480 377050 2688 371090 mdash mdashL2 W3 2160 398150 2400 378120 2656 373210 mdash mdash

208000

210000

212000

214000

216000

218000

224000

222000

220000

1550

1600

1650

1700

1750

1800

Sharing space (TEUs)Transportation cost (yen)

NYN

R=3

NYN

R=45

NYN

R=4

NYN

R=5

NYN

R=35

Figure 8 Yard crane influence of medium-scale experiments

we can find that the sharing space gradually becomes biggerwith the average YCs number in each zone increasing but theyard operation cost has an opposite situation

For the increasing of yard sharing space the mainreason could be that the added YCs relieved the YC loadingpoint constraint and then created more flexible service linespairings among subblocks but this effect is slight only about4

However generally speaking the increase of YCs shoulddecrease the yard operation cost considerably because it canavoid yard crane interzone movement as far as possible Butthese results shown in the figures could not express thisphenomenon obviously there is still only 6 cost decreaseA significant cause of this phenomenon is that the operationcost we considered is on the situation that the objectivefunction is cost-saving pattern (the coefficient 120572 equal to 0)so the yard operation cost we compared has been optimizedIt means that the amount of YCs interzone movements hasbeen decreased to an optimal level and this phenomenoncould be directly identified by Table 3 in Section 51

54 Subblock Volume Analysis The authors are also inter-ested in how the volume of subblock infects the yard space

335000340000345000350000355000360000365000370000375000380000

2350

2400

2450

2500

2550

2600

2650

Sharing space (TEUs)Transportation cost (yen)

NYN

R=3

NYN

R=45

NYN

R=4

NYN

R=5

NYN

R=35

Figure 9 Yard crane influence of large-scale experiments

utilization and yard operation cost In this subsection thenumber of subblocks in each block is divided into 3 4 5and 6 thus the volume of each subblock is equal to 270 200160 and 130 TEUs respectively and the other parameters areunchanged Similar to Section 53 the coefficient 119886 is equal to1 and 0 respectively in the calculation of yard sharing spaceand yard operation cost The detailed results are shown inTable 5

As showed in Figures 10 11 and 12 with the volumeof subblock decreasing and the subblocks in the yard blockincreasing gradually that the pairing of service lines becamemore flexible Consequently the space sharing opportunityincreased and the yard operation cost decreased as wellHowever with the decreasing of yard subblocks volume theyard crane service range is limited and such trends willlimit the increase of the yard crane resource demand in theyard When the number of subblocks in the block reaches acertain value the whole container terminal yard area cannotrun normally Accordingly the volume of yard subblock alsoplays an important role in yard management If the value istoo large the sharing space opportunity will decrease andoperation cost will increase However if the value is too smallthe whole system operation pattern will be broken up

Scientific Programming 11

9000092000940009600098000

100000102000104000106000108000

60065070075080085090095010001050

Sharing space (TEUs)Transportation cost (yen)

NSNB=3

NSNB=6

NSNB=5

NSNB=4

Figure 10 Yard subblock size influence of small-scale experiments

1200

1300

1400

1500

1600

1700

1800

1900

2000

200000

205000

210000

215000

220000

225000

230000

235000

Sharing space (TEUs)Transportation cost (yen)

NSNB=3

NSNB=6

NSNB=5

NSNB=4

Figure 11 Yard subblock size influence of medium-scale experi-ments

6 Conclusions

Motivated by the requirement to relieve the operationdilemma for resource-limited container terminal this paperaddressed the integrated yard space allocation and yard cranedeployment problem Two corresponding counterstrategiesare introduced and then an integrated mathematical modelis formulated to solve the problem Numerical experimentsverified the correctness and accuracy of the proposed modelThis study found that space sharing strategy can increase yardspace utilization and yard crane interzone movement strategycan effectively relieve the shortage of YCs In addition aninteresting phenomenon is discovered that there exists atrade-off between yard space utilization and yard operationcost and the volume of yard subblock also plays a significantrole in container port yard management

340000

350000

360000

370000

380000

390000

400000

2000

2200

2400

2600

2800

2900

2100

2300

2500

2700

Sharing space (TEUs)Transportation cost (yen)

NSNB=3

NSNB=6

NSNB=5

NSNB=4

Figure 12 Yard subblock size influence of large-scale experiments

This research can be extended in many relative areas Inthis paper the service line working windows and yard craneefficiency are determined However these parameters mayfluctuate with the factors associated with natural factors andthe equipment operators in reality Therefore the applicationof uncertainty factors in the integratedmanagement problemis a valuable research direction in the future

Competing Interests

The authors declare that they have no competing interests

Authorsrsquo Contributions

All authors contributed equally and significantly to writingthis article

Acknowledgments

This work is sponsored by National Natural Science Founda-tion ofChina (71602114) ldquoChenguangProgramrdquo supported byShanghai Education Development Foundation and ShanghaiMunicipal Education Commission (14CG48) Shanghai Sail-ing Program (14YF1411200) Doctoral Fund of theMinistry ofEducation (20133121110001) Shanghai Municipal EducationCommission Project (14YZ112) Shanghai Science amp Tech-nology Committee Research Project (15590501700) Shang-hai Maritime University Doctoral Innovation Fund Project(2015ycx063) and Shanghai Maritime University DoctoralExcellent Thesis Training Program (2015BXLP006)

References

[1] D Chang Z H JiangW Yan and J He ldquoIntegrating berth allo-cation and quay crane assignmentsrdquo Transportation Research

12 Scientific Programming

Part E LogisticsampTransportation Review vol 46 no 6 pp 975ndash990 2010

[2] J L He D F Chang W J Mi and W Yan ldquoA hybrid parallelgenetic algorithm for yard crane schedulingrdquo TransportationResearch Part E Logistics and Transportation Review vol 46no 1 pp 136ndash155 2010

[3] J G Jin D Lee and J X Cao ldquoStorage yard management inmaritime container terminalsrdquo Transportation Science 2014

[4] C-H Chen and W Yan ldquoEngineering informatics in portoperations and logisticsrdquoAdvanced Engineering Informatics vol25 no 3 pp 401ndash402 2011

[5] C-H Chen L P Khoo Y T Chong and X F Yin ldquoKnowledgediscovery using genetic algorithm for maritime situationalawarenessrdquo Expert Systems with Applications vol 41 no 6 pp2742ndash2753 2014

[6] J He Y Huang and D Chang ldquoSimulation-based heuristicmethod for container supply chain network optimizationrdquoAdvanced Engineering Informatics vol 29 no 3 pp 339ndash3542015

[7] I F A Vis and R De Koster ldquoTransshipment of containersat a container terminal an overviewrdquo European Journal ofOperational Research vol 147 no 1 pp 1ndash16 2003

[8] D Steenken S Voszlig and R Stahlbock ldquoContainer terminaloperation and operations researchmdasha classification and litera-ture reviewrdquo OR Spectrum vol 26 no 1 pp 3ndash49 2004

[9] R Stahlbock and S Voszlig ldquoOperations research at containerterminals a literature updaterdquo Operations Research-Spektrumvol 30 no 1 pp 1ndash52 2008

[10] X Jiang L H Lee E P Chew Y Han and K C Tan ldquoAcontainer yard storage strategy for improving land utilizationand operation efficiency in a transshipment hub portrdquoEuropeanJournal of Operational Research vol 221 no 1 pp 64ndash73 2012

[11] L H Lee E P Chew K C Tan and Y Han ldquoAn optimizationmodel for storage yardmanagement in transshipment hubsrdquoORSpectrum vol 28 no 4 pp 539ndash561 2006

[12] Y Han L H Lee E P Chew and K Tan ldquoA yard storagestrategy forminimizing traffic congestion in amarine containertransshipment hubrdquo OR Spectrum Quantitative Approaches inManagement vol 30 no 4 pp 697ndash720 2008

[13] X Jiang E P Chew L H Lee and K C Tan ldquoFlexible space-sharing strategy for storage yard management in a transship-ment hub portrdquo OR Spectrum vol 35 no 2 pp 417ndash439 2013

[14] L Zhen ldquoContainer yard template planning under uncertainmaritimemarketrdquo Transportation Research Part E Logistics andTransportation Review vol 69 pp 199ndash217 2014

[15] C Zhang Y-W Wan J Liu and R J Linn ldquoDynamiccrane deployment in container storage yardsrdquo TransportationResearch Part B Methodological vol 36 no 6 pp 537ndash5552002

[16] R K Chung C-L Li andW Lin ldquoInterblock crane deploymentin container terminalsrdquoTransportation Science vol 36 no 1 pp79ndash93 2002

[17] R Linn J-Y Liu Y-W Wan C Q Zhang and K G MurtyldquoRubber tired gantry crane deployment for container yardoperationrdquo Computers amp Industrial Engineering vol 45 no 3pp 429ndash442 2003

[18] Z Cao D-H Lee and Q Meng ldquoDeployment strategies ofdouble-rail-mounted gantry crane systems for loading out-bound containers in container terminalsrdquo International Journalof Production Economics vol 115 no 1 pp 221ndash228 2008

[19] K H Kim and H B Kim ldquoThe optimal sizing of the storagespace and handling facilities for import containersrdquoTransporta-tion Research Part B Methodological vol 36 no 9 pp 821ndash8352002

[20] D-H Lee J G Jin and J H Chen ldquoIntegrated bay allocationand yard crane scheduling problem for transshipment contain-ersrdquo Transportation Research Record vol 2222 no 8 pp 63ndash712011

[21] S H Won X Zhang and K H Kim ldquoWorkload-based yard-planning system in container terminalsrdquo Journal of IntelligentManufacturing vol 23 no 6 pp 2193ndash2206 2012

Submit your manuscripts athttpwwwhindawicom

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Advances in

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Scientific Programming 3

problem the yard crane deployment emphasizes the macroconfigure level Zhang et al [15] addressed crane deploymentproblem with the workload of each block in each period wasgiven and try to find the optimal times and routes of yardcranemovements among yard blocks so that the total delayedworkload in the yard is minimum With the same objectiveChung et al [16] and Linn et al [17] formulated yard cranedeployment problem as a mixed integer linear program theyloosen the restrictions in Zhang et al [15] that each blockshould include not more than two cranes and the maximumnumber of transfers in or out of a block is limited In theabove-mentioned researches the type of the yard crane isa single E-RTG (electric yard crane) system Cao et al [18]focused on the deployment problem of double-rail-mountedgantry yard crane system which has been applied in WesternAutomated Container Terminals An integer programmingmodel was formulated as well as a greedy heuristic algorithma simulated annealing algorithm and a combined yard cranescheduling heuristic were designed to solve the proposedproblem

23 Integrated Management The integration of the yardspace allocation and yard crane deployment problem is alsoregarded by many researchers [10ndash12 19ndash21] due to therelationships between these two problems K H Kim andH B Kim [19] discussed a method to determine the optimalamount of storage space and the optimal number of transferYCs for handling import containers The cost model consistsof the space cost the investment cost of transfer cranes andthe operating cost of transfer cranes and trucks However thismodel cannot give a detailed storage location for containersor group of containers Lee et al [11] Han et al [12] andJiang et al [10] considered yard space allocation and relevantworkload assignment problem and the yard crane resourcerequirement was also included yet the yard crane interblockmovement is not allowed Lee et al [20] addressed theintegrated problem for bay allocation and yard crane schedul-ing in transshipment container terminal and allocated bayresource to fleet containers in a more efficient way Receivingoperation and retrieving operation in the storage yardswere considered simultaneously to achieve a more efficientoperation of the yard crane while bay allocation focused on ablock vision rather than yard overall prospect Won et al [21]proposed an integrated decision-making framework for theyard planning that simultaneously considers storage spaceyard crane and traffic area in the container terminal

The integrated yard space allocation and yard cranedeployment problem studied in this paper follows up thework of Jin et al [3] Instead of dealing with detaileddaily subblock space allocation and yard crane deploymentproblem at the operational level this paper addresses thetactical planning level In addition the subject of this studyis these container terminals where yard space and yardcrane resources are extremely limited the yard space sharingstrategy and yard crane interzone movement strategy areapplied consequently Different from Jin et al [3] this papersimultaneously considers the space allocation and yard cranedeployment in the yard area and not only the operation costbut also the yard storage space utilization is considered

3 Problem Description

Before we elaborate the yard space allocation and yard cranedeployment problem there are some concepts existing in thetext that must be explained

(i) Service Line The service line is service object of thecontainer terminal in a sense a service liner is aset of many voyages with the same departure anddestination Different from Line the line is a generalconcept while the service line is a specific conceptand the object is the container terminal

(ii) Quay Operation Queue The quay operation queue isthe number of quays that service a specified serviceline (loading and unloading operation) simultane-ously The quay operation queue of a service lineis usually determined by the vessel size containervolumes (loading and unloading operation) and theservice line priority level Generally speaking thehigher the priority level of service line the greater thenumber of quay operation queues that the service linehas

(iii) YC Loading Point The YC loading point is the num-ber of YCs servicing a certain service line (loadingoperation) simultaneously Because of the differentoperation efficiency of quay and yard crane thereis a proper matching proportion between the quayoperation queue and YC loading point for a serviceline and it is optimal matching that 1 quay operationqueue deploys 2 or 3 YC loading points

Remarkably for a service line there is at most one YCloading point in one block even if it has two ormore subblocksassigned in one block because of the limitation of YCs Asshowed in Figure 1 there are two service lines service line 1uses vessel Awith 800 TEUs outbound containers and serviceline 2 uses vessel B with 3000 TEUs outbound containersBoth service lines have deployed 4 quay operation queuesAs we can see service line 1 only has 800 TEUs outboundcontainers to be loaded (about 6 subblocks volumes) butbecause line 1 deployed 4 quay operation queues 8 yard YCloading points are needed at least so 8 subblocks locatedin 8 different blocks are assigned to line 1 consequentlyMeanwhile although service line 2 has 3000 TEUs (20subblocks volumes) it only deployed 4 quay operation queues12 yard YC loading points could be fulfilled at most and 20subblocks concentrated which are located in 12 blocks areassigned to service line 2 accordingly

31 Storage Space Allocation The storage space allocationdetermines the container yard stacking position in the sub-block for each service line of the terminal The allocationplan will normally not change once it is determined sincevast shipping companies service lines are relatively stableHowever there has been a realistic problem that it is difficultto calculate the accurate subblocks that each service lineshould be assigned because of the uncertainty of maritimemarket Therefore the volume of outbound containers fluc-tuates frequently If the yard storage space (subblocks) is

4 Scientific Programming

1 loading point for vessel A 1 loading point for vessel B

Subblock 150 TEUs

800 TEUs outbound containersService line 1 vessel A

3000 TEUs outbound containersService line 2 vessel B

S1 S2 S3 S4 S5

S21 S22 S23 S24 S25

S41 S42 S43 S44 S45

S61 S62 S63 S64 S65

S6 S7 S8 S9 S10

S26 S27 S28 S29 S30

S46 S47 S48 S49 S50

S66 S67 S68 S69 S70

S31 S32 S33 S4 S35

S11 S12 S13 S14 S15

S51 S52 S53 S54 S55

S71 S72 S73 S74 S75

S36 S37 S38 S39 S40

S16 S17 S18 S19 S20

S56 S57 S58 S59 S60

S76 S77 S77 S78 S78

Berth

Zone

QC operation queue

(Row)

Figure 1 A typical yard space configuration of container terminal

assigned according to the service line minimal demand it islikely to face storage space shortage for a busy voyage On thecontrary the terminal yard space will not be sufficient

For the container terminal with a static yard template[11 12] all the subblocks in each block have a fixed spacecapacity whichmeans each service line needs to be assigned alarge enough yard storage space to satisfy containers stackingdemand at the peak time To take advantage of the benefitof consignment strategy and increase the yard storage spaceutilization Jiang et al [10] proposed a space sharing strategywhich allows some certain space to be shared betweenneighbor subblocks For a detailed sharing space strategydescription we refer readers to the work given by Jiang et al[10]

In general for a resource-limited container terminal themain concern is the utilization of yard storage in the processof yard space allocation Accordingly the objective couldbe concentrated on the total sharing space between yardneighbor subblocks Constraints that should be consideredwhen allocating storage space mainly include the following

(i) The storage capacity allocated to each service lineshould be sufficient so that it could meet the stackingdemand

(ii) For each service line in order to achieve a high oper-ational efficiency as far as possible the proportion ofquay operation queue and YC loading point would bein the reasonable range

(iii) The YC loading point in the block must be wellcontrolled at any time period otherwise traffic con-gestion can be expected

32 Yard Crane Deployment The yard crane deploymentproblem is to designate and schedule YCs route accordingto the workload requirement in the yard area Many relevantresearches usually focus on the deployment problem betweenyard blocks in the same zone that only the yard craneintrazone movement is considered This is a commendablestrategywhen the terminal yard crane resources are adequate

However there may be a situation that only four YCs arein one zone with 5 or 6 blocks in some container terminals Inthis case 4 YCs should service 5 or 6 blocks the YCs have tomove among different block zones Therefore the yard craneinterzone movement is enabled in this terminal to satisfyoperational requirements In this study we concentrated onthe yard crane interzonemovement rather than the intrazonemovement because the former operation time cost and fuelconsumption cost are much higher than the latter Figure 2shows a diagram of E-RTG interzone movement process Fora detailed yard cranemovement patterns description we referreaders to the works given by Linn et al [17] and Zhang et al[15]

For yard crane deployment the objective is to optimizeworkload distribution of each yard rowduring all the periodsTherefore the optimization objective in this paper is tominimize YCs operation cost when deploying yard craneConstraint that should be considered is to ensure the number

Scientific Programming 5

1

2

3

Electric cables

Figure 2 E-RTG interzone movement process

of YCs deployed in each row can satisfy the containerhandling requirement

4 Mathematic Model

In this section the integrated yard space allocation and yardcrane deployment mathematical model for resource-limitedcontainer terminal is formulatedThe authors raised themaincharacteristics of resource-limited container terminal storagespace allocation and yard crane deployment problem andthen presented the relevant counterstrategies accordingly Foryard space strained problem the space sharing strategy isapplied which has been proposed by Jiang et al [10] and asfor yard crane equipment shortage the yard crane interzonemovement is enabled

41 Assumptions The following assumptions are made in theintegrated model

(1) The yard storage space can satisfy the minimumservice line outbound containers stacking demandand the YCs are sufficient to guarantee the basichandling requirement

(2) The service lines berthing position are given andfixed hence once the service line containers areassigned to the subblocks the minimal inner trucktransportation distances are determined

(3) A subblock can be reserved for only one service lineexcept for part of the storage space which may beshared with its neighbor assigned service lines andwill not change once the storage plan is determined

(4) The YC can only shift to one yard zone in one periodit means that once the yard crane moved from onezone to another then it should be staying in the zonebefore the next planning period is begun

42 Mathematic Formulation This model aims to deal withthe yard space allocation problem and yard crane deploymentproblem at the tactical level and provides the following

results (1) yard storage space allocation plan for outboundcontainers of all the service lines which considers thecontainer volumes quay operation queues YC loading pointsand handling conflicts of service lines in the storage yard(2) yard crane deployment profile including the yard craneassignment plan in the initial period and subsequent yardcrane moving scheme

Sets

119879 set of time periods 119879 = 1 2 119873119879119861 set of yard blocks 119861 = 1 2 119873119861119878 set of yard subblocks 119878 = 1 2 119873119878119878119899119894 set of neighbor subblocks of subblock 119894 isin 119878 119878119899119894 isin 119878119878119904119902 set of subblocks belonging to block 119902 isin 119861 119878119904119902 isin 119878119877 set of yard rows (zone) in the terminal yard 119877 =1 2 119873119877119861119903 set of blocks belonging to row 119903 isin 119877 119861119903 isin 119861119871 set of service lines of terminal 119871 = 1 2 119873119871119884 set of YCs 119884 = 1 2 119873119884

Parameters

119888min119898 minimal outbound containers of service line 119898 isin 119871

(TEUs)119888max119898 maximal outbound containers of service line 119898 isin 119871

(TEUs)119901119898 quay operation queues of service line119898 isin 119871

120583min minimal YC loading points that one quay operationqueue demands

120583max maximal YC loading points that one quay operationqueue can satisfy

119905119904119898 time period to start handling of service line119898 isin 119871119905119890119898 time period to end handling of service line119898 isin 119871ℎ119898119905 handling parameter of service line119898 isin 119871 equal to 1 if119905 isin [119905119904119898 119905119890119898] otherwise equal to 0

6 Scientific Programming

V119904 maximal space capacity of each subblock (TEUs)

V119887 maximal space capacity of each yard block (TEUs)

120575119887 maximal YCs enabled operating in one yard block120575119903 maximal YCs enabled operating in one block row

120596119898119899 yard space sharing space when subblocks of serviceline 119898 isin 119871 and service line 119899 isin 119871 are neighbored (inthis paper120596119898119899 isin 0 1 it is usually determined by thecontainer buildup pattern of two service lines [14])

120579 fixed capacity of one sharing space (TEUs)119889119905119894119898 inner truck moving distance (loading and unloading)

if service line119898 isin 119871 is assigned to subblock 119894 isin 119878 (km)1198891198881199031199031015840 yard cranemovement distance between row 119903 isin 119877 and

row 1199031015840 isin 119877 (km)120593 inner truck transportation cost (yenkmTEU)120590 fixed time consumption of yard crane interzone

movement (h)120587 yard crane time cost (yenh)120588 yard crane movement cost (yenm)

1205821199031199031015840 yard crane interzone movement cost between row 119903 isin119877 and row 1199031015840 isin 119877 119903 = 1199031015840 (yen) where 1205821199031199031015840 = 120590120587 + 1198891198881199031199031015840120588if 119903 = 1199031015840 1205821199031199031015840 = 0

120576 a small and positive constant

Decision Variables

119909119894119898 isin 0 1 1 if subblock 119894 isin 119878was assigned to serviceline119898 isin 119871 0 otherwise1199101199031199031015840119905 isin 119873 YCs moving from row 119903 isin 119877 to row 1199031015840 isin 119877at the end of time period 119905 isin 119879 (and 1199101199041199030 is initial YCsof row 119903 isin 119877 in the beginning of the period)119911119898119902 isin 0 1 the number of YC loading points ofservice line119898 isin 119871 in block 119902 isin 119861119908119889119903119905 isin 119873 minimal yard crane requirement of row 119903 isin119877 in time period 119905 isin 119879119908119886119903119905 isin 119873 the number of YCs assigned to row 119903 isin 119877 intime period 119905 isin 119879

Objective Function

maximize 1198911 = sum119894isin119878

sum119895isin119878119899119894

sum119898119899isin119871

119909119894119898119909119895119899120596119898119899120579 (1)

minimize 1198912 = 1198911199052 + 1198911198882 (2)

1198911199052 = sum119894isin119904

sum119898isin119871

119909119894119898119889119905119894119898120593V119904 (3)

1198911198882 = sum119903isin119877

sum1199031015840isin119877

sum119905isin119879

11991011990311990310158401199051205821199031199031015840 (4)

The mathematical model proposed in this section is amultiobjective optimal model hence the authors transferredit into a single-objective problem by the method of weightedallocation Define 120572 as the coefficient of yard storage space

in the process of terminal operation management and usecoefficient 120572 to combine the two objectives Furthermorebecause the dimensions of two objectives are different thusnondimensional processing is needed Note that 119891max

1 and119891min1 are the independent maximal and minimal value of 1198911

respectively 119891max2 and 119891min

2 are the independent maximaland minimal value of 1198912 Therefore the integrated objectivefunction can be expressed as follows

max 119891 = 120572 (1198911 minus 119891min1 )

(119891max1 minus 119891min

1 ) +(1 minus 120572) (119891max

2 minus 1198912)(119891max2 minus 119891min

2 ) (5)

In formula (5) the coefficient 120572 could be set as0 01 10 with a step size of 01 This step could beadjusted manually according to problem size and terminaloperatorrsquos preference By changing the value of 120572 differentsets of solutions can be obtained In other words when 120572is smaller the solutions are more space-utilizing On thecontrary with the increase of 120572 the solutions are more cost-saving

Constraints

sum119898isin119871

119909119894119898 le 1 forall119894 isin 119878 (6)

sum119894isin119904

119909119894119898 ge lceil119888min119898

V119904rceil forall119898 isin 119871 (7)

sum119894isin119904

119909119894119898 le lceil119888max119898

V119904rceil forall119898 isin 119871 (8)

sum119894isin119878

sum119898isin119871

119909119894119898 = 119873119878 (9)

119911119898119902 le sum119894isin119878119904119902

119909119894119898forall119898 isin 119871 119902 isin 119861

(10)

119911119898119902 ge sum119894isin119878119904119902

119909119894119898120576

forall119898 isin 119871 119902 isin 119861(11)

sum119902isin119861

119911119898119902 ge 120583min119901119898 forall119898 isin 119871 (12)

sum119902isin119861

119911119898119902 le 120583max119901119898 forall119898 isin 119871 (13)

lceil119888max119898

V119904rceil ge 120583min119901119898 forall119898 isin 119871 (14)

sum119898isin119871

119911119898119902ℎ119898119905 le 120575119887 forall119902 isin 119861 119905 isin 119879 (15)

119908119889119903119905 = sum119898isin119871

sum119902isin119861119903

119911119898119902ℎ119898119905forall119903 isin 119877 119905 isin 119879

(16)

Scientific Programming 7

119908119889119903119905 le 120575119887 forall119903 isin 119877 119905 isin 119879 (17)

sum119898isin119871

119909119894119898ℎ119898119905 + 120576sum119895isin119878119899119894

sum119898isin119871

119909119895119898ℎ119898119905 le 1 forall119894 isin 119878 119905 isin 119879 (18)

sum119903isin119877

1199101199041199030 = 119873119884 (19)

sum1199031015840isin119877

1199101199031199031015840119905 = 1199101199041199030 forall119903 isin 119877 119905 = 1 (20)

sum1199031015840isin119877

1199101199031199031015840119905 = sum1199031015840isin119877

1199101199031015840119903(119905minus1)forall119903 isin 119877 2 le 119905 le 119873119879 minus 1

(21)

1199101199041199030 = sum1199031015840isin119877

1199101199031015840119903119905forall119903 isin 119877 119905 = 119873119879

(22)

119908119886119903119905 = 1199101199041199030 forall119903 isin 119877 119905 = 1 (23)

119908119886119903119905 = sum1199031015840isin119877

1199101199031015840119903(119905minus1)forall119903 isin 119877 119905 isin 119879 119905 = 1

(24)

119908119886119903119905 ge 119908119889119903119905 forall119903 isin 119877 119905 isin 119879 (25)

119908119886119903119905 le 120575119903 forall119903 isin 119877 119905 isin 119879 (26)

119909119894119898 isin 0 1 forall119894 isin 119878 119898 isin 119871 (27)

1199101199041199030 isin 119873 forall119903 isin 119877 (28)

1199101199031199031015840119905 isin 119873forall119903 1199031015840 isin 119877 119905 isin 119879 (29)

119911119902119898 isin 0 1forall119898 isin 119871 119902 isin 119861 (30)

119908119886119903119905 119908119889119903119905 isin 119873 forall119903 isin 119877 119905 isin 119879 (31)

The constraints of the mathematical model are composedof three parts the yard space allocation constraints theyard crane deployment constraints and the variables rangeconstraints

Equations (6) to (18) are the constraints of the first partwhich defines the rules of yard space allocation Equation (6)states that each subblock should be reserved for at most oneservice line during the entire planning horizon Equations (7)and (8) state that the subblocks assigned to the service linemust satisfy the outbound containers storage demand of theservice line Considering the service line outbound containervolumes are not generally fixed and the yard storage spaceis extremely limited the loosened constraints are presentedEquation (9) ensures that all the subblocks should be assignedto a service line Equations (10) and (11) are the calculationequations of service line YC loading points in a block equalto 1 if there is at least one subblock reserved for the service

line but otherwise equal to 0 Equations (12) to (14) state therelationship between the service line quay operation queuein the seaside and the YC loading point in the yard areaEquation (15) ensures themaximal handling YCs in the blockEquations (16) and (17) restrict the maximal handling YCsin the yard row Equation (18) states that when one of thesubblocks is in loading state the other neighbor subblocksare unavailable for service line that should be handled at thesame time

Equations (19) to (26) are the constraints of the secondpart which defines the rules of yard crane deploymentEquation (19) guarantees that the summation of initial YCsdeployment in each row is equal to the number of YCsEquations (20) to (22) ensure the YCs resource flow balancein the process of YCs interzone movement in each period ofplanning horizon Equations (23) and (24) are the calculationequations of YCs in each yard row Equations (25) and (26)ensure that the YCs operating in the row should satisfy theoperational demand and not exceed the maximal YCs boundin the row at the same time

Finally the domains of variables defined by (27) to (31)are the constraints of the third part

Linear Transformation As formula (1) is a nonlinear functiona linear transformation operation is applied After lineartransformation formula (1) is equal to

max 1198911 = sum119894isin119878

sum119895isin119878119899119894

sum119898119899isin119871

120601119894119895119898119899120596119898119899120579120601119894119895119898119899 le 119909119894119898 forall119894 isin 119878 119895 isin 119878119899119894 119898 119899 isin 119871120601119894119895119898119899 le 119909119895119899 forall119894 isin 119878 119895 isin 119878119899119894 119898 119899 isin 119871120601119894119895119898119899 ge 119909119894119898 + 119909119895119899 minus 1

forall119894 isin 119878 119895 isin 119878119899119894 119898 119899 isin 119871120601119894119895119898119899 isin 0 1 forall119894 isin 119878 119895 isin 119878119899119894 119898 119899 isin 119871

(32)

5 Numerical Experiment

To evaluate the effectiveness of the proposed model aseries of experiments with different scales are conductedSection 51 introduces the parameters used for generating theexperiments Section 52 analyzes the trade-off between yardstorage space resource utilization and yard operation costSection 53 researches the effects of YCs on yard storage spaceand operational cost Section 54 explores the influence ofsubblock volume on the yard management The integratedmodel in this paper is solved by ILOG CPLEX 124 and all ofthe computation experiments are conducted on aworkstationwith Inter Xeon CPU with 64GHz RAM

51 Instances At present many of the container line arrivalpatterns are weekly arrival In other words the voyage ofservice line arrives at the terminal once a weekTherefore theplanning horizon of this experiment is 1 week and each dayis split into 3 periods of 8 hours in consideration of practicalworking shift in the container terminal The experiment in

8 Scientific Programming

Table 1 Configuration parameters of container terminal yard

Class 119873119871(periods)

119873119861(blocks)

119873119878(subblocks)

119873119877(rows)

119873119884(YCs)

Class S 6 8 32 2 6Class M 8 16 64 4 12Class L 10 24 96 6 18

Table 2 Configuration parameters of yard crane and intertruck

Parameters 120583min 120583max 120575119887 120575119903 120593 120588 120590 120587Value 2 3 2 6 15 24 05 200

this paper considers three different storage yard scales (smallmedium and large) more precisely the instances with 6 to10 service lines 6 to 18 YCs and 8 to 24 blocks resulting inclasses 6 times 8 times 6 (class S) 8 times 16 times 12 (class M) and 10 times 24 times18 (class L) are tested (Table 1)

For all the classes the authors assume that the capacityof each block is 800 TEUs and the subblock capacity (V119887) is200 TEUs Meanwhile the maximal sharing space capacityof each subblock is equal to 20 TEUs (10 V119887) The yardcrane handling parameters and intertruck transportationparameters are shown in Table 2

For each class three scenarios of service line loadingrequirement are tested denoted by W1 W2 and W3 Theloading requirement is determined by the service line quayoperation queues (input data 119901119898 isin 119873 which are generatedwith discrete uniform distributions DU[2 3] DU[3 4] andDU[4 5] resp) the name of the instance indicates the levelof the loading requirement low requirement (W1) generalrequirement (W2) and high requirement (W3)

52 Yard Space Resource Analysis Based on space sharingstrategy the yard storage space utilization is increased owingto the sharing storage space between neighbor subblocks Asshowed in Table 3 the optimal yard operation cost equal to99990 yen and 800TEUsrsquo extra storage space (sharing space) arecreated (119886 = 0 cost-saving pattern) if space sharing strategyis applied in the yard Obviously this strategy can relieveterminal yard space scarce situation to a certain extent

Meanwhile when coefficient 119886 takes 1 it means thatthis model considers yard space allocation problem (space-utilizing pattern) firstly and then the yard crane deploymentproblem (cost-saving pattern) it is the nonintegrated patternin this situation Accordingly with the value of 119886 decreasingthe yard crane deployment is integrated with the yard spaceallocation problem gradually

Furthermore Figures 3 4 5 and 6 show the rela-tionships between yard storage space and yard operationcost of different instances scales As we can see with theincreasing of coefficient 119886 the yard sharing space increasedsynchronously as well as the yard operation cost Hence thereis no ultimate solution with the maximum space sharingand the minimum operation cost Which one should bechosen from these nondominated solutions is determined bythe terminal operators according to the terminal reality If

720 750 810780 840

105000

95000

115000

125000

135000

145000

870 900

a = 0

a = 02

a = 04

a = 06

a = 08

a = 1

Sharing space (TEUs)

Tran

spor

tatio

n co

st (yen

)

Figure 3 Relationships between yard space and operation cost ofsmall-scale experiments

1100 1200 14001300 1500

235000

220000

250000

265000

280000

295000

1600 1700

a = 0

a = 02

a = 04

a = 06

a = 08

a = 1

Sharing space (TEUs)

Tran

spor

tatio

n co

st (yen

)

Figure 4 Relationships between yard space and operation cost ofmedium-scale experiments

1950 2050 22502150 2350

395000

375000

415000

435000

455000

475000

2450 2550

a = 0

a = 02

a = 04

a = 06

a = 08

a = 1

Sharing space (TEUs)

Tran

spor

tatio

n co

st (yen

)

Figure 5 Relationships between yard space and operation cost oflarge-scale experiments

Scientific Programming 9

Table 3 Results of instances with different coefficient values

Instances119886 = 1 119886 = 08 119886 = 06 119886 = 04 119886 = 02 119886 = 01198911

(TEUs)1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

S W1 880 128800 880 110880 840 108900 800 103820 800 99990 800 99990S W2 880 129380 840 119960 840 110880 800 107910 760 102960 760 99990S W3 880 133340 840 127640 800 118800 760 108900 720 102960 680 99990M W1 1680 293150 1600 268500 1480 241600 1360 228830 1240 222450 1160 221760M W2 1600 286480 1560 261460 1440 239900 1320 228670 1240 224960 1160 221950M W3 1560 282360 1520 264300 1440 241860 1320 230100 1200 225960 1120 222140L W1 2480 468460 2400 432570 2360 403120 2200 387550 2120 380350 2080 376180L W2 2480 467820 2400 432800 2320 405670 2160 387610 2120 380640 2040 377050L W3 2400 468680 2360 433130 2280 405880 2160 388060 2080 381020 2000 378120

Table 4 Results of instances with different YCs

Instances119873119884119873119877 = 3 119873119884119873119877 = 35 119873119884119873119877 = 4 119873119884119873119877 = 45 119873119884119873119877 = 51198911

(TEUs)1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

S1 W1 960 99990 980 98040 980 97160 1000 96500 1000 96320S1 W2 960 99990 960 98630 980 97640 980 96500 1000 96320S1 W3 960 99990 960 99160 980 98420 980 97930 1000 96950M1 W1 1680 221760 1700 217730 1780 214200 1820 211770 1820 210040M1 W2 1600 221950 1640 218780 1700 215980 1760 213530 1760 211690M1 W3 1580 222140 1620 219420 1680 216560 1700 213840 1760 211870L1 W1 2480 376180 2540 367550 2580 360430 2640 354660 2640 351530L1 W2 2480 377050 2520 368580 2540 361910 2580 354960 2600 351600L1 W3 2420 378120 2460 368990 2500 362320 2540 355740 2600 352690

Δf1

Δf2

Sharing space (TEUs)

Tran

spor

tatio

n co

st (yen

)

tan 1205792 =Δf2Δf1

1205791

1205792

1205793

Figure 6 Relationships between yard space and operation cost

the container terminal yard storage is extremely scarce thatcould infect yard operation the operators should create morestorage space and the space-utilizing oriented strategy maybe adopted that is 119886 should take a bigger value otherwisethe cost saving should be the primary selection It is worthnoting that the marginal cost of yard sharing space (tan 120579)grows nonlinearly with the increase of coefficient 11988653 Yard Crane Resource Analysis In this section the effectsof total YCs on yard storage space utilization and yardoperation cost are tested We changed the number of YCs in

95000

96000

97000

98000

99000

100000

101000

940

950

960

970

980

990

1000

1010

Sharing space (TEUs)Transportation cost (yen)

NYN

R=3

NYN

R=45

NYN

R=4

NYN

R=5

NYN

R=35

Figure 7 Yard crane influence of small-scale experiments

the yard and the other parameters are unchanged For thisgroup of experiments consider the yard sharing space andyard operation cost separately so the coefficient 119886 is equal to1 and 0 respectively in the calculation of yard sharing spaceand yard operation cost The detailed results are shown inTable 4

Figures 7 8 and 9 show the effects of YCs on yard sharingspace and yard operation cost intuitively From these figures

10 Scientific Programming

Table 5 Results of instances with different subblock volume

Instances119873119878119873119861 = 3 119873119878119873119861 = 4 119873119878119873119861 = 5 119873119878119873119861 = 61198911

(TEUs)1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

S2 W1 756 106550 880 99990 960 95680 mdash mdashS2 W2 756 106550 880 99990 960 96280 mdash mdashS2 W3 756 106550 880 99990 960 99200 mdash mdashM2 W1 1404 231680 1680 221760 1888 217440 1950 210870M2 W2 1404 231760 1600 221950 1856 215210 mdash mdashM2 W3 1350 235930 1560 222140 1824 218130 mdash mdashL2 W1 2214 394550 2480 376180 2720 366960 2938 359620L2 W2 2214 396640 2480 377050 2688 371090 mdash mdashL2 W3 2160 398150 2400 378120 2656 373210 mdash mdash

208000

210000

212000

214000

216000

218000

224000

222000

220000

1550

1600

1650

1700

1750

1800

Sharing space (TEUs)Transportation cost (yen)

NYN

R=3

NYN

R=45

NYN

R=4

NYN

R=5

NYN

R=35

Figure 8 Yard crane influence of medium-scale experiments

we can find that the sharing space gradually becomes biggerwith the average YCs number in each zone increasing but theyard operation cost has an opposite situation

For the increasing of yard sharing space the mainreason could be that the added YCs relieved the YC loadingpoint constraint and then created more flexible service linespairings among subblocks but this effect is slight only about4

However generally speaking the increase of YCs shoulddecrease the yard operation cost considerably because it canavoid yard crane interzone movement as far as possible Butthese results shown in the figures could not express thisphenomenon obviously there is still only 6 cost decreaseA significant cause of this phenomenon is that the operationcost we considered is on the situation that the objectivefunction is cost-saving pattern (the coefficient 120572 equal to 0)so the yard operation cost we compared has been optimizedIt means that the amount of YCs interzone movements hasbeen decreased to an optimal level and this phenomenoncould be directly identified by Table 3 in Section 51

54 Subblock Volume Analysis The authors are also inter-ested in how the volume of subblock infects the yard space

335000340000345000350000355000360000365000370000375000380000

2350

2400

2450

2500

2550

2600

2650

Sharing space (TEUs)Transportation cost (yen)

NYN

R=3

NYN

R=45

NYN

R=4

NYN

R=5

NYN

R=35

Figure 9 Yard crane influence of large-scale experiments

utilization and yard operation cost In this subsection thenumber of subblocks in each block is divided into 3 4 5and 6 thus the volume of each subblock is equal to 270 200160 and 130 TEUs respectively and the other parameters areunchanged Similar to Section 53 the coefficient 119886 is equal to1 and 0 respectively in the calculation of yard sharing spaceand yard operation cost The detailed results are shown inTable 5

As showed in Figures 10 11 and 12 with the volumeof subblock decreasing and the subblocks in the yard blockincreasing gradually that the pairing of service lines becamemore flexible Consequently the space sharing opportunityincreased and the yard operation cost decreased as wellHowever with the decreasing of yard subblocks volume theyard crane service range is limited and such trends willlimit the increase of the yard crane resource demand in theyard When the number of subblocks in the block reaches acertain value the whole container terminal yard area cannotrun normally Accordingly the volume of yard subblock alsoplays an important role in yard management If the value istoo large the sharing space opportunity will decrease andoperation cost will increase However if the value is too smallthe whole system operation pattern will be broken up

Scientific Programming 11

9000092000940009600098000

100000102000104000106000108000

60065070075080085090095010001050

Sharing space (TEUs)Transportation cost (yen)

NSNB=3

NSNB=6

NSNB=5

NSNB=4

Figure 10 Yard subblock size influence of small-scale experiments

1200

1300

1400

1500

1600

1700

1800

1900

2000

200000

205000

210000

215000

220000

225000

230000

235000

Sharing space (TEUs)Transportation cost (yen)

NSNB=3

NSNB=6

NSNB=5

NSNB=4

Figure 11 Yard subblock size influence of medium-scale experi-ments

6 Conclusions

Motivated by the requirement to relieve the operationdilemma for resource-limited container terminal this paperaddressed the integrated yard space allocation and yard cranedeployment problem Two corresponding counterstrategiesare introduced and then an integrated mathematical modelis formulated to solve the problem Numerical experimentsverified the correctness and accuracy of the proposed modelThis study found that space sharing strategy can increase yardspace utilization and yard crane interzone movement strategycan effectively relieve the shortage of YCs In addition aninteresting phenomenon is discovered that there exists atrade-off between yard space utilization and yard operationcost and the volume of yard subblock also plays a significantrole in container port yard management

340000

350000

360000

370000

380000

390000

400000

2000

2200

2400

2600

2800

2900

2100

2300

2500

2700

Sharing space (TEUs)Transportation cost (yen)

NSNB=3

NSNB=6

NSNB=5

NSNB=4

Figure 12 Yard subblock size influence of large-scale experiments

This research can be extended in many relative areas Inthis paper the service line working windows and yard craneefficiency are determined However these parameters mayfluctuate with the factors associated with natural factors andthe equipment operators in reality Therefore the applicationof uncertainty factors in the integratedmanagement problemis a valuable research direction in the future

Competing Interests

The authors declare that they have no competing interests

Authorsrsquo Contributions

All authors contributed equally and significantly to writingthis article

Acknowledgments

This work is sponsored by National Natural Science Founda-tion ofChina (71602114) ldquoChenguangProgramrdquo supported byShanghai Education Development Foundation and ShanghaiMunicipal Education Commission (14CG48) Shanghai Sail-ing Program (14YF1411200) Doctoral Fund of theMinistry ofEducation (20133121110001) Shanghai Municipal EducationCommission Project (14YZ112) Shanghai Science amp Tech-nology Committee Research Project (15590501700) Shang-hai Maritime University Doctoral Innovation Fund Project(2015ycx063) and Shanghai Maritime University DoctoralExcellent Thesis Training Program (2015BXLP006)

References

[1] D Chang Z H JiangW Yan and J He ldquoIntegrating berth allo-cation and quay crane assignmentsrdquo Transportation Research

12 Scientific Programming

Part E LogisticsampTransportation Review vol 46 no 6 pp 975ndash990 2010

[2] J L He D F Chang W J Mi and W Yan ldquoA hybrid parallelgenetic algorithm for yard crane schedulingrdquo TransportationResearch Part E Logistics and Transportation Review vol 46no 1 pp 136ndash155 2010

[3] J G Jin D Lee and J X Cao ldquoStorage yard management inmaritime container terminalsrdquo Transportation Science 2014

[4] C-H Chen and W Yan ldquoEngineering informatics in portoperations and logisticsrdquoAdvanced Engineering Informatics vol25 no 3 pp 401ndash402 2011

[5] C-H Chen L P Khoo Y T Chong and X F Yin ldquoKnowledgediscovery using genetic algorithm for maritime situationalawarenessrdquo Expert Systems with Applications vol 41 no 6 pp2742ndash2753 2014

[6] J He Y Huang and D Chang ldquoSimulation-based heuristicmethod for container supply chain network optimizationrdquoAdvanced Engineering Informatics vol 29 no 3 pp 339ndash3542015

[7] I F A Vis and R De Koster ldquoTransshipment of containersat a container terminal an overviewrdquo European Journal ofOperational Research vol 147 no 1 pp 1ndash16 2003

[8] D Steenken S Voszlig and R Stahlbock ldquoContainer terminaloperation and operations researchmdasha classification and litera-ture reviewrdquo OR Spectrum vol 26 no 1 pp 3ndash49 2004

[9] R Stahlbock and S Voszlig ldquoOperations research at containerterminals a literature updaterdquo Operations Research-Spektrumvol 30 no 1 pp 1ndash52 2008

[10] X Jiang L H Lee E P Chew Y Han and K C Tan ldquoAcontainer yard storage strategy for improving land utilizationand operation efficiency in a transshipment hub portrdquoEuropeanJournal of Operational Research vol 221 no 1 pp 64ndash73 2012

[11] L H Lee E P Chew K C Tan and Y Han ldquoAn optimizationmodel for storage yardmanagement in transshipment hubsrdquoORSpectrum vol 28 no 4 pp 539ndash561 2006

[12] Y Han L H Lee E P Chew and K Tan ldquoA yard storagestrategy forminimizing traffic congestion in amarine containertransshipment hubrdquo OR Spectrum Quantitative Approaches inManagement vol 30 no 4 pp 697ndash720 2008

[13] X Jiang E P Chew L H Lee and K C Tan ldquoFlexible space-sharing strategy for storage yard management in a transship-ment hub portrdquo OR Spectrum vol 35 no 2 pp 417ndash439 2013

[14] L Zhen ldquoContainer yard template planning under uncertainmaritimemarketrdquo Transportation Research Part E Logistics andTransportation Review vol 69 pp 199ndash217 2014

[15] C Zhang Y-W Wan J Liu and R J Linn ldquoDynamiccrane deployment in container storage yardsrdquo TransportationResearch Part B Methodological vol 36 no 6 pp 537ndash5552002

[16] R K Chung C-L Li andW Lin ldquoInterblock crane deploymentin container terminalsrdquoTransportation Science vol 36 no 1 pp79ndash93 2002

[17] R Linn J-Y Liu Y-W Wan C Q Zhang and K G MurtyldquoRubber tired gantry crane deployment for container yardoperationrdquo Computers amp Industrial Engineering vol 45 no 3pp 429ndash442 2003

[18] Z Cao D-H Lee and Q Meng ldquoDeployment strategies ofdouble-rail-mounted gantry crane systems for loading out-bound containers in container terminalsrdquo International Journalof Production Economics vol 115 no 1 pp 221ndash228 2008

[19] K H Kim and H B Kim ldquoThe optimal sizing of the storagespace and handling facilities for import containersrdquoTransporta-tion Research Part B Methodological vol 36 no 9 pp 821ndash8352002

[20] D-H Lee J G Jin and J H Chen ldquoIntegrated bay allocationand yard crane scheduling problem for transshipment contain-ersrdquo Transportation Research Record vol 2222 no 8 pp 63ndash712011

[21] S H Won X Zhang and K H Kim ldquoWorkload-based yard-planning system in container terminalsrdquo Journal of IntelligentManufacturing vol 23 no 6 pp 2193ndash2206 2012

Submit your manuscripts athttpwwwhindawicom

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Human-ComputerInteraction

Advances in

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4 Scientific Programming

1 loading point for vessel A 1 loading point for vessel B

Subblock 150 TEUs

800 TEUs outbound containersService line 1 vessel A

3000 TEUs outbound containersService line 2 vessel B

S1 S2 S3 S4 S5

S21 S22 S23 S24 S25

S41 S42 S43 S44 S45

S61 S62 S63 S64 S65

S6 S7 S8 S9 S10

S26 S27 S28 S29 S30

S46 S47 S48 S49 S50

S66 S67 S68 S69 S70

S31 S32 S33 S4 S35

S11 S12 S13 S14 S15

S51 S52 S53 S54 S55

S71 S72 S73 S74 S75

S36 S37 S38 S39 S40

S16 S17 S18 S19 S20

S56 S57 S58 S59 S60

S76 S77 S77 S78 S78

Berth

Zone

QC operation queue

(Row)

Figure 1 A typical yard space configuration of container terminal

assigned according to the service line minimal demand it islikely to face storage space shortage for a busy voyage On thecontrary the terminal yard space will not be sufficient

For the container terminal with a static yard template[11 12] all the subblocks in each block have a fixed spacecapacity whichmeans each service line needs to be assigned alarge enough yard storage space to satisfy containers stackingdemand at the peak time To take advantage of the benefitof consignment strategy and increase the yard storage spaceutilization Jiang et al [10] proposed a space sharing strategywhich allows some certain space to be shared betweenneighbor subblocks For a detailed sharing space strategydescription we refer readers to the work given by Jiang et al[10]

In general for a resource-limited container terminal themain concern is the utilization of yard storage in the processof yard space allocation Accordingly the objective couldbe concentrated on the total sharing space between yardneighbor subblocks Constraints that should be consideredwhen allocating storage space mainly include the following

(i) The storage capacity allocated to each service lineshould be sufficient so that it could meet the stackingdemand

(ii) For each service line in order to achieve a high oper-ational efficiency as far as possible the proportion ofquay operation queue and YC loading point would bein the reasonable range

(iii) The YC loading point in the block must be wellcontrolled at any time period otherwise traffic con-gestion can be expected

32 Yard Crane Deployment The yard crane deploymentproblem is to designate and schedule YCs route accordingto the workload requirement in the yard area Many relevantresearches usually focus on the deployment problem betweenyard blocks in the same zone that only the yard craneintrazone movement is considered This is a commendablestrategywhen the terminal yard crane resources are adequate

However there may be a situation that only four YCs arein one zone with 5 or 6 blocks in some container terminals Inthis case 4 YCs should service 5 or 6 blocks the YCs have tomove among different block zones Therefore the yard craneinterzone movement is enabled in this terminal to satisfyoperational requirements In this study we concentrated onthe yard crane interzonemovement rather than the intrazonemovement because the former operation time cost and fuelconsumption cost are much higher than the latter Figure 2shows a diagram of E-RTG interzone movement process Fora detailed yard cranemovement patterns description we referreaders to the works given by Linn et al [17] and Zhang et al[15]

For yard crane deployment the objective is to optimizeworkload distribution of each yard rowduring all the periodsTherefore the optimization objective in this paper is tominimize YCs operation cost when deploying yard craneConstraint that should be considered is to ensure the number

Scientific Programming 5

1

2

3

Electric cables

Figure 2 E-RTG interzone movement process

of YCs deployed in each row can satisfy the containerhandling requirement

4 Mathematic Model

In this section the integrated yard space allocation and yardcrane deployment mathematical model for resource-limitedcontainer terminal is formulatedThe authors raised themaincharacteristics of resource-limited container terminal storagespace allocation and yard crane deployment problem andthen presented the relevant counterstrategies accordingly Foryard space strained problem the space sharing strategy isapplied which has been proposed by Jiang et al [10] and asfor yard crane equipment shortage the yard crane interzonemovement is enabled

41 Assumptions The following assumptions are made in theintegrated model

(1) The yard storage space can satisfy the minimumservice line outbound containers stacking demandand the YCs are sufficient to guarantee the basichandling requirement

(2) The service lines berthing position are given andfixed hence once the service line containers areassigned to the subblocks the minimal inner trucktransportation distances are determined

(3) A subblock can be reserved for only one service lineexcept for part of the storage space which may beshared with its neighbor assigned service lines andwill not change once the storage plan is determined

(4) The YC can only shift to one yard zone in one periodit means that once the yard crane moved from onezone to another then it should be staying in the zonebefore the next planning period is begun

42 Mathematic Formulation This model aims to deal withthe yard space allocation problem and yard crane deploymentproblem at the tactical level and provides the following

results (1) yard storage space allocation plan for outboundcontainers of all the service lines which considers thecontainer volumes quay operation queues YC loading pointsand handling conflicts of service lines in the storage yard(2) yard crane deployment profile including the yard craneassignment plan in the initial period and subsequent yardcrane moving scheme

Sets

119879 set of time periods 119879 = 1 2 119873119879119861 set of yard blocks 119861 = 1 2 119873119861119878 set of yard subblocks 119878 = 1 2 119873119878119878119899119894 set of neighbor subblocks of subblock 119894 isin 119878 119878119899119894 isin 119878119878119904119902 set of subblocks belonging to block 119902 isin 119861 119878119904119902 isin 119878119877 set of yard rows (zone) in the terminal yard 119877 =1 2 119873119877119861119903 set of blocks belonging to row 119903 isin 119877 119861119903 isin 119861119871 set of service lines of terminal 119871 = 1 2 119873119871119884 set of YCs 119884 = 1 2 119873119884

Parameters

119888min119898 minimal outbound containers of service line 119898 isin 119871

(TEUs)119888max119898 maximal outbound containers of service line 119898 isin 119871

(TEUs)119901119898 quay operation queues of service line119898 isin 119871

120583min minimal YC loading points that one quay operationqueue demands

120583max maximal YC loading points that one quay operationqueue can satisfy

119905119904119898 time period to start handling of service line119898 isin 119871119905119890119898 time period to end handling of service line119898 isin 119871ℎ119898119905 handling parameter of service line119898 isin 119871 equal to 1 if119905 isin [119905119904119898 119905119890119898] otherwise equal to 0

6 Scientific Programming

V119904 maximal space capacity of each subblock (TEUs)

V119887 maximal space capacity of each yard block (TEUs)

120575119887 maximal YCs enabled operating in one yard block120575119903 maximal YCs enabled operating in one block row

120596119898119899 yard space sharing space when subblocks of serviceline 119898 isin 119871 and service line 119899 isin 119871 are neighbored (inthis paper120596119898119899 isin 0 1 it is usually determined by thecontainer buildup pattern of two service lines [14])

120579 fixed capacity of one sharing space (TEUs)119889119905119894119898 inner truck moving distance (loading and unloading)

if service line119898 isin 119871 is assigned to subblock 119894 isin 119878 (km)1198891198881199031199031015840 yard cranemovement distance between row 119903 isin 119877 and

row 1199031015840 isin 119877 (km)120593 inner truck transportation cost (yenkmTEU)120590 fixed time consumption of yard crane interzone

movement (h)120587 yard crane time cost (yenh)120588 yard crane movement cost (yenm)

1205821199031199031015840 yard crane interzone movement cost between row 119903 isin119877 and row 1199031015840 isin 119877 119903 = 1199031015840 (yen) where 1205821199031199031015840 = 120590120587 + 1198891198881199031199031015840120588if 119903 = 1199031015840 1205821199031199031015840 = 0

120576 a small and positive constant

Decision Variables

119909119894119898 isin 0 1 1 if subblock 119894 isin 119878was assigned to serviceline119898 isin 119871 0 otherwise1199101199031199031015840119905 isin 119873 YCs moving from row 119903 isin 119877 to row 1199031015840 isin 119877at the end of time period 119905 isin 119879 (and 1199101199041199030 is initial YCsof row 119903 isin 119877 in the beginning of the period)119911119898119902 isin 0 1 the number of YC loading points ofservice line119898 isin 119871 in block 119902 isin 119861119908119889119903119905 isin 119873 minimal yard crane requirement of row 119903 isin119877 in time period 119905 isin 119879119908119886119903119905 isin 119873 the number of YCs assigned to row 119903 isin 119877 intime period 119905 isin 119879

Objective Function

maximize 1198911 = sum119894isin119878

sum119895isin119878119899119894

sum119898119899isin119871

119909119894119898119909119895119899120596119898119899120579 (1)

minimize 1198912 = 1198911199052 + 1198911198882 (2)

1198911199052 = sum119894isin119904

sum119898isin119871

119909119894119898119889119905119894119898120593V119904 (3)

1198911198882 = sum119903isin119877

sum1199031015840isin119877

sum119905isin119879

11991011990311990310158401199051205821199031199031015840 (4)

The mathematical model proposed in this section is amultiobjective optimal model hence the authors transferredit into a single-objective problem by the method of weightedallocation Define 120572 as the coefficient of yard storage space

in the process of terminal operation management and usecoefficient 120572 to combine the two objectives Furthermorebecause the dimensions of two objectives are different thusnondimensional processing is needed Note that 119891max

1 and119891min1 are the independent maximal and minimal value of 1198911

respectively 119891max2 and 119891min

2 are the independent maximaland minimal value of 1198912 Therefore the integrated objectivefunction can be expressed as follows

max 119891 = 120572 (1198911 minus 119891min1 )

(119891max1 minus 119891min

1 ) +(1 minus 120572) (119891max

2 minus 1198912)(119891max2 minus 119891min

2 ) (5)

In formula (5) the coefficient 120572 could be set as0 01 10 with a step size of 01 This step could beadjusted manually according to problem size and terminaloperatorrsquos preference By changing the value of 120572 differentsets of solutions can be obtained In other words when 120572is smaller the solutions are more space-utilizing On thecontrary with the increase of 120572 the solutions are more cost-saving

Constraints

sum119898isin119871

119909119894119898 le 1 forall119894 isin 119878 (6)

sum119894isin119904

119909119894119898 ge lceil119888min119898

V119904rceil forall119898 isin 119871 (7)

sum119894isin119904

119909119894119898 le lceil119888max119898

V119904rceil forall119898 isin 119871 (8)

sum119894isin119878

sum119898isin119871

119909119894119898 = 119873119878 (9)

119911119898119902 le sum119894isin119878119904119902

119909119894119898forall119898 isin 119871 119902 isin 119861

(10)

119911119898119902 ge sum119894isin119878119904119902

119909119894119898120576

forall119898 isin 119871 119902 isin 119861(11)

sum119902isin119861

119911119898119902 ge 120583min119901119898 forall119898 isin 119871 (12)

sum119902isin119861

119911119898119902 le 120583max119901119898 forall119898 isin 119871 (13)

lceil119888max119898

V119904rceil ge 120583min119901119898 forall119898 isin 119871 (14)

sum119898isin119871

119911119898119902ℎ119898119905 le 120575119887 forall119902 isin 119861 119905 isin 119879 (15)

119908119889119903119905 = sum119898isin119871

sum119902isin119861119903

119911119898119902ℎ119898119905forall119903 isin 119877 119905 isin 119879

(16)

Scientific Programming 7

119908119889119903119905 le 120575119887 forall119903 isin 119877 119905 isin 119879 (17)

sum119898isin119871

119909119894119898ℎ119898119905 + 120576sum119895isin119878119899119894

sum119898isin119871

119909119895119898ℎ119898119905 le 1 forall119894 isin 119878 119905 isin 119879 (18)

sum119903isin119877

1199101199041199030 = 119873119884 (19)

sum1199031015840isin119877

1199101199031199031015840119905 = 1199101199041199030 forall119903 isin 119877 119905 = 1 (20)

sum1199031015840isin119877

1199101199031199031015840119905 = sum1199031015840isin119877

1199101199031015840119903(119905minus1)forall119903 isin 119877 2 le 119905 le 119873119879 minus 1

(21)

1199101199041199030 = sum1199031015840isin119877

1199101199031015840119903119905forall119903 isin 119877 119905 = 119873119879

(22)

119908119886119903119905 = 1199101199041199030 forall119903 isin 119877 119905 = 1 (23)

119908119886119903119905 = sum1199031015840isin119877

1199101199031015840119903(119905minus1)forall119903 isin 119877 119905 isin 119879 119905 = 1

(24)

119908119886119903119905 ge 119908119889119903119905 forall119903 isin 119877 119905 isin 119879 (25)

119908119886119903119905 le 120575119903 forall119903 isin 119877 119905 isin 119879 (26)

119909119894119898 isin 0 1 forall119894 isin 119878 119898 isin 119871 (27)

1199101199041199030 isin 119873 forall119903 isin 119877 (28)

1199101199031199031015840119905 isin 119873forall119903 1199031015840 isin 119877 119905 isin 119879 (29)

119911119902119898 isin 0 1forall119898 isin 119871 119902 isin 119861 (30)

119908119886119903119905 119908119889119903119905 isin 119873 forall119903 isin 119877 119905 isin 119879 (31)

The constraints of the mathematical model are composedof three parts the yard space allocation constraints theyard crane deployment constraints and the variables rangeconstraints

Equations (6) to (18) are the constraints of the first partwhich defines the rules of yard space allocation Equation (6)states that each subblock should be reserved for at most oneservice line during the entire planning horizon Equations (7)and (8) state that the subblocks assigned to the service linemust satisfy the outbound containers storage demand of theservice line Considering the service line outbound containervolumes are not generally fixed and the yard storage spaceis extremely limited the loosened constraints are presentedEquation (9) ensures that all the subblocks should be assignedto a service line Equations (10) and (11) are the calculationequations of service line YC loading points in a block equalto 1 if there is at least one subblock reserved for the service

line but otherwise equal to 0 Equations (12) to (14) state therelationship between the service line quay operation queuein the seaside and the YC loading point in the yard areaEquation (15) ensures themaximal handling YCs in the blockEquations (16) and (17) restrict the maximal handling YCsin the yard row Equation (18) states that when one of thesubblocks is in loading state the other neighbor subblocksare unavailable for service line that should be handled at thesame time

Equations (19) to (26) are the constraints of the secondpart which defines the rules of yard crane deploymentEquation (19) guarantees that the summation of initial YCsdeployment in each row is equal to the number of YCsEquations (20) to (22) ensure the YCs resource flow balancein the process of YCs interzone movement in each period ofplanning horizon Equations (23) and (24) are the calculationequations of YCs in each yard row Equations (25) and (26)ensure that the YCs operating in the row should satisfy theoperational demand and not exceed the maximal YCs boundin the row at the same time

Finally the domains of variables defined by (27) to (31)are the constraints of the third part

Linear Transformation As formula (1) is a nonlinear functiona linear transformation operation is applied After lineartransformation formula (1) is equal to

max 1198911 = sum119894isin119878

sum119895isin119878119899119894

sum119898119899isin119871

120601119894119895119898119899120596119898119899120579120601119894119895119898119899 le 119909119894119898 forall119894 isin 119878 119895 isin 119878119899119894 119898 119899 isin 119871120601119894119895119898119899 le 119909119895119899 forall119894 isin 119878 119895 isin 119878119899119894 119898 119899 isin 119871120601119894119895119898119899 ge 119909119894119898 + 119909119895119899 minus 1

forall119894 isin 119878 119895 isin 119878119899119894 119898 119899 isin 119871120601119894119895119898119899 isin 0 1 forall119894 isin 119878 119895 isin 119878119899119894 119898 119899 isin 119871

(32)

5 Numerical Experiment

To evaluate the effectiveness of the proposed model aseries of experiments with different scales are conductedSection 51 introduces the parameters used for generating theexperiments Section 52 analyzes the trade-off between yardstorage space resource utilization and yard operation costSection 53 researches the effects of YCs on yard storage spaceand operational cost Section 54 explores the influence ofsubblock volume on the yard management The integratedmodel in this paper is solved by ILOG CPLEX 124 and all ofthe computation experiments are conducted on aworkstationwith Inter Xeon CPU with 64GHz RAM

51 Instances At present many of the container line arrivalpatterns are weekly arrival In other words the voyage ofservice line arrives at the terminal once a weekTherefore theplanning horizon of this experiment is 1 week and each dayis split into 3 periods of 8 hours in consideration of practicalworking shift in the container terminal The experiment in

8 Scientific Programming

Table 1 Configuration parameters of container terminal yard

Class 119873119871(periods)

119873119861(blocks)

119873119878(subblocks)

119873119877(rows)

119873119884(YCs)

Class S 6 8 32 2 6Class M 8 16 64 4 12Class L 10 24 96 6 18

Table 2 Configuration parameters of yard crane and intertruck

Parameters 120583min 120583max 120575119887 120575119903 120593 120588 120590 120587Value 2 3 2 6 15 24 05 200

this paper considers three different storage yard scales (smallmedium and large) more precisely the instances with 6 to10 service lines 6 to 18 YCs and 8 to 24 blocks resulting inclasses 6 times 8 times 6 (class S) 8 times 16 times 12 (class M) and 10 times 24 times18 (class L) are tested (Table 1)

For all the classes the authors assume that the capacityof each block is 800 TEUs and the subblock capacity (V119887) is200 TEUs Meanwhile the maximal sharing space capacityof each subblock is equal to 20 TEUs (10 V119887) The yardcrane handling parameters and intertruck transportationparameters are shown in Table 2

For each class three scenarios of service line loadingrequirement are tested denoted by W1 W2 and W3 Theloading requirement is determined by the service line quayoperation queues (input data 119901119898 isin 119873 which are generatedwith discrete uniform distributions DU[2 3] DU[3 4] andDU[4 5] resp) the name of the instance indicates the levelof the loading requirement low requirement (W1) generalrequirement (W2) and high requirement (W3)

52 Yard Space Resource Analysis Based on space sharingstrategy the yard storage space utilization is increased owingto the sharing storage space between neighbor subblocks Asshowed in Table 3 the optimal yard operation cost equal to99990 yen and 800TEUsrsquo extra storage space (sharing space) arecreated (119886 = 0 cost-saving pattern) if space sharing strategyis applied in the yard Obviously this strategy can relieveterminal yard space scarce situation to a certain extent

Meanwhile when coefficient 119886 takes 1 it means thatthis model considers yard space allocation problem (space-utilizing pattern) firstly and then the yard crane deploymentproblem (cost-saving pattern) it is the nonintegrated patternin this situation Accordingly with the value of 119886 decreasingthe yard crane deployment is integrated with the yard spaceallocation problem gradually

Furthermore Figures 3 4 5 and 6 show the rela-tionships between yard storage space and yard operationcost of different instances scales As we can see with theincreasing of coefficient 119886 the yard sharing space increasedsynchronously as well as the yard operation cost Hence thereis no ultimate solution with the maximum space sharingand the minimum operation cost Which one should bechosen from these nondominated solutions is determined bythe terminal operators according to the terminal reality If

720 750 810780 840

105000

95000

115000

125000

135000

145000

870 900

a = 0

a = 02

a = 04

a = 06

a = 08

a = 1

Sharing space (TEUs)

Tran

spor

tatio

n co

st (yen

)

Figure 3 Relationships between yard space and operation cost ofsmall-scale experiments

1100 1200 14001300 1500

235000

220000

250000

265000

280000

295000

1600 1700

a = 0

a = 02

a = 04

a = 06

a = 08

a = 1

Sharing space (TEUs)

Tran

spor

tatio

n co

st (yen

)

Figure 4 Relationships between yard space and operation cost ofmedium-scale experiments

1950 2050 22502150 2350

395000

375000

415000

435000

455000

475000

2450 2550

a = 0

a = 02

a = 04

a = 06

a = 08

a = 1

Sharing space (TEUs)

Tran

spor

tatio

n co

st (yen

)

Figure 5 Relationships between yard space and operation cost oflarge-scale experiments

Scientific Programming 9

Table 3 Results of instances with different coefficient values

Instances119886 = 1 119886 = 08 119886 = 06 119886 = 04 119886 = 02 119886 = 01198911

(TEUs)1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

S W1 880 128800 880 110880 840 108900 800 103820 800 99990 800 99990S W2 880 129380 840 119960 840 110880 800 107910 760 102960 760 99990S W3 880 133340 840 127640 800 118800 760 108900 720 102960 680 99990M W1 1680 293150 1600 268500 1480 241600 1360 228830 1240 222450 1160 221760M W2 1600 286480 1560 261460 1440 239900 1320 228670 1240 224960 1160 221950M W3 1560 282360 1520 264300 1440 241860 1320 230100 1200 225960 1120 222140L W1 2480 468460 2400 432570 2360 403120 2200 387550 2120 380350 2080 376180L W2 2480 467820 2400 432800 2320 405670 2160 387610 2120 380640 2040 377050L W3 2400 468680 2360 433130 2280 405880 2160 388060 2080 381020 2000 378120

Table 4 Results of instances with different YCs

Instances119873119884119873119877 = 3 119873119884119873119877 = 35 119873119884119873119877 = 4 119873119884119873119877 = 45 119873119884119873119877 = 51198911

(TEUs)1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

S1 W1 960 99990 980 98040 980 97160 1000 96500 1000 96320S1 W2 960 99990 960 98630 980 97640 980 96500 1000 96320S1 W3 960 99990 960 99160 980 98420 980 97930 1000 96950M1 W1 1680 221760 1700 217730 1780 214200 1820 211770 1820 210040M1 W2 1600 221950 1640 218780 1700 215980 1760 213530 1760 211690M1 W3 1580 222140 1620 219420 1680 216560 1700 213840 1760 211870L1 W1 2480 376180 2540 367550 2580 360430 2640 354660 2640 351530L1 W2 2480 377050 2520 368580 2540 361910 2580 354960 2600 351600L1 W3 2420 378120 2460 368990 2500 362320 2540 355740 2600 352690

Δf1

Δf2

Sharing space (TEUs)

Tran

spor

tatio

n co

st (yen

)

tan 1205792 =Δf2Δf1

1205791

1205792

1205793

Figure 6 Relationships between yard space and operation cost

the container terminal yard storage is extremely scarce thatcould infect yard operation the operators should create morestorage space and the space-utilizing oriented strategy maybe adopted that is 119886 should take a bigger value otherwisethe cost saving should be the primary selection It is worthnoting that the marginal cost of yard sharing space (tan 120579)grows nonlinearly with the increase of coefficient 11988653 Yard Crane Resource Analysis In this section the effectsof total YCs on yard storage space utilization and yardoperation cost are tested We changed the number of YCs in

95000

96000

97000

98000

99000

100000

101000

940

950

960

970

980

990

1000

1010

Sharing space (TEUs)Transportation cost (yen)

NYN

R=3

NYN

R=45

NYN

R=4

NYN

R=5

NYN

R=35

Figure 7 Yard crane influence of small-scale experiments

the yard and the other parameters are unchanged For thisgroup of experiments consider the yard sharing space andyard operation cost separately so the coefficient 119886 is equal to1 and 0 respectively in the calculation of yard sharing spaceand yard operation cost The detailed results are shown inTable 4

Figures 7 8 and 9 show the effects of YCs on yard sharingspace and yard operation cost intuitively From these figures

10 Scientific Programming

Table 5 Results of instances with different subblock volume

Instances119873119878119873119861 = 3 119873119878119873119861 = 4 119873119878119873119861 = 5 119873119878119873119861 = 61198911

(TEUs)1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

S2 W1 756 106550 880 99990 960 95680 mdash mdashS2 W2 756 106550 880 99990 960 96280 mdash mdashS2 W3 756 106550 880 99990 960 99200 mdash mdashM2 W1 1404 231680 1680 221760 1888 217440 1950 210870M2 W2 1404 231760 1600 221950 1856 215210 mdash mdashM2 W3 1350 235930 1560 222140 1824 218130 mdash mdashL2 W1 2214 394550 2480 376180 2720 366960 2938 359620L2 W2 2214 396640 2480 377050 2688 371090 mdash mdashL2 W3 2160 398150 2400 378120 2656 373210 mdash mdash

208000

210000

212000

214000

216000

218000

224000

222000

220000

1550

1600

1650

1700

1750

1800

Sharing space (TEUs)Transportation cost (yen)

NYN

R=3

NYN

R=45

NYN

R=4

NYN

R=5

NYN

R=35

Figure 8 Yard crane influence of medium-scale experiments

we can find that the sharing space gradually becomes biggerwith the average YCs number in each zone increasing but theyard operation cost has an opposite situation

For the increasing of yard sharing space the mainreason could be that the added YCs relieved the YC loadingpoint constraint and then created more flexible service linespairings among subblocks but this effect is slight only about4

However generally speaking the increase of YCs shoulddecrease the yard operation cost considerably because it canavoid yard crane interzone movement as far as possible Butthese results shown in the figures could not express thisphenomenon obviously there is still only 6 cost decreaseA significant cause of this phenomenon is that the operationcost we considered is on the situation that the objectivefunction is cost-saving pattern (the coefficient 120572 equal to 0)so the yard operation cost we compared has been optimizedIt means that the amount of YCs interzone movements hasbeen decreased to an optimal level and this phenomenoncould be directly identified by Table 3 in Section 51

54 Subblock Volume Analysis The authors are also inter-ested in how the volume of subblock infects the yard space

335000340000345000350000355000360000365000370000375000380000

2350

2400

2450

2500

2550

2600

2650

Sharing space (TEUs)Transportation cost (yen)

NYN

R=3

NYN

R=45

NYN

R=4

NYN

R=5

NYN

R=35

Figure 9 Yard crane influence of large-scale experiments

utilization and yard operation cost In this subsection thenumber of subblocks in each block is divided into 3 4 5and 6 thus the volume of each subblock is equal to 270 200160 and 130 TEUs respectively and the other parameters areunchanged Similar to Section 53 the coefficient 119886 is equal to1 and 0 respectively in the calculation of yard sharing spaceand yard operation cost The detailed results are shown inTable 5

As showed in Figures 10 11 and 12 with the volumeof subblock decreasing and the subblocks in the yard blockincreasing gradually that the pairing of service lines becamemore flexible Consequently the space sharing opportunityincreased and the yard operation cost decreased as wellHowever with the decreasing of yard subblocks volume theyard crane service range is limited and such trends willlimit the increase of the yard crane resource demand in theyard When the number of subblocks in the block reaches acertain value the whole container terminal yard area cannotrun normally Accordingly the volume of yard subblock alsoplays an important role in yard management If the value istoo large the sharing space opportunity will decrease andoperation cost will increase However if the value is too smallthe whole system operation pattern will be broken up

Scientific Programming 11

9000092000940009600098000

100000102000104000106000108000

60065070075080085090095010001050

Sharing space (TEUs)Transportation cost (yen)

NSNB=3

NSNB=6

NSNB=5

NSNB=4

Figure 10 Yard subblock size influence of small-scale experiments

1200

1300

1400

1500

1600

1700

1800

1900

2000

200000

205000

210000

215000

220000

225000

230000

235000

Sharing space (TEUs)Transportation cost (yen)

NSNB=3

NSNB=6

NSNB=5

NSNB=4

Figure 11 Yard subblock size influence of medium-scale experi-ments

6 Conclusions

Motivated by the requirement to relieve the operationdilemma for resource-limited container terminal this paperaddressed the integrated yard space allocation and yard cranedeployment problem Two corresponding counterstrategiesare introduced and then an integrated mathematical modelis formulated to solve the problem Numerical experimentsverified the correctness and accuracy of the proposed modelThis study found that space sharing strategy can increase yardspace utilization and yard crane interzone movement strategycan effectively relieve the shortage of YCs In addition aninteresting phenomenon is discovered that there exists atrade-off between yard space utilization and yard operationcost and the volume of yard subblock also plays a significantrole in container port yard management

340000

350000

360000

370000

380000

390000

400000

2000

2200

2400

2600

2800

2900

2100

2300

2500

2700

Sharing space (TEUs)Transportation cost (yen)

NSNB=3

NSNB=6

NSNB=5

NSNB=4

Figure 12 Yard subblock size influence of large-scale experiments

This research can be extended in many relative areas Inthis paper the service line working windows and yard craneefficiency are determined However these parameters mayfluctuate with the factors associated with natural factors andthe equipment operators in reality Therefore the applicationof uncertainty factors in the integratedmanagement problemis a valuable research direction in the future

Competing Interests

The authors declare that they have no competing interests

Authorsrsquo Contributions

All authors contributed equally and significantly to writingthis article

Acknowledgments

This work is sponsored by National Natural Science Founda-tion ofChina (71602114) ldquoChenguangProgramrdquo supported byShanghai Education Development Foundation and ShanghaiMunicipal Education Commission (14CG48) Shanghai Sail-ing Program (14YF1411200) Doctoral Fund of theMinistry ofEducation (20133121110001) Shanghai Municipal EducationCommission Project (14YZ112) Shanghai Science amp Tech-nology Committee Research Project (15590501700) Shang-hai Maritime University Doctoral Innovation Fund Project(2015ycx063) and Shanghai Maritime University DoctoralExcellent Thesis Training Program (2015BXLP006)

References

[1] D Chang Z H JiangW Yan and J He ldquoIntegrating berth allo-cation and quay crane assignmentsrdquo Transportation Research

12 Scientific Programming

Part E LogisticsampTransportation Review vol 46 no 6 pp 975ndash990 2010

[2] J L He D F Chang W J Mi and W Yan ldquoA hybrid parallelgenetic algorithm for yard crane schedulingrdquo TransportationResearch Part E Logistics and Transportation Review vol 46no 1 pp 136ndash155 2010

[3] J G Jin D Lee and J X Cao ldquoStorage yard management inmaritime container terminalsrdquo Transportation Science 2014

[4] C-H Chen and W Yan ldquoEngineering informatics in portoperations and logisticsrdquoAdvanced Engineering Informatics vol25 no 3 pp 401ndash402 2011

[5] C-H Chen L P Khoo Y T Chong and X F Yin ldquoKnowledgediscovery using genetic algorithm for maritime situationalawarenessrdquo Expert Systems with Applications vol 41 no 6 pp2742ndash2753 2014

[6] J He Y Huang and D Chang ldquoSimulation-based heuristicmethod for container supply chain network optimizationrdquoAdvanced Engineering Informatics vol 29 no 3 pp 339ndash3542015

[7] I F A Vis and R De Koster ldquoTransshipment of containersat a container terminal an overviewrdquo European Journal ofOperational Research vol 147 no 1 pp 1ndash16 2003

[8] D Steenken S Voszlig and R Stahlbock ldquoContainer terminaloperation and operations researchmdasha classification and litera-ture reviewrdquo OR Spectrum vol 26 no 1 pp 3ndash49 2004

[9] R Stahlbock and S Voszlig ldquoOperations research at containerterminals a literature updaterdquo Operations Research-Spektrumvol 30 no 1 pp 1ndash52 2008

[10] X Jiang L H Lee E P Chew Y Han and K C Tan ldquoAcontainer yard storage strategy for improving land utilizationand operation efficiency in a transshipment hub portrdquoEuropeanJournal of Operational Research vol 221 no 1 pp 64ndash73 2012

[11] L H Lee E P Chew K C Tan and Y Han ldquoAn optimizationmodel for storage yardmanagement in transshipment hubsrdquoORSpectrum vol 28 no 4 pp 539ndash561 2006

[12] Y Han L H Lee E P Chew and K Tan ldquoA yard storagestrategy forminimizing traffic congestion in amarine containertransshipment hubrdquo OR Spectrum Quantitative Approaches inManagement vol 30 no 4 pp 697ndash720 2008

[13] X Jiang E P Chew L H Lee and K C Tan ldquoFlexible space-sharing strategy for storage yard management in a transship-ment hub portrdquo OR Spectrum vol 35 no 2 pp 417ndash439 2013

[14] L Zhen ldquoContainer yard template planning under uncertainmaritimemarketrdquo Transportation Research Part E Logistics andTransportation Review vol 69 pp 199ndash217 2014

[15] C Zhang Y-W Wan J Liu and R J Linn ldquoDynamiccrane deployment in container storage yardsrdquo TransportationResearch Part B Methodological vol 36 no 6 pp 537ndash5552002

[16] R K Chung C-L Li andW Lin ldquoInterblock crane deploymentin container terminalsrdquoTransportation Science vol 36 no 1 pp79ndash93 2002

[17] R Linn J-Y Liu Y-W Wan C Q Zhang and K G MurtyldquoRubber tired gantry crane deployment for container yardoperationrdquo Computers amp Industrial Engineering vol 45 no 3pp 429ndash442 2003

[18] Z Cao D-H Lee and Q Meng ldquoDeployment strategies ofdouble-rail-mounted gantry crane systems for loading out-bound containers in container terminalsrdquo International Journalof Production Economics vol 115 no 1 pp 221ndash228 2008

[19] K H Kim and H B Kim ldquoThe optimal sizing of the storagespace and handling facilities for import containersrdquoTransporta-tion Research Part B Methodological vol 36 no 9 pp 821ndash8352002

[20] D-H Lee J G Jin and J H Chen ldquoIntegrated bay allocationand yard crane scheduling problem for transshipment contain-ersrdquo Transportation Research Record vol 2222 no 8 pp 63ndash712011

[21] S H Won X Zhang and K H Kim ldquoWorkload-based yard-planning system in container terminalsrdquo Journal of IntelligentManufacturing vol 23 no 6 pp 2193ndash2206 2012

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Scientific Programming 5

1

2

3

Electric cables

Figure 2 E-RTG interzone movement process

of YCs deployed in each row can satisfy the containerhandling requirement

4 Mathematic Model

In this section the integrated yard space allocation and yardcrane deployment mathematical model for resource-limitedcontainer terminal is formulatedThe authors raised themaincharacteristics of resource-limited container terminal storagespace allocation and yard crane deployment problem andthen presented the relevant counterstrategies accordingly Foryard space strained problem the space sharing strategy isapplied which has been proposed by Jiang et al [10] and asfor yard crane equipment shortage the yard crane interzonemovement is enabled

41 Assumptions The following assumptions are made in theintegrated model

(1) The yard storage space can satisfy the minimumservice line outbound containers stacking demandand the YCs are sufficient to guarantee the basichandling requirement

(2) The service lines berthing position are given andfixed hence once the service line containers areassigned to the subblocks the minimal inner trucktransportation distances are determined

(3) A subblock can be reserved for only one service lineexcept for part of the storage space which may beshared with its neighbor assigned service lines andwill not change once the storage plan is determined

(4) The YC can only shift to one yard zone in one periodit means that once the yard crane moved from onezone to another then it should be staying in the zonebefore the next planning period is begun

42 Mathematic Formulation This model aims to deal withthe yard space allocation problem and yard crane deploymentproblem at the tactical level and provides the following

results (1) yard storage space allocation plan for outboundcontainers of all the service lines which considers thecontainer volumes quay operation queues YC loading pointsand handling conflicts of service lines in the storage yard(2) yard crane deployment profile including the yard craneassignment plan in the initial period and subsequent yardcrane moving scheme

Sets

119879 set of time periods 119879 = 1 2 119873119879119861 set of yard blocks 119861 = 1 2 119873119861119878 set of yard subblocks 119878 = 1 2 119873119878119878119899119894 set of neighbor subblocks of subblock 119894 isin 119878 119878119899119894 isin 119878119878119904119902 set of subblocks belonging to block 119902 isin 119861 119878119904119902 isin 119878119877 set of yard rows (zone) in the terminal yard 119877 =1 2 119873119877119861119903 set of blocks belonging to row 119903 isin 119877 119861119903 isin 119861119871 set of service lines of terminal 119871 = 1 2 119873119871119884 set of YCs 119884 = 1 2 119873119884

Parameters

119888min119898 minimal outbound containers of service line 119898 isin 119871

(TEUs)119888max119898 maximal outbound containers of service line 119898 isin 119871

(TEUs)119901119898 quay operation queues of service line119898 isin 119871

120583min minimal YC loading points that one quay operationqueue demands

120583max maximal YC loading points that one quay operationqueue can satisfy

119905119904119898 time period to start handling of service line119898 isin 119871119905119890119898 time period to end handling of service line119898 isin 119871ℎ119898119905 handling parameter of service line119898 isin 119871 equal to 1 if119905 isin [119905119904119898 119905119890119898] otherwise equal to 0

6 Scientific Programming

V119904 maximal space capacity of each subblock (TEUs)

V119887 maximal space capacity of each yard block (TEUs)

120575119887 maximal YCs enabled operating in one yard block120575119903 maximal YCs enabled operating in one block row

120596119898119899 yard space sharing space when subblocks of serviceline 119898 isin 119871 and service line 119899 isin 119871 are neighbored (inthis paper120596119898119899 isin 0 1 it is usually determined by thecontainer buildup pattern of two service lines [14])

120579 fixed capacity of one sharing space (TEUs)119889119905119894119898 inner truck moving distance (loading and unloading)

if service line119898 isin 119871 is assigned to subblock 119894 isin 119878 (km)1198891198881199031199031015840 yard cranemovement distance between row 119903 isin 119877 and

row 1199031015840 isin 119877 (km)120593 inner truck transportation cost (yenkmTEU)120590 fixed time consumption of yard crane interzone

movement (h)120587 yard crane time cost (yenh)120588 yard crane movement cost (yenm)

1205821199031199031015840 yard crane interzone movement cost between row 119903 isin119877 and row 1199031015840 isin 119877 119903 = 1199031015840 (yen) where 1205821199031199031015840 = 120590120587 + 1198891198881199031199031015840120588if 119903 = 1199031015840 1205821199031199031015840 = 0

120576 a small and positive constant

Decision Variables

119909119894119898 isin 0 1 1 if subblock 119894 isin 119878was assigned to serviceline119898 isin 119871 0 otherwise1199101199031199031015840119905 isin 119873 YCs moving from row 119903 isin 119877 to row 1199031015840 isin 119877at the end of time period 119905 isin 119879 (and 1199101199041199030 is initial YCsof row 119903 isin 119877 in the beginning of the period)119911119898119902 isin 0 1 the number of YC loading points ofservice line119898 isin 119871 in block 119902 isin 119861119908119889119903119905 isin 119873 minimal yard crane requirement of row 119903 isin119877 in time period 119905 isin 119879119908119886119903119905 isin 119873 the number of YCs assigned to row 119903 isin 119877 intime period 119905 isin 119879

Objective Function

maximize 1198911 = sum119894isin119878

sum119895isin119878119899119894

sum119898119899isin119871

119909119894119898119909119895119899120596119898119899120579 (1)

minimize 1198912 = 1198911199052 + 1198911198882 (2)

1198911199052 = sum119894isin119904

sum119898isin119871

119909119894119898119889119905119894119898120593V119904 (3)

1198911198882 = sum119903isin119877

sum1199031015840isin119877

sum119905isin119879

11991011990311990310158401199051205821199031199031015840 (4)

The mathematical model proposed in this section is amultiobjective optimal model hence the authors transferredit into a single-objective problem by the method of weightedallocation Define 120572 as the coefficient of yard storage space

in the process of terminal operation management and usecoefficient 120572 to combine the two objectives Furthermorebecause the dimensions of two objectives are different thusnondimensional processing is needed Note that 119891max

1 and119891min1 are the independent maximal and minimal value of 1198911

respectively 119891max2 and 119891min

2 are the independent maximaland minimal value of 1198912 Therefore the integrated objectivefunction can be expressed as follows

max 119891 = 120572 (1198911 minus 119891min1 )

(119891max1 minus 119891min

1 ) +(1 minus 120572) (119891max

2 minus 1198912)(119891max2 minus 119891min

2 ) (5)

In formula (5) the coefficient 120572 could be set as0 01 10 with a step size of 01 This step could beadjusted manually according to problem size and terminaloperatorrsquos preference By changing the value of 120572 differentsets of solutions can be obtained In other words when 120572is smaller the solutions are more space-utilizing On thecontrary with the increase of 120572 the solutions are more cost-saving

Constraints

sum119898isin119871

119909119894119898 le 1 forall119894 isin 119878 (6)

sum119894isin119904

119909119894119898 ge lceil119888min119898

V119904rceil forall119898 isin 119871 (7)

sum119894isin119904

119909119894119898 le lceil119888max119898

V119904rceil forall119898 isin 119871 (8)

sum119894isin119878

sum119898isin119871

119909119894119898 = 119873119878 (9)

119911119898119902 le sum119894isin119878119904119902

119909119894119898forall119898 isin 119871 119902 isin 119861

(10)

119911119898119902 ge sum119894isin119878119904119902

119909119894119898120576

forall119898 isin 119871 119902 isin 119861(11)

sum119902isin119861

119911119898119902 ge 120583min119901119898 forall119898 isin 119871 (12)

sum119902isin119861

119911119898119902 le 120583max119901119898 forall119898 isin 119871 (13)

lceil119888max119898

V119904rceil ge 120583min119901119898 forall119898 isin 119871 (14)

sum119898isin119871

119911119898119902ℎ119898119905 le 120575119887 forall119902 isin 119861 119905 isin 119879 (15)

119908119889119903119905 = sum119898isin119871

sum119902isin119861119903

119911119898119902ℎ119898119905forall119903 isin 119877 119905 isin 119879

(16)

Scientific Programming 7

119908119889119903119905 le 120575119887 forall119903 isin 119877 119905 isin 119879 (17)

sum119898isin119871

119909119894119898ℎ119898119905 + 120576sum119895isin119878119899119894

sum119898isin119871

119909119895119898ℎ119898119905 le 1 forall119894 isin 119878 119905 isin 119879 (18)

sum119903isin119877

1199101199041199030 = 119873119884 (19)

sum1199031015840isin119877

1199101199031199031015840119905 = 1199101199041199030 forall119903 isin 119877 119905 = 1 (20)

sum1199031015840isin119877

1199101199031199031015840119905 = sum1199031015840isin119877

1199101199031015840119903(119905minus1)forall119903 isin 119877 2 le 119905 le 119873119879 minus 1

(21)

1199101199041199030 = sum1199031015840isin119877

1199101199031015840119903119905forall119903 isin 119877 119905 = 119873119879

(22)

119908119886119903119905 = 1199101199041199030 forall119903 isin 119877 119905 = 1 (23)

119908119886119903119905 = sum1199031015840isin119877

1199101199031015840119903(119905minus1)forall119903 isin 119877 119905 isin 119879 119905 = 1

(24)

119908119886119903119905 ge 119908119889119903119905 forall119903 isin 119877 119905 isin 119879 (25)

119908119886119903119905 le 120575119903 forall119903 isin 119877 119905 isin 119879 (26)

119909119894119898 isin 0 1 forall119894 isin 119878 119898 isin 119871 (27)

1199101199041199030 isin 119873 forall119903 isin 119877 (28)

1199101199031199031015840119905 isin 119873forall119903 1199031015840 isin 119877 119905 isin 119879 (29)

119911119902119898 isin 0 1forall119898 isin 119871 119902 isin 119861 (30)

119908119886119903119905 119908119889119903119905 isin 119873 forall119903 isin 119877 119905 isin 119879 (31)

The constraints of the mathematical model are composedof three parts the yard space allocation constraints theyard crane deployment constraints and the variables rangeconstraints

Equations (6) to (18) are the constraints of the first partwhich defines the rules of yard space allocation Equation (6)states that each subblock should be reserved for at most oneservice line during the entire planning horizon Equations (7)and (8) state that the subblocks assigned to the service linemust satisfy the outbound containers storage demand of theservice line Considering the service line outbound containervolumes are not generally fixed and the yard storage spaceis extremely limited the loosened constraints are presentedEquation (9) ensures that all the subblocks should be assignedto a service line Equations (10) and (11) are the calculationequations of service line YC loading points in a block equalto 1 if there is at least one subblock reserved for the service

line but otherwise equal to 0 Equations (12) to (14) state therelationship between the service line quay operation queuein the seaside and the YC loading point in the yard areaEquation (15) ensures themaximal handling YCs in the blockEquations (16) and (17) restrict the maximal handling YCsin the yard row Equation (18) states that when one of thesubblocks is in loading state the other neighbor subblocksare unavailable for service line that should be handled at thesame time

Equations (19) to (26) are the constraints of the secondpart which defines the rules of yard crane deploymentEquation (19) guarantees that the summation of initial YCsdeployment in each row is equal to the number of YCsEquations (20) to (22) ensure the YCs resource flow balancein the process of YCs interzone movement in each period ofplanning horizon Equations (23) and (24) are the calculationequations of YCs in each yard row Equations (25) and (26)ensure that the YCs operating in the row should satisfy theoperational demand and not exceed the maximal YCs boundin the row at the same time

Finally the domains of variables defined by (27) to (31)are the constraints of the third part

Linear Transformation As formula (1) is a nonlinear functiona linear transformation operation is applied After lineartransformation formula (1) is equal to

max 1198911 = sum119894isin119878

sum119895isin119878119899119894

sum119898119899isin119871

120601119894119895119898119899120596119898119899120579120601119894119895119898119899 le 119909119894119898 forall119894 isin 119878 119895 isin 119878119899119894 119898 119899 isin 119871120601119894119895119898119899 le 119909119895119899 forall119894 isin 119878 119895 isin 119878119899119894 119898 119899 isin 119871120601119894119895119898119899 ge 119909119894119898 + 119909119895119899 minus 1

forall119894 isin 119878 119895 isin 119878119899119894 119898 119899 isin 119871120601119894119895119898119899 isin 0 1 forall119894 isin 119878 119895 isin 119878119899119894 119898 119899 isin 119871

(32)

5 Numerical Experiment

To evaluate the effectiveness of the proposed model aseries of experiments with different scales are conductedSection 51 introduces the parameters used for generating theexperiments Section 52 analyzes the trade-off between yardstorage space resource utilization and yard operation costSection 53 researches the effects of YCs on yard storage spaceand operational cost Section 54 explores the influence ofsubblock volume on the yard management The integratedmodel in this paper is solved by ILOG CPLEX 124 and all ofthe computation experiments are conducted on aworkstationwith Inter Xeon CPU with 64GHz RAM

51 Instances At present many of the container line arrivalpatterns are weekly arrival In other words the voyage ofservice line arrives at the terminal once a weekTherefore theplanning horizon of this experiment is 1 week and each dayis split into 3 periods of 8 hours in consideration of practicalworking shift in the container terminal The experiment in

8 Scientific Programming

Table 1 Configuration parameters of container terminal yard

Class 119873119871(periods)

119873119861(blocks)

119873119878(subblocks)

119873119877(rows)

119873119884(YCs)

Class S 6 8 32 2 6Class M 8 16 64 4 12Class L 10 24 96 6 18

Table 2 Configuration parameters of yard crane and intertruck

Parameters 120583min 120583max 120575119887 120575119903 120593 120588 120590 120587Value 2 3 2 6 15 24 05 200

this paper considers three different storage yard scales (smallmedium and large) more precisely the instances with 6 to10 service lines 6 to 18 YCs and 8 to 24 blocks resulting inclasses 6 times 8 times 6 (class S) 8 times 16 times 12 (class M) and 10 times 24 times18 (class L) are tested (Table 1)

For all the classes the authors assume that the capacityof each block is 800 TEUs and the subblock capacity (V119887) is200 TEUs Meanwhile the maximal sharing space capacityof each subblock is equal to 20 TEUs (10 V119887) The yardcrane handling parameters and intertruck transportationparameters are shown in Table 2

For each class three scenarios of service line loadingrequirement are tested denoted by W1 W2 and W3 Theloading requirement is determined by the service line quayoperation queues (input data 119901119898 isin 119873 which are generatedwith discrete uniform distributions DU[2 3] DU[3 4] andDU[4 5] resp) the name of the instance indicates the levelof the loading requirement low requirement (W1) generalrequirement (W2) and high requirement (W3)

52 Yard Space Resource Analysis Based on space sharingstrategy the yard storage space utilization is increased owingto the sharing storage space between neighbor subblocks Asshowed in Table 3 the optimal yard operation cost equal to99990 yen and 800TEUsrsquo extra storage space (sharing space) arecreated (119886 = 0 cost-saving pattern) if space sharing strategyis applied in the yard Obviously this strategy can relieveterminal yard space scarce situation to a certain extent

Meanwhile when coefficient 119886 takes 1 it means thatthis model considers yard space allocation problem (space-utilizing pattern) firstly and then the yard crane deploymentproblem (cost-saving pattern) it is the nonintegrated patternin this situation Accordingly with the value of 119886 decreasingthe yard crane deployment is integrated with the yard spaceallocation problem gradually

Furthermore Figures 3 4 5 and 6 show the rela-tionships between yard storage space and yard operationcost of different instances scales As we can see with theincreasing of coefficient 119886 the yard sharing space increasedsynchronously as well as the yard operation cost Hence thereis no ultimate solution with the maximum space sharingand the minimum operation cost Which one should bechosen from these nondominated solutions is determined bythe terminal operators according to the terminal reality If

720 750 810780 840

105000

95000

115000

125000

135000

145000

870 900

a = 0

a = 02

a = 04

a = 06

a = 08

a = 1

Sharing space (TEUs)

Tran

spor

tatio

n co

st (yen

)

Figure 3 Relationships between yard space and operation cost ofsmall-scale experiments

1100 1200 14001300 1500

235000

220000

250000

265000

280000

295000

1600 1700

a = 0

a = 02

a = 04

a = 06

a = 08

a = 1

Sharing space (TEUs)

Tran

spor

tatio

n co

st (yen

)

Figure 4 Relationships between yard space and operation cost ofmedium-scale experiments

1950 2050 22502150 2350

395000

375000

415000

435000

455000

475000

2450 2550

a = 0

a = 02

a = 04

a = 06

a = 08

a = 1

Sharing space (TEUs)

Tran

spor

tatio

n co

st (yen

)

Figure 5 Relationships between yard space and operation cost oflarge-scale experiments

Scientific Programming 9

Table 3 Results of instances with different coefficient values

Instances119886 = 1 119886 = 08 119886 = 06 119886 = 04 119886 = 02 119886 = 01198911

(TEUs)1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

S W1 880 128800 880 110880 840 108900 800 103820 800 99990 800 99990S W2 880 129380 840 119960 840 110880 800 107910 760 102960 760 99990S W3 880 133340 840 127640 800 118800 760 108900 720 102960 680 99990M W1 1680 293150 1600 268500 1480 241600 1360 228830 1240 222450 1160 221760M W2 1600 286480 1560 261460 1440 239900 1320 228670 1240 224960 1160 221950M W3 1560 282360 1520 264300 1440 241860 1320 230100 1200 225960 1120 222140L W1 2480 468460 2400 432570 2360 403120 2200 387550 2120 380350 2080 376180L W2 2480 467820 2400 432800 2320 405670 2160 387610 2120 380640 2040 377050L W3 2400 468680 2360 433130 2280 405880 2160 388060 2080 381020 2000 378120

Table 4 Results of instances with different YCs

Instances119873119884119873119877 = 3 119873119884119873119877 = 35 119873119884119873119877 = 4 119873119884119873119877 = 45 119873119884119873119877 = 51198911

(TEUs)1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

S1 W1 960 99990 980 98040 980 97160 1000 96500 1000 96320S1 W2 960 99990 960 98630 980 97640 980 96500 1000 96320S1 W3 960 99990 960 99160 980 98420 980 97930 1000 96950M1 W1 1680 221760 1700 217730 1780 214200 1820 211770 1820 210040M1 W2 1600 221950 1640 218780 1700 215980 1760 213530 1760 211690M1 W3 1580 222140 1620 219420 1680 216560 1700 213840 1760 211870L1 W1 2480 376180 2540 367550 2580 360430 2640 354660 2640 351530L1 W2 2480 377050 2520 368580 2540 361910 2580 354960 2600 351600L1 W3 2420 378120 2460 368990 2500 362320 2540 355740 2600 352690

Δf1

Δf2

Sharing space (TEUs)

Tran

spor

tatio

n co

st (yen

)

tan 1205792 =Δf2Δf1

1205791

1205792

1205793

Figure 6 Relationships between yard space and operation cost

the container terminal yard storage is extremely scarce thatcould infect yard operation the operators should create morestorage space and the space-utilizing oriented strategy maybe adopted that is 119886 should take a bigger value otherwisethe cost saving should be the primary selection It is worthnoting that the marginal cost of yard sharing space (tan 120579)grows nonlinearly with the increase of coefficient 11988653 Yard Crane Resource Analysis In this section the effectsof total YCs on yard storage space utilization and yardoperation cost are tested We changed the number of YCs in

95000

96000

97000

98000

99000

100000

101000

940

950

960

970

980

990

1000

1010

Sharing space (TEUs)Transportation cost (yen)

NYN

R=3

NYN

R=45

NYN

R=4

NYN

R=5

NYN

R=35

Figure 7 Yard crane influence of small-scale experiments

the yard and the other parameters are unchanged For thisgroup of experiments consider the yard sharing space andyard operation cost separately so the coefficient 119886 is equal to1 and 0 respectively in the calculation of yard sharing spaceand yard operation cost The detailed results are shown inTable 4

Figures 7 8 and 9 show the effects of YCs on yard sharingspace and yard operation cost intuitively From these figures

10 Scientific Programming

Table 5 Results of instances with different subblock volume

Instances119873119878119873119861 = 3 119873119878119873119861 = 4 119873119878119873119861 = 5 119873119878119873119861 = 61198911

(TEUs)1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

S2 W1 756 106550 880 99990 960 95680 mdash mdashS2 W2 756 106550 880 99990 960 96280 mdash mdashS2 W3 756 106550 880 99990 960 99200 mdash mdashM2 W1 1404 231680 1680 221760 1888 217440 1950 210870M2 W2 1404 231760 1600 221950 1856 215210 mdash mdashM2 W3 1350 235930 1560 222140 1824 218130 mdash mdashL2 W1 2214 394550 2480 376180 2720 366960 2938 359620L2 W2 2214 396640 2480 377050 2688 371090 mdash mdashL2 W3 2160 398150 2400 378120 2656 373210 mdash mdash

208000

210000

212000

214000

216000

218000

224000

222000

220000

1550

1600

1650

1700

1750

1800

Sharing space (TEUs)Transportation cost (yen)

NYN

R=3

NYN

R=45

NYN

R=4

NYN

R=5

NYN

R=35

Figure 8 Yard crane influence of medium-scale experiments

we can find that the sharing space gradually becomes biggerwith the average YCs number in each zone increasing but theyard operation cost has an opposite situation

For the increasing of yard sharing space the mainreason could be that the added YCs relieved the YC loadingpoint constraint and then created more flexible service linespairings among subblocks but this effect is slight only about4

However generally speaking the increase of YCs shoulddecrease the yard operation cost considerably because it canavoid yard crane interzone movement as far as possible Butthese results shown in the figures could not express thisphenomenon obviously there is still only 6 cost decreaseA significant cause of this phenomenon is that the operationcost we considered is on the situation that the objectivefunction is cost-saving pattern (the coefficient 120572 equal to 0)so the yard operation cost we compared has been optimizedIt means that the amount of YCs interzone movements hasbeen decreased to an optimal level and this phenomenoncould be directly identified by Table 3 in Section 51

54 Subblock Volume Analysis The authors are also inter-ested in how the volume of subblock infects the yard space

335000340000345000350000355000360000365000370000375000380000

2350

2400

2450

2500

2550

2600

2650

Sharing space (TEUs)Transportation cost (yen)

NYN

R=3

NYN

R=45

NYN

R=4

NYN

R=5

NYN

R=35

Figure 9 Yard crane influence of large-scale experiments

utilization and yard operation cost In this subsection thenumber of subblocks in each block is divided into 3 4 5and 6 thus the volume of each subblock is equal to 270 200160 and 130 TEUs respectively and the other parameters areunchanged Similar to Section 53 the coefficient 119886 is equal to1 and 0 respectively in the calculation of yard sharing spaceand yard operation cost The detailed results are shown inTable 5

As showed in Figures 10 11 and 12 with the volumeof subblock decreasing and the subblocks in the yard blockincreasing gradually that the pairing of service lines becamemore flexible Consequently the space sharing opportunityincreased and the yard operation cost decreased as wellHowever with the decreasing of yard subblocks volume theyard crane service range is limited and such trends willlimit the increase of the yard crane resource demand in theyard When the number of subblocks in the block reaches acertain value the whole container terminal yard area cannotrun normally Accordingly the volume of yard subblock alsoplays an important role in yard management If the value istoo large the sharing space opportunity will decrease andoperation cost will increase However if the value is too smallthe whole system operation pattern will be broken up

Scientific Programming 11

9000092000940009600098000

100000102000104000106000108000

60065070075080085090095010001050

Sharing space (TEUs)Transportation cost (yen)

NSNB=3

NSNB=6

NSNB=5

NSNB=4

Figure 10 Yard subblock size influence of small-scale experiments

1200

1300

1400

1500

1600

1700

1800

1900

2000

200000

205000

210000

215000

220000

225000

230000

235000

Sharing space (TEUs)Transportation cost (yen)

NSNB=3

NSNB=6

NSNB=5

NSNB=4

Figure 11 Yard subblock size influence of medium-scale experi-ments

6 Conclusions

Motivated by the requirement to relieve the operationdilemma for resource-limited container terminal this paperaddressed the integrated yard space allocation and yard cranedeployment problem Two corresponding counterstrategiesare introduced and then an integrated mathematical modelis formulated to solve the problem Numerical experimentsverified the correctness and accuracy of the proposed modelThis study found that space sharing strategy can increase yardspace utilization and yard crane interzone movement strategycan effectively relieve the shortage of YCs In addition aninteresting phenomenon is discovered that there exists atrade-off between yard space utilization and yard operationcost and the volume of yard subblock also plays a significantrole in container port yard management

340000

350000

360000

370000

380000

390000

400000

2000

2200

2400

2600

2800

2900

2100

2300

2500

2700

Sharing space (TEUs)Transportation cost (yen)

NSNB=3

NSNB=6

NSNB=5

NSNB=4

Figure 12 Yard subblock size influence of large-scale experiments

This research can be extended in many relative areas Inthis paper the service line working windows and yard craneefficiency are determined However these parameters mayfluctuate with the factors associated with natural factors andthe equipment operators in reality Therefore the applicationof uncertainty factors in the integratedmanagement problemis a valuable research direction in the future

Competing Interests

The authors declare that they have no competing interests

Authorsrsquo Contributions

All authors contributed equally and significantly to writingthis article

Acknowledgments

This work is sponsored by National Natural Science Founda-tion ofChina (71602114) ldquoChenguangProgramrdquo supported byShanghai Education Development Foundation and ShanghaiMunicipal Education Commission (14CG48) Shanghai Sail-ing Program (14YF1411200) Doctoral Fund of theMinistry ofEducation (20133121110001) Shanghai Municipal EducationCommission Project (14YZ112) Shanghai Science amp Tech-nology Committee Research Project (15590501700) Shang-hai Maritime University Doctoral Innovation Fund Project(2015ycx063) and Shanghai Maritime University DoctoralExcellent Thesis Training Program (2015BXLP006)

References

[1] D Chang Z H JiangW Yan and J He ldquoIntegrating berth allo-cation and quay crane assignmentsrdquo Transportation Research

12 Scientific Programming

Part E LogisticsampTransportation Review vol 46 no 6 pp 975ndash990 2010

[2] J L He D F Chang W J Mi and W Yan ldquoA hybrid parallelgenetic algorithm for yard crane schedulingrdquo TransportationResearch Part E Logistics and Transportation Review vol 46no 1 pp 136ndash155 2010

[3] J G Jin D Lee and J X Cao ldquoStorage yard management inmaritime container terminalsrdquo Transportation Science 2014

[4] C-H Chen and W Yan ldquoEngineering informatics in portoperations and logisticsrdquoAdvanced Engineering Informatics vol25 no 3 pp 401ndash402 2011

[5] C-H Chen L P Khoo Y T Chong and X F Yin ldquoKnowledgediscovery using genetic algorithm for maritime situationalawarenessrdquo Expert Systems with Applications vol 41 no 6 pp2742ndash2753 2014

[6] J He Y Huang and D Chang ldquoSimulation-based heuristicmethod for container supply chain network optimizationrdquoAdvanced Engineering Informatics vol 29 no 3 pp 339ndash3542015

[7] I F A Vis and R De Koster ldquoTransshipment of containersat a container terminal an overviewrdquo European Journal ofOperational Research vol 147 no 1 pp 1ndash16 2003

[8] D Steenken S Voszlig and R Stahlbock ldquoContainer terminaloperation and operations researchmdasha classification and litera-ture reviewrdquo OR Spectrum vol 26 no 1 pp 3ndash49 2004

[9] R Stahlbock and S Voszlig ldquoOperations research at containerterminals a literature updaterdquo Operations Research-Spektrumvol 30 no 1 pp 1ndash52 2008

[10] X Jiang L H Lee E P Chew Y Han and K C Tan ldquoAcontainer yard storage strategy for improving land utilizationand operation efficiency in a transshipment hub portrdquoEuropeanJournal of Operational Research vol 221 no 1 pp 64ndash73 2012

[11] L H Lee E P Chew K C Tan and Y Han ldquoAn optimizationmodel for storage yardmanagement in transshipment hubsrdquoORSpectrum vol 28 no 4 pp 539ndash561 2006

[12] Y Han L H Lee E P Chew and K Tan ldquoA yard storagestrategy forminimizing traffic congestion in amarine containertransshipment hubrdquo OR Spectrum Quantitative Approaches inManagement vol 30 no 4 pp 697ndash720 2008

[13] X Jiang E P Chew L H Lee and K C Tan ldquoFlexible space-sharing strategy for storage yard management in a transship-ment hub portrdquo OR Spectrum vol 35 no 2 pp 417ndash439 2013

[14] L Zhen ldquoContainer yard template planning under uncertainmaritimemarketrdquo Transportation Research Part E Logistics andTransportation Review vol 69 pp 199ndash217 2014

[15] C Zhang Y-W Wan J Liu and R J Linn ldquoDynamiccrane deployment in container storage yardsrdquo TransportationResearch Part B Methodological vol 36 no 6 pp 537ndash5552002

[16] R K Chung C-L Li andW Lin ldquoInterblock crane deploymentin container terminalsrdquoTransportation Science vol 36 no 1 pp79ndash93 2002

[17] R Linn J-Y Liu Y-W Wan C Q Zhang and K G MurtyldquoRubber tired gantry crane deployment for container yardoperationrdquo Computers amp Industrial Engineering vol 45 no 3pp 429ndash442 2003

[18] Z Cao D-H Lee and Q Meng ldquoDeployment strategies ofdouble-rail-mounted gantry crane systems for loading out-bound containers in container terminalsrdquo International Journalof Production Economics vol 115 no 1 pp 221ndash228 2008

[19] K H Kim and H B Kim ldquoThe optimal sizing of the storagespace and handling facilities for import containersrdquoTransporta-tion Research Part B Methodological vol 36 no 9 pp 821ndash8352002

[20] D-H Lee J G Jin and J H Chen ldquoIntegrated bay allocationand yard crane scheduling problem for transshipment contain-ersrdquo Transportation Research Record vol 2222 no 8 pp 63ndash712011

[21] S H Won X Zhang and K H Kim ldquoWorkload-based yard-planning system in container terminalsrdquo Journal of IntelligentManufacturing vol 23 no 6 pp 2193ndash2206 2012

Submit your manuscripts athttpwwwhindawicom

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Applied Computational Intelligence and Soft Computing

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httpwwwhindawicom Volume 2014

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

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6 Scientific Programming

V119904 maximal space capacity of each subblock (TEUs)

V119887 maximal space capacity of each yard block (TEUs)

120575119887 maximal YCs enabled operating in one yard block120575119903 maximal YCs enabled operating in one block row

120596119898119899 yard space sharing space when subblocks of serviceline 119898 isin 119871 and service line 119899 isin 119871 are neighbored (inthis paper120596119898119899 isin 0 1 it is usually determined by thecontainer buildup pattern of two service lines [14])

120579 fixed capacity of one sharing space (TEUs)119889119905119894119898 inner truck moving distance (loading and unloading)

if service line119898 isin 119871 is assigned to subblock 119894 isin 119878 (km)1198891198881199031199031015840 yard cranemovement distance between row 119903 isin 119877 and

row 1199031015840 isin 119877 (km)120593 inner truck transportation cost (yenkmTEU)120590 fixed time consumption of yard crane interzone

movement (h)120587 yard crane time cost (yenh)120588 yard crane movement cost (yenm)

1205821199031199031015840 yard crane interzone movement cost between row 119903 isin119877 and row 1199031015840 isin 119877 119903 = 1199031015840 (yen) where 1205821199031199031015840 = 120590120587 + 1198891198881199031199031015840120588if 119903 = 1199031015840 1205821199031199031015840 = 0

120576 a small and positive constant

Decision Variables

119909119894119898 isin 0 1 1 if subblock 119894 isin 119878was assigned to serviceline119898 isin 119871 0 otherwise1199101199031199031015840119905 isin 119873 YCs moving from row 119903 isin 119877 to row 1199031015840 isin 119877at the end of time period 119905 isin 119879 (and 1199101199041199030 is initial YCsof row 119903 isin 119877 in the beginning of the period)119911119898119902 isin 0 1 the number of YC loading points ofservice line119898 isin 119871 in block 119902 isin 119861119908119889119903119905 isin 119873 minimal yard crane requirement of row 119903 isin119877 in time period 119905 isin 119879119908119886119903119905 isin 119873 the number of YCs assigned to row 119903 isin 119877 intime period 119905 isin 119879

Objective Function

maximize 1198911 = sum119894isin119878

sum119895isin119878119899119894

sum119898119899isin119871

119909119894119898119909119895119899120596119898119899120579 (1)

minimize 1198912 = 1198911199052 + 1198911198882 (2)

1198911199052 = sum119894isin119904

sum119898isin119871

119909119894119898119889119905119894119898120593V119904 (3)

1198911198882 = sum119903isin119877

sum1199031015840isin119877

sum119905isin119879

11991011990311990310158401199051205821199031199031015840 (4)

The mathematical model proposed in this section is amultiobjective optimal model hence the authors transferredit into a single-objective problem by the method of weightedallocation Define 120572 as the coefficient of yard storage space

in the process of terminal operation management and usecoefficient 120572 to combine the two objectives Furthermorebecause the dimensions of two objectives are different thusnondimensional processing is needed Note that 119891max

1 and119891min1 are the independent maximal and minimal value of 1198911

respectively 119891max2 and 119891min

2 are the independent maximaland minimal value of 1198912 Therefore the integrated objectivefunction can be expressed as follows

max 119891 = 120572 (1198911 minus 119891min1 )

(119891max1 minus 119891min

1 ) +(1 minus 120572) (119891max

2 minus 1198912)(119891max2 minus 119891min

2 ) (5)

In formula (5) the coefficient 120572 could be set as0 01 10 with a step size of 01 This step could beadjusted manually according to problem size and terminaloperatorrsquos preference By changing the value of 120572 differentsets of solutions can be obtained In other words when 120572is smaller the solutions are more space-utilizing On thecontrary with the increase of 120572 the solutions are more cost-saving

Constraints

sum119898isin119871

119909119894119898 le 1 forall119894 isin 119878 (6)

sum119894isin119904

119909119894119898 ge lceil119888min119898

V119904rceil forall119898 isin 119871 (7)

sum119894isin119904

119909119894119898 le lceil119888max119898

V119904rceil forall119898 isin 119871 (8)

sum119894isin119878

sum119898isin119871

119909119894119898 = 119873119878 (9)

119911119898119902 le sum119894isin119878119904119902

119909119894119898forall119898 isin 119871 119902 isin 119861

(10)

119911119898119902 ge sum119894isin119878119904119902

119909119894119898120576

forall119898 isin 119871 119902 isin 119861(11)

sum119902isin119861

119911119898119902 ge 120583min119901119898 forall119898 isin 119871 (12)

sum119902isin119861

119911119898119902 le 120583max119901119898 forall119898 isin 119871 (13)

lceil119888max119898

V119904rceil ge 120583min119901119898 forall119898 isin 119871 (14)

sum119898isin119871

119911119898119902ℎ119898119905 le 120575119887 forall119902 isin 119861 119905 isin 119879 (15)

119908119889119903119905 = sum119898isin119871

sum119902isin119861119903

119911119898119902ℎ119898119905forall119903 isin 119877 119905 isin 119879

(16)

Scientific Programming 7

119908119889119903119905 le 120575119887 forall119903 isin 119877 119905 isin 119879 (17)

sum119898isin119871

119909119894119898ℎ119898119905 + 120576sum119895isin119878119899119894

sum119898isin119871

119909119895119898ℎ119898119905 le 1 forall119894 isin 119878 119905 isin 119879 (18)

sum119903isin119877

1199101199041199030 = 119873119884 (19)

sum1199031015840isin119877

1199101199031199031015840119905 = 1199101199041199030 forall119903 isin 119877 119905 = 1 (20)

sum1199031015840isin119877

1199101199031199031015840119905 = sum1199031015840isin119877

1199101199031015840119903(119905minus1)forall119903 isin 119877 2 le 119905 le 119873119879 minus 1

(21)

1199101199041199030 = sum1199031015840isin119877

1199101199031015840119903119905forall119903 isin 119877 119905 = 119873119879

(22)

119908119886119903119905 = 1199101199041199030 forall119903 isin 119877 119905 = 1 (23)

119908119886119903119905 = sum1199031015840isin119877

1199101199031015840119903(119905minus1)forall119903 isin 119877 119905 isin 119879 119905 = 1

(24)

119908119886119903119905 ge 119908119889119903119905 forall119903 isin 119877 119905 isin 119879 (25)

119908119886119903119905 le 120575119903 forall119903 isin 119877 119905 isin 119879 (26)

119909119894119898 isin 0 1 forall119894 isin 119878 119898 isin 119871 (27)

1199101199041199030 isin 119873 forall119903 isin 119877 (28)

1199101199031199031015840119905 isin 119873forall119903 1199031015840 isin 119877 119905 isin 119879 (29)

119911119902119898 isin 0 1forall119898 isin 119871 119902 isin 119861 (30)

119908119886119903119905 119908119889119903119905 isin 119873 forall119903 isin 119877 119905 isin 119879 (31)

The constraints of the mathematical model are composedof three parts the yard space allocation constraints theyard crane deployment constraints and the variables rangeconstraints

Equations (6) to (18) are the constraints of the first partwhich defines the rules of yard space allocation Equation (6)states that each subblock should be reserved for at most oneservice line during the entire planning horizon Equations (7)and (8) state that the subblocks assigned to the service linemust satisfy the outbound containers storage demand of theservice line Considering the service line outbound containervolumes are not generally fixed and the yard storage spaceis extremely limited the loosened constraints are presentedEquation (9) ensures that all the subblocks should be assignedto a service line Equations (10) and (11) are the calculationequations of service line YC loading points in a block equalto 1 if there is at least one subblock reserved for the service

line but otherwise equal to 0 Equations (12) to (14) state therelationship between the service line quay operation queuein the seaside and the YC loading point in the yard areaEquation (15) ensures themaximal handling YCs in the blockEquations (16) and (17) restrict the maximal handling YCsin the yard row Equation (18) states that when one of thesubblocks is in loading state the other neighbor subblocksare unavailable for service line that should be handled at thesame time

Equations (19) to (26) are the constraints of the secondpart which defines the rules of yard crane deploymentEquation (19) guarantees that the summation of initial YCsdeployment in each row is equal to the number of YCsEquations (20) to (22) ensure the YCs resource flow balancein the process of YCs interzone movement in each period ofplanning horizon Equations (23) and (24) are the calculationequations of YCs in each yard row Equations (25) and (26)ensure that the YCs operating in the row should satisfy theoperational demand and not exceed the maximal YCs boundin the row at the same time

Finally the domains of variables defined by (27) to (31)are the constraints of the third part

Linear Transformation As formula (1) is a nonlinear functiona linear transformation operation is applied After lineartransformation formula (1) is equal to

max 1198911 = sum119894isin119878

sum119895isin119878119899119894

sum119898119899isin119871

120601119894119895119898119899120596119898119899120579120601119894119895119898119899 le 119909119894119898 forall119894 isin 119878 119895 isin 119878119899119894 119898 119899 isin 119871120601119894119895119898119899 le 119909119895119899 forall119894 isin 119878 119895 isin 119878119899119894 119898 119899 isin 119871120601119894119895119898119899 ge 119909119894119898 + 119909119895119899 minus 1

forall119894 isin 119878 119895 isin 119878119899119894 119898 119899 isin 119871120601119894119895119898119899 isin 0 1 forall119894 isin 119878 119895 isin 119878119899119894 119898 119899 isin 119871

(32)

5 Numerical Experiment

To evaluate the effectiveness of the proposed model aseries of experiments with different scales are conductedSection 51 introduces the parameters used for generating theexperiments Section 52 analyzes the trade-off between yardstorage space resource utilization and yard operation costSection 53 researches the effects of YCs on yard storage spaceand operational cost Section 54 explores the influence ofsubblock volume on the yard management The integratedmodel in this paper is solved by ILOG CPLEX 124 and all ofthe computation experiments are conducted on aworkstationwith Inter Xeon CPU with 64GHz RAM

51 Instances At present many of the container line arrivalpatterns are weekly arrival In other words the voyage ofservice line arrives at the terminal once a weekTherefore theplanning horizon of this experiment is 1 week and each dayis split into 3 periods of 8 hours in consideration of practicalworking shift in the container terminal The experiment in

8 Scientific Programming

Table 1 Configuration parameters of container terminal yard

Class 119873119871(periods)

119873119861(blocks)

119873119878(subblocks)

119873119877(rows)

119873119884(YCs)

Class S 6 8 32 2 6Class M 8 16 64 4 12Class L 10 24 96 6 18

Table 2 Configuration parameters of yard crane and intertruck

Parameters 120583min 120583max 120575119887 120575119903 120593 120588 120590 120587Value 2 3 2 6 15 24 05 200

this paper considers three different storage yard scales (smallmedium and large) more precisely the instances with 6 to10 service lines 6 to 18 YCs and 8 to 24 blocks resulting inclasses 6 times 8 times 6 (class S) 8 times 16 times 12 (class M) and 10 times 24 times18 (class L) are tested (Table 1)

For all the classes the authors assume that the capacityof each block is 800 TEUs and the subblock capacity (V119887) is200 TEUs Meanwhile the maximal sharing space capacityof each subblock is equal to 20 TEUs (10 V119887) The yardcrane handling parameters and intertruck transportationparameters are shown in Table 2

For each class three scenarios of service line loadingrequirement are tested denoted by W1 W2 and W3 Theloading requirement is determined by the service line quayoperation queues (input data 119901119898 isin 119873 which are generatedwith discrete uniform distributions DU[2 3] DU[3 4] andDU[4 5] resp) the name of the instance indicates the levelof the loading requirement low requirement (W1) generalrequirement (W2) and high requirement (W3)

52 Yard Space Resource Analysis Based on space sharingstrategy the yard storage space utilization is increased owingto the sharing storage space between neighbor subblocks Asshowed in Table 3 the optimal yard operation cost equal to99990 yen and 800TEUsrsquo extra storage space (sharing space) arecreated (119886 = 0 cost-saving pattern) if space sharing strategyis applied in the yard Obviously this strategy can relieveterminal yard space scarce situation to a certain extent

Meanwhile when coefficient 119886 takes 1 it means thatthis model considers yard space allocation problem (space-utilizing pattern) firstly and then the yard crane deploymentproblem (cost-saving pattern) it is the nonintegrated patternin this situation Accordingly with the value of 119886 decreasingthe yard crane deployment is integrated with the yard spaceallocation problem gradually

Furthermore Figures 3 4 5 and 6 show the rela-tionships between yard storage space and yard operationcost of different instances scales As we can see with theincreasing of coefficient 119886 the yard sharing space increasedsynchronously as well as the yard operation cost Hence thereis no ultimate solution with the maximum space sharingand the minimum operation cost Which one should bechosen from these nondominated solutions is determined bythe terminal operators according to the terminal reality If

720 750 810780 840

105000

95000

115000

125000

135000

145000

870 900

a = 0

a = 02

a = 04

a = 06

a = 08

a = 1

Sharing space (TEUs)

Tran

spor

tatio

n co

st (yen

)

Figure 3 Relationships between yard space and operation cost ofsmall-scale experiments

1100 1200 14001300 1500

235000

220000

250000

265000

280000

295000

1600 1700

a = 0

a = 02

a = 04

a = 06

a = 08

a = 1

Sharing space (TEUs)

Tran

spor

tatio

n co

st (yen

)

Figure 4 Relationships between yard space and operation cost ofmedium-scale experiments

1950 2050 22502150 2350

395000

375000

415000

435000

455000

475000

2450 2550

a = 0

a = 02

a = 04

a = 06

a = 08

a = 1

Sharing space (TEUs)

Tran

spor

tatio

n co

st (yen

)

Figure 5 Relationships between yard space and operation cost oflarge-scale experiments

Scientific Programming 9

Table 3 Results of instances with different coefficient values

Instances119886 = 1 119886 = 08 119886 = 06 119886 = 04 119886 = 02 119886 = 01198911

(TEUs)1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

S W1 880 128800 880 110880 840 108900 800 103820 800 99990 800 99990S W2 880 129380 840 119960 840 110880 800 107910 760 102960 760 99990S W3 880 133340 840 127640 800 118800 760 108900 720 102960 680 99990M W1 1680 293150 1600 268500 1480 241600 1360 228830 1240 222450 1160 221760M W2 1600 286480 1560 261460 1440 239900 1320 228670 1240 224960 1160 221950M W3 1560 282360 1520 264300 1440 241860 1320 230100 1200 225960 1120 222140L W1 2480 468460 2400 432570 2360 403120 2200 387550 2120 380350 2080 376180L W2 2480 467820 2400 432800 2320 405670 2160 387610 2120 380640 2040 377050L W3 2400 468680 2360 433130 2280 405880 2160 388060 2080 381020 2000 378120

Table 4 Results of instances with different YCs

Instances119873119884119873119877 = 3 119873119884119873119877 = 35 119873119884119873119877 = 4 119873119884119873119877 = 45 119873119884119873119877 = 51198911

(TEUs)1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

S1 W1 960 99990 980 98040 980 97160 1000 96500 1000 96320S1 W2 960 99990 960 98630 980 97640 980 96500 1000 96320S1 W3 960 99990 960 99160 980 98420 980 97930 1000 96950M1 W1 1680 221760 1700 217730 1780 214200 1820 211770 1820 210040M1 W2 1600 221950 1640 218780 1700 215980 1760 213530 1760 211690M1 W3 1580 222140 1620 219420 1680 216560 1700 213840 1760 211870L1 W1 2480 376180 2540 367550 2580 360430 2640 354660 2640 351530L1 W2 2480 377050 2520 368580 2540 361910 2580 354960 2600 351600L1 W3 2420 378120 2460 368990 2500 362320 2540 355740 2600 352690

Δf1

Δf2

Sharing space (TEUs)

Tran

spor

tatio

n co

st (yen

)

tan 1205792 =Δf2Δf1

1205791

1205792

1205793

Figure 6 Relationships between yard space and operation cost

the container terminal yard storage is extremely scarce thatcould infect yard operation the operators should create morestorage space and the space-utilizing oriented strategy maybe adopted that is 119886 should take a bigger value otherwisethe cost saving should be the primary selection It is worthnoting that the marginal cost of yard sharing space (tan 120579)grows nonlinearly with the increase of coefficient 11988653 Yard Crane Resource Analysis In this section the effectsof total YCs on yard storage space utilization and yardoperation cost are tested We changed the number of YCs in

95000

96000

97000

98000

99000

100000

101000

940

950

960

970

980

990

1000

1010

Sharing space (TEUs)Transportation cost (yen)

NYN

R=3

NYN

R=45

NYN

R=4

NYN

R=5

NYN

R=35

Figure 7 Yard crane influence of small-scale experiments

the yard and the other parameters are unchanged For thisgroup of experiments consider the yard sharing space andyard operation cost separately so the coefficient 119886 is equal to1 and 0 respectively in the calculation of yard sharing spaceand yard operation cost The detailed results are shown inTable 4

Figures 7 8 and 9 show the effects of YCs on yard sharingspace and yard operation cost intuitively From these figures

10 Scientific Programming

Table 5 Results of instances with different subblock volume

Instances119873119878119873119861 = 3 119873119878119873119861 = 4 119873119878119873119861 = 5 119873119878119873119861 = 61198911

(TEUs)1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

S2 W1 756 106550 880 99990 960 95680 mdash mdashS2 W2 756 106550 880 99990 960 96280 mdash mdashS2 W3 756 106550 880 99990 960 99200 mdash mdashM2 W1 1404 231680 1680 221760 1888 217440 1950 210870M2 W2 1404 231760 1600 221950 1856 215210 mdash mdashM2 W3 1350 235930 1560 222140 1824 218130 mdash mdashL2 W1 2214 394550 2480 376180 2720 366960 2938 359620L2 W2 2214 396640 2480 377050 2688 371090 mdash mdashL2 W3 2160 398150 2400 378120 2656 373210 mdash mdash

208000

210000

212000

214000

216000

218000

224000

222000

220000

1550

1600

1650

1700

1750

1800

Sharing space (TEUs)Transportation cost (yen)

NYN

R=3

NYN

R=45

NYN

R=4

NYN

R=5

NYN

R=35

Figure 8 Yard crane influence of medium-scale experiments

we can find that the sharing space gradually becomes biggerwith the average YCs number in each zone increasing but theyard operation cost has an opposite situation

For the increasing of yard sharing space the mainreason could be that the added YCs relieved the YC loadingpoint constraint and then created more flexible service linespairings among subblocks but this effect is slight only about4

However generally speaking the increase of YCs shoulddecrease the yard operation cost considerably because it canavoid yard crane interzone movement as far as possible Butthese results shown in the figures could not express thisphenomenon obviously there is still only 6 cost decreaseA significant cause of this phenomenon is that the operationcost we considered is on the situation that the objectivefunction is cost-saving pattern (the coefficient 120572 equal to 0)so the yard operation cost we compared has been optimizedIt means that the amount of YCs interzone movements hasbeen decreased to an optimal level and this phenomenoncould be directly identified by Table 3 in Section 51

54 Subblock Volume Analysis The authors are also inter-ested in how the volume of subblock infects the yard space

335000340000345000350000355000360000365000370000375000380000

2350

2400

2450

2500

2550

2600

2650

Sharing space (TEUs)Transportation cost (yen)

NYN

R=3

NYN

R=45

NYN

R=4

NYN

R=5

NYN

R=35

Figure 9 Yard crane influence of large-scale experiments

utilization and yard operation cost In this subsection thenumber of subblocks in each block is divided into 3 4 5and 6 thus the volume of each subblock is equal to 270 200160 and 130 TEUs respectively and the other parameters areunchanged Similar to Section 53 the coefficient 119886 is equal to1 and 0 respectively in the calculation of yard sharing spaceand yard operation cost The detailed results are shown inTable 5

As showed in Figures 10 11 and 12 with the volumeof subblock decreasing and the subblocks in the yard blockincreasing gradually that the pairing of service lines becamemore flexible Consequently the space sharing opportunityincreased and the yard operation cost decreased as wellHowever with the decreasing of yard subblocks volume theyard crane service range is limited and such trends willlimit the increase of the yard crane resource demand in theyard When the number of subblocks in the block reaches acertain value the whole container terminal yard area cannotrun normally Accordingly the volume of yard subblock alsoplays an important role in yard management If the value istoo large the sharing space opportunity will decrease andoperation cost will increase However if the value is too smallthe whole system operation pattern will be broken up

Scientific Programming 11

9000092000940009600098000

100000102000104000106000108000

60065070075080085090095010001050

Sharing space (TEUs)Transportation cost (yen)

NSNB=3

NSNB=6

NSNB=5

NSNB=4

Figure 10 Yard subblock size influence of small-scale experiments

1200

1300

1400

1500

1600

1700

1800

1900

2000

200000

205000

210000

215000

220000

225000

230000

235000

Sharing space (TEUs)Transportation cost (yen)

NSNB=3

NSNB=6

NSNB=5

NSNB=4

Figure 11 Yard subblock size influence of medium-scale experi-ments

6 Conclusions

Motivated by the requirement to relieve the operationdilemma for resource-limited container terminal this paperaddressed the integrated yard space allocation and yard cranedeployment problem Two corresponding counterstrategiesare introduced and then an integrated mathematical modelis formulated to solve the problem Numerical experimentsverified the correctness and accuracy of the proposed modelThis study found that space sharing strategy can increase yardspace utilization and yard crane interzone movement strategycan effectively relieve the shortage of YCs In addition aninteresting phenomenon is discovered that there exists atrade-off between yard space utilization and yard operationcost and the volume of yard subblock also plays a significantrole in container port yard management

340000

350000

360000

370000

380000

390000

400000

2000

2200

2400

2600

2800

2900

2100

2300

2500

2700

Sharing space (TEUs)Transportation cost (yen)

NSNB=3

NSNB=6

NSNB=5

NSNB=4

Figure 12 Yard subblock size influence of large-scale experiments

This research can be extended in many relative areas Inthis paper the service line working windows and yard craneefficiency are determined However these parameters mayfluctuate with the factors associated with natural factors andthe equipment operators in reality Therefore the applicationof uncertainty factors in the integratedmanagement problemis a valuable research direction in the future

Competing Interests

The authors declare that they have no competing interests

Authorsrsquo Contributions

All authors contributed equally and significantly to writingthis article

Acknowledgments

This work is sponsored by National Natural Science Founda-tion ofChina (71602114) ldquoChenguangProgramrdquo supported byShanghai Education Development Foundation and ShanghaiMunicipal Education Commission (14CG48) Shanghai Sail-ing Program (14YF1411200) Doctoral Fund of theMinistry ofEducation (20133121110001) Shanghai Municipal EducationCommission Project (14YZ112) Shanghai Science amp Tech-nology Committee Research Project (15590501700) Shang-hai Maritime University Doctoral Innovation Fund Project(2015ycx063) and Shanghai Maritime University DoctoralExcellent Thesis Training Program (2015BXLP006)

References

[1] D Chang Z H JiangW Yan and J He ldquoIntegrating berth allo-cation and quay crane assignmentsrdquo Transportation Research

12 Scientific Programming

Part E LogisticsampTransportation Review vol 46 no 6 pp 975ndash990 2010

[2] J L He D F Chang W J Mi and W Yan ldquoA hybrid parallelgenetic algorithm for yard crane schedulingrdquo TransportationResearch Part E Logistics and Transportation Review vol 46no 1 pp 136ndash155 2010

[3] J G Jin D Lee and J X Cao ldquoStorage yard management inmaritime container terminalsrdquo Transportation Science 2014

[4] C-H Chen and W Yan ldquoEngineering informatics in portoperations and logisticsrdquoAdvanced Engineering Informatics vol25 no 3 pp 401ndash402 2011

[5] C-H Chen L P Khoo Y T Chong and X F Yin ldquoKnowledgediscovery using genetic algorithm for maritime situationalawarenessrdquo Expert Systems with Applications vol 41 no 6 pp2742ndash2753 2014

[6] J He Y Huang and D Chang ldquoSimulation-based heuristicmethod for container supply chain network optimizationrdquoAdvanced Engineering Informatics vol 29 no 3 pp 339ndash3542015

[7] I F A Vis and R De Koster ldquoTransshipment of containersat a container terminal an overviewrdquo European Journal ofOperational Research vol 147 no 1 pp 1ndash16 2003

[8] D Steenken S Voszlig and R Stahlbock ldquoContainer terminaloperation and operations researchmdasha classification and litera-ture reviewrdquo OR Spectrum vol 26 no 1 pp 3ndash49 2004

[9] R Stahlbock and S Voszlig ldquoOperations research at containerterminals a literature updaterdquo Operations Research-Spektrumvol 30 no 1 pp 1ndash52 2008

[10] X Jiang L H Lee E P Chew Y Han and K C Tan ldquoAcontainer yard storage strategy for improving land utilizationand operation efficiency in a transshipment hub portrdquoEuropeanJournal of Operational Research vol 221 no 1 pp 64ndash73 2012

[11] L H Lee E P Chew K C Tan and Y Han ldquoAn optimizationmodel for storage yardmanagement in transshipment hubsrdquoORSpectrum vol 28 no 4 pp 539ndash561 2006

[12] Y Han L H Lee E P Chew and K Tan ldquoA yard storagestrategy forminimizing traffic congestion in amarine containertransshipment hubrdquo OR Spectrum Quantitative Approaches inManagement vol 30 no 4 pp 697ndash720 2008

[13] X Jiang E P Chew L H Lee and K C Tan ldquoFlexible space-sharing strategy for storage yard management in a transship-ment hub portrdquo OR Spectrum vol 35 no 2 pp 417ndash439 2013

[14] L Zhen ldquoContainer yard template planning under uncertainmaritimemarketrdquo Transportation Research Part E Logistics andTransportation Review vol 69 pp 199ndash217 2014

[15] C Zhang Y-W Wan J Liu and R J Linn ldquoDynamiccrane deployment in container storage yardsrdquo TransportationResearch Part B Methodological vol 36 no 6 pp 537ndash5552002

[16] R K Chung C-L Li andW Lin ldquoInterblock crane deploymentin container terminalsrdquoTransportation Science vol 36 no 1 pp79ndash93 2002

[17] R Linn J-Y Liu Y-W Wan C Q Zhang and K G MurtyldquoRubber tired gantry crane deployment for container yardoperationrdquo Computers amp Industrial Engineering vol 45 no 3pp 429ndash442 2003

[18] Z Cao D-H Lee and Q Meng ldquoDeployment strategies ofdouble-rail-mounted gantry crane systems for loading out-bound containers in container terminalsrdquo International Journalof Production Economics vol 115 no 1 pp 221ndash228 2008

[19] K H Kim and H B Kim ldquoThe optimal sizing of the storagespace and handling facilities for import containersrdquoTransporta-tion Research Part B Methodological vol 36 no 9 pp 821ndash8352002

[20] D-H Lee J G Jin and J H Chen ldquoIntegrated bay allocationand yard crane scheduling problem for transshipment contain-ersrdquo Transportation Research Record vol 2222 no 8 pp 63ndash712011

[21] S H Won X Zhang and K H Kim ldquoWorkload-based yard-planning system in container terminalsrdquo Journal of IntelligentManufacturing vol 23 no 6 pp 2193ndash2206 2012

Submit your manuscripts athttpwwwhindawicom

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Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

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Scientific Programming 7

119908119889119903119905 le 120575119887 forall119903 isin 119877 119905 isin 119879 (17)

sum119898isin119871

119909119894119898ℎ119898119905 + 120576sum119895isin119878119899119894

sum119898isin119871

119909119895119898ℎ119898119905 le 1 forall119894 isin 119878 119905 isin 119879 (18)

sum119903isin119877

1199101199041199030 = 119873119884 (19)

sum1199031015840isin119877

1199101199031199031015840119905 = 1199101199041199030 forall119903 isin 119877 119905 = 1 (20)

sum1199031015840isin119877

1199101199031199031015840119905 = sum1199031015840isin119877

1199101199031015840119903(119905minus1)forall119903 isin 119877 2 le 119905 le 119873119879 minus 1

(21)

1199101199041199030 = sum1199031015840isin119877

1199101199031015840119903119905forall119903 isin 119877 119905 = 119873119879

(22)

119908119886119903119905 = 1199101199041199030 forall119903 isin 119877 119905 = 1 (23)

119908119886119903119905 = sum1199031015840isin119877

1199101199031015840119903(119905minus1)forall119903 isin 119877 119905 isin 119879 119905 = 1

(24)

119908119886119903119905 ge 119908119889119903119905 forall119903 isin 119877 119905 isin 119879 (25)

119908119886119903119905 le 120575119903 forall119903 isin 119877 119905 isin 119879 (26)

119909119894119898 isin 0 1 forall119894 isin 119878 119898 isin 119871 (27)

1199101199041199030 isin 119873 forall119903 isin 119877 (28)

1199101199031199031015840119905 isin 119873forall119903 1199031015840 isin 119877 119905 isin 119879 (29)

119911119902119898 isin 0 1forall119898 isin 119871 119902 isin 119861 (30)

119908119886119903119905 119908119889119903119905 isin 119873 forall119903 isin 119877 119905 isin 119879 (31)

The constraints of the mathematical model are composedof three parts the yard space allocation constraints theyard crane deployment constraints and the variables rangeconstraints

Equations (6) to (18) are the constraints of the first partwhich defines the rules of yard space allocation Equation (6)states that each subblock should be reserved for at most oneservice line during the entire planning horizon Equations (7)and (8) state that the subblocks assigned to the service linemust satisfy the outbound containers storage demand of theservice line Considering the service line outbound containervolumes are not generally fixed and the yard storage spaceis extremely limited the loosened constraints are presentedEquation (9) ensures that all the subblocks should be assignedto a service line Equations (10) and (11) are the calculationequations of service line YC loading points in a block equalto 1 if there is at least one subblock reserved for the service

line but otherwise equal to 0 Equations (12) to (14) state therelationship between the service line quay operation queuein the seaside and the YC loading point in the yard areaEquation (15) ensures themaximal handling YCs in the blockEquations (16) and (17) restrict the maximal handling YCsin the yard row Equation (18) states that when one of thesubblocks is in loading state the other neighbor subblocksare unavailable for service line that should be handled at thesame time

Equations (19) to (26) are the constraints of the secondpart which defines the rules of yard crane deploymentEquation (19) guarantees that the summation of initial YCsdeployment in each row is equal to the number of YCsEquations (20) to (22) ensure the YCs resource flow balancein the process of YCs interzone movement in each period ofplanning horizon Equations (23) and (24) are the calculationequations of YCs in each yard row Equations (25) and (26)ensure that the YCs operating in the row should satisfy theoperational demand and not exceed the maximal YCs boundin the row at the same time

Finally the domains of variables defined by (27) to (31)are the constraints of the third part

Linear Transformation As formula (1) is a nonlinear functiona linear transformation operation is applied After lineartransformation formula (1) is equal to

max 1198911 = sum119894isin119878

sum119895isin119878119899119894

sum119898119899isin119871

120601119894119895119898119899120596119898119899120579120601119894119895119898119899 le 119909119894119898 forall119894 isin 119878 119895 isin 119878119899119894 119898 119899 isin 119871120601119894119895119898119899 le 119909119895119899 forall119894 isin 119878 119895 isin 119878119899119894 119898 119899 isin 119871120601119894119895119898119899 ge 119909119894119898 + 119909119895119899 minus 1

forall119894 isin 119878 119895 isin 119878119899119894 119898 119899 isin 119871120601119894119895119898119899 isin 0 1 forall119894 isin 119878 119895 isin 119878119899119894 119898 119899 isin 119871

(32)

5 Numerical Experiment

To evaluate the effectiveness of the proposed model aseries of experiments with different scales are conductedSection 51 introduces the parameters used for generating theexperiments Section 52 analyzes the trade-off between yardstorage space resource utilization and yard operation costSection 53 researches the effects of YCs on yard storage spaceand operational cost Section 54 explores the influence ofsubblock volume on the yard management The integratedmodel in this paper is solved by ILOG CPLEX 124 and all ofthe computation experiments are conducted on aworkstationwith Inter Xeon CPU with 64GHz RAM

51 Instances At present many of the container line arrivalpatterns are weekly arrival In other words the voyage ofservice line arrives at the terminal once a weekTherefore theplanning horizon of this experiment is 1 week and each dayis split into 3 periods of 8 hours in consideration of practicalworking shift in the container terminal The experiment in

8 Scientific Programming

Table 1 Configuration parameters of container terminal yard

Class 119873119871(periods)

119873119861(blocks)

119873119878(subblocks)

119873119877(rows)

119873119884(YCs)

Class S 6 8 32 2 6Class M 8 16 64 4 12Class L 10 24 96 6 18

Table 2 Configuration parameters of yard crane and intertruck

Parameters 120583min 120583max 120575119887 120575119903 120593 120588 120590 120587Value 2 3 2 6 15 24 05 200

this paper considers three different storage yard scales (smallmedium and large) more precisely the instances with 6 to10 service lines 6 to 18 YCs and 8 to 24 blocks resulting inclasses 6 times 8 times 6 (class S) 8 times 16 times 12 (class M) and 10 times 24 times18 (class L) are tested (Table 1)

For all the classes the authors assume that the capacityof each block is 800 TEUs and the subblock capacity (V119887) is200 TEUs Meanwhile the maximal sharing space capacityof each subblock is equal to 20 TEUs (10 V119887) The yardcrane handling parameters and intertruck transportationparameters are shown in Table 2

For each class three scenarios of service line loadingrequirement are tested denoted by W1 W2 and W3 Theloading requirement is determined by the service line quayoperation queues (input data 119901119898 isin 119873 which are generatedwith discrete uniform distributions DU[2 3] DU[3 4] andDU[4 5] resp) the name of the instance indicates the levelof the loading requirement low requirement (W1) generalrequirement (W2) and high requirement (W3)

52 Yard Space Resource Analysis Based on space sharingstrategy the yard storage space utilization is increased owingto the sharing storage space between neighbor subblocks Asshowed in Table 3 the optimal yard operation cost equal to99990 yen and 800TEUsrsquo extra storage space (sharing space) arecreated (119886 = 0 cost-saving pattern) if space sharing strategyis applied in the yard Obviously this strategy can relieveterminal yard space scarce situation to a certain extent

Meanwhile when coefficient 119886 takes 1 it means thatthis model considers yard space allocation problem (space-utilizing pattern) firstly and then the yard crane deploymentproblem (cost-saving pattern) it is the nonintegrated patternin this situation Accordingly with the value of 119886 decreasingthe yard crane deployment is integrated with the yard spaceallocation problem gradually

Furthermore Figures 3 4 5 and 6 show the rela-tionships between yard storage space and yard operationcost of different instances scales As we can see with theincreasing of coefficient 119886 the yard sharing space increasedsynchronously as well as the yard operation cost Hence thereis no ultimate solution with the maximum space sharingand the minimum operation cost Which one should bechosen from these nondominated solutions is determined bythe terminal operators according to the terminal reality If

720 750 810780 840

105000

95000

115000

125000

135000

145000

870 900

a = 0

a = 02

a = 04

a = 06

a = 08

a = 1

Sharing space (TEUs)

Tran

spor

tatio

n co

st (yen

)

Figure 3 Relationships between yard space and operation cost ofsmall-scale experiments

1100 1200 14001300 1500

235000

220000

250000

265000

280000

295000

1600 1700

a = 0

a = 02

a = 04

a = 06

a = 08

a = 1

Sharing space (TEUs)

Tran

spor

tatio

n co

st (yen

)

Figure 4 Relationships between yard space and operation cost ofmedium-scale experiments

1950 2050 22502150 2350

395000

375000

415000

435000

455000

475000

2450 2550

a = 0

a = 02

a = 04

a = 06

a = 08

a = 1

Sharing space (TEUs)

Tran

spor

tatio

n co

st (yen

)

Figure 5 Relationships between yard space and operation cost oflarge-scale experiments

Scientific Programming 9

Table 3 Results of instances with different coefficient values

Instances119886 = 1 119886 = 08 119886 = 06 119886 = 04 119886 = 02 119886 = 01198911

(TEUs)1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

S W1 880 128800 880 110880 840 108900 800 103820 800 99990 800 99990S W2 880 129380 840 119960 840 110880 800 107910 760 102960 760 99990S W3 880 133340 840 127640 800 118800 760 108900 720 102960 680 99990M W1 1680 293150 1600 268500 1480 241600 1360 228830 1240 222450 1160 221760M W2 1600 286480 1560 261460 1440 239900 1320 228670 1240 224960 1160 221950M W3 1560 282360 1520 264300 1440 241860 1320 230100 1200 225960 1120 222140L W1 2480 468460 2400 432570 2360 403120 2200 387550 2120 380350 2080 376180L W2 2480 467820 2400 432800 2320 405670 2160 387610 2120 380640 2040 377050L W3 2400 468680 2360 433130 2280 405880 2160 388060 2080 381020 2000 378120

Table 4 Results of instances with different YCs

Instances119873119884119873119877 = 3 119873119884119873119877 = 35 119873119884119873119877 = 4 119873119884119873119877 = 45 119873119884119873119877 = 51198911

(TEUs)1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

S1 W1 960 99990 980 98040 980 97160 1000 96500 1000 96320S1 W2 960 99990 960 98630 980 97640 980 96500 1000 96320S1 W3 960 99990 960 99160 980 98420 980 97930 1000 96950M1 W1 1680 221760 1700 217730 1780 214200 1820 211770 1820 210040M1 W2 1600 221950 1640 218780 1700 215980 1760 213530 1760 211690M1 W3 1580 222140 1620 219420 1680 216560 1700 213840 1760 211870L1 W1 2480 376180 2540 367550 2580 360430 2640 354660 2640 351530L1 W2 2480 377050 2520 368580 2540 361910 2580 354960 2600 351600L1 W3 2420 378120 2460 368990 2500 362320 2540 355740 2600 352690

Δf1

Δf2

Sharing space (TEUs)

Tran

spor

tatio

n co

st (yen

)

tan 1205792 =Δf2Δf1

1205791

1205792

1205793

Figure 6 Relationships between yard space and operation cost

the container terminal yard storage is extremely scarce thatcould infect yard operation the operators should create morestorage space and the space-utilizing oriented strategy maybe adopted that is 119886 should take a bigger value otherwisethe cost saving should be the primary selection It is worthnoting that the marginal cost of yard sharing space (tan 120579)grows nonlinearly with the increase of coefficient 11988653 Yard Crane Resource Analysis In this section the effectsof total YCs on yard storage space utilization and yardoperation cost are tested We changed the number of YCs in

95000

96000

97000

98000

99000

100000

101000

940

950

960

970

980

990

1000

1010

Sharing space (TEUs)Transportation cost (yen)

NYN

R=3

NYN

R=45

NYN

R=4

NYN

R=5

NYN

R=35

Figure 7 Yard crane influence of small-scale experiments

the yard and the other parameters are unchanged For thisgroup of experiments consider the yard sharing space andyard operation cost separately so the coefficient 119886 is equal to1 and 0 respectively in the calculation of yard sharing spaceand yard operation cost The detailed results are shown inTable 4

Figures 7 8 and 9 show the effects of YCs on yard sharingspace and yard operation cost intuitively From these figures

10 Scientific Programming

Table 5 Results of instances with different subblock volume

Instances119873119878119873119861 = 3 119873119878119873119861 = 4 119873119878119873119861 = 5 119873119878119873119861 = 61198911

(TEUs)1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

S2 W1 756 106550 880 99990 960 95680 mdash mdashS2 W2 756 106550 880 99990 960 96280 mdash mdashS2 W3 756 106550 880 99990 960 99200 mdash mdashM2 W1 1404 231680 1680 221760 1888 217440 1950 210870M2 W2 1404 231760 1600 221950 1856 215210 mdash mdashM2 W3 1350 235930 1560 222140 1824 218130 mdash mdashL2 W1 2214 394550 2480 376180 2720 366960 2938 359620L2 W2 2214 396640 2480 377050 2688 371090 mdash mdashL2 W3 2160 398150 2400 378120 2656 373210 mdash mdash

208000

210000

212000

214000

216000

218000

224000

222000

220000

1550

1600

1650

1700

1750

1800

Sharing space (TEUs)Transportation cost (yen)

NYN

R=3

NYN

R=45

NYN

R=4

NYN

R=5

NYN

R=35

Figure 8 Yard crane influence of medium-scale experiments

we can find that the sharing space gradually becomes biggerwith the average YCs number in each zone increasing but theyard operation cost has an opposite situation

For the increasing of yard sharing space the mainreason could be that the added YCs relieved the YC loadingpoint constraint and then created more flexible service linespairings among subblocks but this effect is slight only about4

However generally speaking the increase of YCs shoulddecrease the yard operation cost considerably because it canavoid yard crane interzone movement as far as possible Butthese results shown in the figures could not express thisphenomenon obviously there is still only 6 cost decreaseA significant cause of this phenomenon is that the operationcost we considered is on the situation that the objectivefunction is cost-saving pattern (the coefficient 120572 equal to 0)so the yard operation cost we compared has been optimizedIt means that the amount of YCs interzone movements hasbeen decreased to an optimal level and this phenomenoncould be directly identified by Table 3 in Section 51

54 Subblock Volume Analysis The authors are also inter-ested in how the volume of subblock infects the yard space

335000340000345000350000355000360000365000370000375000380000

2350

2400

2450

2500

2550

2600

2650

Sharing space (TEUs)Transportation cost (yen)

NYN

R=3

NYN

R=45

NYN

R=4

NYN

R=5

NYN

R=35

Figure 9 Yard crane influence of large-scale experiments

utilization and yard operation cost In this subsection thenumber of subblocks in each block is divided into 3 4 5and 6 thus the volume of each subblock is equal to 270 200160 and 130 TEUs respectively and the other parameters areunchanged Similar to Section 53 the coefficient 119886 is equal to1 and 0 respectively in the calculation of yard sharing spaceand yard operation cost The detailed results are shown inTable 5

As showed in Figures 10 11 and 12 with the volumeof subblock decreasing and the subblocks in the yard blockincreasing gradually that the pairing of service lines becamemore flexible Consequently the space sharing opportunityincreased and the yard operation cost decreased as wellHowever with the decreasing of yard subblocks volume theyard crane service range is limited and such trends willlimit the increase of the yard crane resource demand in theyard When the number of subblocks in the block reaches acertain value the whole container terminal yard area cannotrun normally Accordingly the volume of yard subblock alsoplays an important role in yard management If the value istoo large the sharing space opportunity will decrease andoperation cost will increase However if the value is too smallthe whole system operation pattern will be broken up

Scientific Programming 11

9000092000940009600098000

100000102000104000106000108000

60065070075080085090095010001050

Sharing space (TEUs)Transportation cost (yen)

NSNB=3

NSNB=6

NSNB=5

NSNB=4

Figure 10 Yard subblock size influence of small-scale experiments

1200

1300

1400

1500

1600

1700

1800

1900

2000

200000

205000

210000

215000

220000

225000

230000

235000

Sharing space (TEUs)Transportation cost (yen)

NSNB=3

NSNB=6

NSNB=5

NSNB=4

Figure 11 Yard subblock size influence of medium-scale experi-ments

6 Conclusions

Motivated by the requirement to relieve the operationdilemma for resource-limited container terminal this paperaddressed the integrated yard space allocation and yard cranedeployment problem Two corresponding counterstrategiesare introduced and then an integrated mathematical modelis formulated to solve the problem Numerical experimentsverified the correctness and accuracy of the proposed modelThis study found that space sharing strategy can increase yardspace utilization and yard crane interzone movement strategycan effectively relieve the shortage of YCs In addition aninteresting phenomenon is discovered that there exists atrade-off between yard space utilization and yard operationcost and the volume of yard subblock also plays a significantrole in container port yard management

340000

350000

360000

370000

380000

390000

400000

2000

2200

2400

2600

2800

2900

2100

2300

2500

2700

Sharing space (TEUs)Transportation cost (yen)

NSNB=3

NSNB=6

NSNB=5

NSNB=4

Figure 12 Yard subblock size influence of large-scale experiments

This research can be extended in many relative areas Inthis paper the service line working windows and yard craneefficiency are determined However these parameters mayfluctuate with the factors associated with natural factors andthe equipment operators in reality Therefore the applicationof uncertainty factors in the integratedmanagement problemis a valuable research direction in the future

Competing Interests

The authors declare that they have no competing interests

Authorsrsquo Contributions

All authors contributed equally and significantly to writingthis article

Acknowledgments

This work is sponsored by National Natural Science Founda-tion ofChina (71602114) ldquoChenguangProgramrdquo supported byShanghai Education Development Foundation and ShanghaiMunicipal Education Commission (14CG48) Shanghai Sail-ing Program (14YF1411200) Doctoral Fund of theMinistry ofEducation (20133121110001) Shanghai Municipal EducationCommission Project (14YZ112) Shanghai Science amp Tech-nology Committee Research Project (15590501700) Shang-hai Maritime University Doctoral Innovation Fund Project(2015ycx063) and Shanghai Maritime University DoctoralExcellent Thesis Training Program (2015BXLP006)

References

[1] D Chang Z H JiangW Yan and J He ldquoIntegrating berth allo-cation and quay crane assignmentsrdquo Transportation Research

12 Scientific Programming

Part E LogisticsampTransportation Review vol 46 no 6 pp 975ndash990 2010

[2] J L He D F Chang W J Mi and W Yan ldquoA hybrid parallelgenetic algorithm for yard crane schedulingrdquo TransportationResearch Part E Logistics and Transportation Review vol 46no 1 pp 136ndash155 2010

[3] J G Jin D Lee and J X Cao ldquoStorage yard management inmaritime container terminalsrdquo Transportation Science 2014

[4] C-H Chen and W Yan ldquoEngineering informatics in portoperations and logisticsrdquoAdvanced Engineering Informatics vol25 no 3 pp 401ndash402 2011

[5] C-H Chen L P Khoo Y T Chong and X F Yin ldquoKnowledgediscovery using genetic algorithm for maritime situationalawarenessrdquo Expert Systems with Applications vol 41 no 6 pp2742ndash2753 2014

[6] J He Y Huang and D Chang ldquoSimulation-based heuristicmethod for container supply chain network optimizationrdquoAdvanced Engineering Informatics vol 29 no 3 pp 339ndash3542015

[7] I F A Vis and R De Koster ldquoTransshipment of containersat a container terminal an overviewrdquo European Journal ofOperational Research vol 147 no 1 pp 1ndash16 2003

[8] D Steenken S Voszlig and R Stahlbock ldquoContainer terminaloperation and operations researchmdasha classification and litera-ture reviewrdquo OR Spectrum vol 26 no 1 pp 3ndash49 2004

[9] R Stahlbock and S Voszlig ldquoOperations research at containerterminals a literature updaterdquo Operations Research-Spektrumvol 30 no 1 pp 1ndash52 2008

[10] X Jiang L H Lee E P Chew Y Han and K C Tan ldquoAcontainer yard storage strategy for improving land utilizationand operation efficiency in a transshipment hub portrdquoEuropeanJournal of Operational Research vol 221 no 1 pp 64ndash73 2012

[11] L H Lee E P Chew K C Tan and Y Han ldquoAn optimizationmodel for storage yardmanagement in transshipment hubsrdquoORSpectrum vol 28 no 4 pp 539ndash561 2006

[12] Y Han L H Lee E P Chew and K Tan ldquoA yard storagestrategy forminimizing traffic congestion in amarine containertransshipment hubrdquo OR Spectrum Quantitative Approaches inManagement vol 30 no 4 pp 697ndash720 2008

[13] X Jiang E P Chew L H Lee and K C Tan ldquoFlexible space-sharing strategy for storage yard management in a transship-ment hub portrdquo OR Spectrum vol 35 no 2 pp 417ndash439 2013

[14] L Zhen ldquoContainer yard template planning under uncertainmaritimemarketrdquo Transportation Research Part E Logistics andTransportation Review vol 69 pp 199ndash217 2014

[15] C Zhang Y-W Wan J Liu and R J Linn ldquoDynamiccrane deployment in container storage yardsrdquo TransportationResearch Part B Methodological vol 36 no 6 pp 537ndash5552002

[16] R K Chung C-L Li andW Lin ldquoInterblock crane deploymentin container terminalsrdquoTransportation Science vol 36 no 1 pp79ndash93 2002

[17] R Linn J-Y Liu Y-W Wan C Q Zhang and K G MurtyldquoRubber tired gantry crane deployment for container yardoperationrdquo Computers amp Industrial Engineering vol 45 no 3pp 429ndash442 2003

[18] Z Cao D-H Lee and Q Meng ldquoDeployment strategies ofdouble-rail-mounted gantry crane systems for loading out-bound containers in container terminalsrdquo International Journalof Production Economics vol 115 no 1 pp 221ndash228 2008

[19] K H Kim and H B Kim ldquoThe optimal sizing of the storagespace and handling facilities for import containersrdquoTransporta-tion Research Part B Methodological vol 36 no 9 pp 821ndash8352002

[20] D-H Lee J G Jin and J H Chen ldquoIntegrated bay allocationand yard crane scheduling problem for transshipment contain-ersrdquo Transportation Research Record vol 2222 no 8 pp 63ndash712011

[21] S H Won X Zhang and K H Kim ldquoWorkload-based yard-planning system in container terminalsrdquo Journal of IntelligentManufacturing vol 23 no 6 pp 2193ndash2206 2012

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

8 Scientific Programming

Table 1 Configuration parameters of container terminal yard

Class 119873119871(periods)

119873119861(blocks)

119873119878(subblocks)

119873119877(rows)

119873119884(YCs)

Class S 6 8 32 2 6Class M 8 16 64 4 12Class L 10 24 96 6 18

Table 2 Configuration parameters of yard crane and intertruck

Parameters 120583min 120583max 120575119887 120575119903 120593 120588 120590 120587Value 2 3 2 6 15 24 05 200

this paper considers three different storage yard scales (smallmedium and large) more precisely the instances with 6 to10 service lines 6 to 18 YCs and 8 to 24 blocks resulting inclasses 6 times 8 times 6 (class S) 8 times 16 times 12 (class M) and 10 times 24 times18 (class L) are tested (Table 1)

For all the classes the authors assume that the capacityof each block is 800 TEUs and the subblock capacity (V119887) is200 TEUs Meanwhile the maximal sharing space capacityof each subblock is equal to 20 TEUs (10 V119887) The yardcrane handling parameters and intertruck transportationparameters are shown in Table 2

For each class three scenarios of service line loadingrequirement are tested denoted by W1 W2 and W3 Theloading requirement is determined by the service line quayoperation queues (input data 119901119898 isin 119873 which are generatedwith discrete uniform distributions DU[2 3] DU[3 4] andDU[4 5] resp) the name of the instance indicates the levelof the loading requirement low requirement (W1) generalrequirement (W2) and high requirement (W3)

52 Yard Space Resource Analysis Based on space sharingstrategy the yard storage space utilization is increased owingto the sharing storage space between neighbor subblocks Asshowed in Table 3 the optimal yard operation cost equal to99990 yen and 800TEUsrsquo extra storage space (sharing space) arecreated (119886 = 0 cost-saving pattern) if space sharing strategyis applied in the yard Obviously this strategy can relieveterminal yard space scarce situation to a certain extent

Meanwhile when coefficient 119886 takes 1 it means thatthis model considers yard space allocation problem (space-utilizing pattern) firstly and then the yard crane deploymentproblem (cost-saving pattern) it is the nonintegrated patternin this situation Accordingly with the value of 119886 decreasingthe yard crane deployment is integrated with the yard spaceallocation problem gradually

Furthermore Figures 3 4 5 and 6 show the rela-tionships between yard storage space and yard operationcost of different instances scales As we can see with theincreasing of coefficient 119886 the yard sharing space increasedsynchronously as well as the yard operation cost Hence thereis no ultimate solution with the maximum space sharingand the minimum operation cost Which one should bechosen from these nondominated solutions is determined bythe terminal operators according to the terminal reality If

720 750 810780 840

105000

95000

115000

125000

135000

145000

870 900

a = 0

a = 02

a = 04

a = 06

a = 08

a = 1

Sharing space (TEUs)

Tran

spor

tatio

n co

st (yen

)

Figure 3 Relationships between yard space and operation cost ofsmall-scale experiments

1100 1200 14001300 1500

235000

220000

250000

265000

280000

295000

1600 1700

a = 0

a = 02

a = 04

a = 06

a = 08

a = 1

Sharing space (TEUs)

Tran

spor

tatio

n co

st (yen

)

Figure 4 Relationships between yard space and operation cost ofmedium-scale experiments

1950 2050 22502150 2350

395000

375000

415000

435000

455000

475000

2450 2550

a = 0

a = 02

a = 04

a = 06

a = 08

a = 1

Sharing space (TEUs)

Tran

spor

tatio

n co

st (yen

)

Figure 5 Relationships between yard space and operation cost oflarge-scale experiments

Scientific Programming 9

Table 3 Results of instances with different coefficient values

Instances119886 = 1 119886 = 08 119886 = 06 119886 = 04 119886 = 02 119886 = 01198911

(TEUs)1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

S W1 880 128800 880 110880 840 108900 800 103820 800 99990 800 99990S W2 880 129380 840 119960 840 110880 800 107910 760 102960 760 99990S W3 880 133340 840 127640 800 118800 760 108900 720 102960 680 99990M W1 1680 293150 1600 268500 1480 241600 1360 228830 1240 222450 1160 221760M W2 1600 286480 1560 261460 1440 239900 1320 228670 1240 224960 1160 221950M W3 1560 282360 1520 264300 1440 241860 1320 230100 1200 225960 1120 222140L W1 2480 468460 2400 432570 2360 403120 2200 387550 2120 380350 2080 376180L W2 2480 467820 2400 432800 2320 405670 2160 387610 2120 380640 2040 377050L W3 2400 468680 2360 433130 2280 405880 2160 388060 2080 381020 2000 378120

Table 4 Results of instances with different YCs

Instances119873119884119873119877 = 3 119873119884119873119877 = 35 119873119884119873119877 = 4 119873119884119873119877 = 45 119873119884119873119877 = 51198911

(TEUs)1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

S1 W1 960 99990 980 98040 980 97160 1000 96500 1000 96320S1 W2 960 99990 960 98630 980 97640 980 96500 1000 96320S1 W3 960 99990 960 99160 980 98420 980 97930 1000 96950M1 W1 1680 221760 1700 217730 1780 214200 1820 211770 1820 210040M1 W2 1600 221950 1640 218780 1700 215980 1760 213530 1760 211690M1 W3 1580 222140 1620 219420 1680 216560 1700 213840 1760 211870L1 W1 2480 376180 2540 367550 2580 360430 2640 354660 2640 351530L1 W2 2480 377050 2520 368580 2540 361910 2580 354960 2600 351600L1 W3 2420 378120 2460 368990 2500 362320 2540 355740 2600 352690

Δf1

Δf2

Sharing space (TEUs)

Tran

spor

tatio

n co

st (yen

)

tan 1205792 =Δf2Δf1

1205791

1205792

1205793

Figure 6 Relationships between yard space and operation cost

the container terminal yard storage is extremely scarce thatcould infect yard operation the operators should create morestorage space and the space-utilizing oriented strategy maybe adopted that is 119886 should take a bigger value otherwisethe cost saving should be the primary selection It is worthnoting that the marginal cost of yard sharing space (tan 120579)grows nonlinearly with the increase of coefficient 11988653 Yard Crane Resource Analysis In this section the effectsof total YCs on yard storage space utilization and yardoperation cost are tested We changed the number of YCs in

95000

96000

97000

98000

99000

100000

101000

940

950

960

970

980

990

1000

1010

Sharing space (TEUs)Transportation cost (yen)

NYN

R=3

NYN

R=45

NYN

R=4

NYN

R=5

NYN

R=35

Figure 7 Yard crane influence of small-scale experiments

the yard and the other parameters are unchanged For thisgroup of experiments consider the yard sharing space andyard operation cost separately so the coefficient 119886 is equal to1 and 0 respectively in the calculation of yard sharing spaceand yard operation cost The detailed results are shown inTable 4

Figures 7 8 and 9 show the effects of YCs on yard sharingspace and yard operation cost intuitively From these figures

10 Scientific Programming

Table 5 Results of instances with different subblock volume

Instances119873119878119873119861 = 3 119873119878119873119861 = 4 119873119878119873119861 = 5 119873119878119873119861 = 61198911

(TEUs)1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

S2 W1 756 106550 880 99990 960 95680 mdash mdashS2 W2 756 106550 880 99990 960 96280 mdash mdashS2 W3 756 106550 880 99990 960 99200 mdash mdashM2 W1 1404 231680 1680 221760 1888 217440 1950 210870M2 W2 1404 231760 1600 221950 1856 215210 mdash mdashM2 W3 1350 235930 1560 222140 1824 218130 mdash mdashL2 W1 2214 394550 2480 376180 2720 366960 2938 359620L2 W2 2214 396640 2480 377050 2688 371090 mdash mdashL2 W3 2160 398150 2400 378120 2656 373210 mdash mdash

208000

210000

212000

214000

216000

218000

224000

222000

220000

1550

1600

1650

1700

1750

1800

Sharing space (TEUs)Transportation cost (yen)

NYN

R=3

NYN

R=45

NYN

R=4

NYN

R=5

NYN

R=35

Figure 8 Yard crane influence of medium-scale experiments

we can find that the sharing space gradually becomes biggerwith the average YCs number in each zone increasing but theyard operation cost has an opposite situation

For the increasing of yard sharing space the mainreason could be that the added YCs relieved the YC loadingpoint constraint and then created more flexible service linespairings among subblocks but this effect is slight only about4

However generally speaking the increase of YCs shoulddecrease the yard operation cost considerably because it canavoid yard crane interzone movement as far as possible Butthese results shown in the figures could not express thisphenomenon obviously there is still only 6 cost decreaseA significant cause of this phenomenon is that the operationcost we considered is on the situation that the objectivefunction is cost-saving pattern (the coefficient 120572 equal to 0)so the yard operation cost we compared has been optimizedIt means that the amount of YCs interzone movements hasbeen decreased to an optimal level and this phenomenoncould be directly identified by Table 3 in Section 51

54 Subblock Volume Analysis The authors are also inter-ested in how the volume of subblock infects the yard space

335000340000345000350000355000360000365000370000375000380000

2350

2400

2450

2500

2550

2600

2650

Sharing space (TEUs)Transportation cost (yen)

NYN

R=3

NYN

R=45

NYN

R=4

NYN

R=5

NYN

R=35

Figure 9 Yard crane influence of large-scale experiments

utilization and yard operation cost In this subsection thenumber of subblocks in each block is divided into 3 4 5and 6 thus the volume of each subblock is equal to 270 200160 and 130 TEUs respectively and the other parameters areunchanged Similar to Section 53 the coefficient 119886 is equal to1 and 0 respectively in the calculation of yard sharing spaceand yard operation cost The detailed results are shown inTable 5

As showed in Figures 10 11 and 12 with the volumeof subblock decreasing and the subblocks in the yard blockincreasing gradually that the pairing of service lines becamemore flexible Consequently the space sharing opportunityincreased and the yard operation cost decreased as wellHowever with the decreasing of yard subblocks volume theyard crane service range is limited and such trends willlimit the increase of the yard crane resource demand in theyard When the number of subblocks in the block reaches acertain value the whole container terminal yard area cannotrun normally Accordingly the volume of yard subblock alsoplays an important role in yard management If the value istoo large the sharing space opportunity will decrease andoperation cost will increase However if the value is too smallthe whole system operation pattern will be broken up

Scientific Programming 11

9000092000940009600098000

100000102000104000106000108000

60065070075080085090095010001050

Sharing space (TEUs)Transportation cost (yen)

NSNB=3

NSNB=6

NSNB=5

NSNB=4

Figure 10 Yard subblock size influence of small-scale experiments

1200

1300

1400

1500

1600

1700

1800

1900

2000

200000

205000

210000

215000

220000

225000

230000

235000

Sharing space (TEUs)Transportation cost (yen)

NSNB=3

NSNB=6

NSNB=5

NSNB=4

Figure 11 Yard subblock size influence of medium-scale experi-ments

6 Conclusions

Motivated by the requirement to relieve the operationdilemma for resource-limited container terminal this paperaddressed the integrated yard space allocation and yard cranedeployment problem Two corresponding counterstrategiesare introduced and then an integrated mathematical modelis formulated to solve the problem Numerical experimentsverified the correctness and accuracy of the proposed modelThis study found that space sharing strategy can increase yardspace utilization and yard crane interzone movement strategycan effectively relieve the shortage of YCs In addition aninteresting phenomenon is discovered that there exists atrade-off between yard space utilization and yard operationcost and the volume of yard subblock also plays a significantrole in container port yard management

340000

350000

360000

370000

380000

390000

400000

2000

2200

2400

2600

2800

2900

2100

2300

2500

2700

Sharing space (TEUs)Transportation cost (yen)

NSNB=3

NSNB=6

NSNB=5

NSNB=4

Figure 12 Yard subblock size influence of large-scale experiments

This research can be extended in many relative areas Inthis paper the service line working windows and yard craneefficiency are determined However these parameters mayfluctuate with the factors associated with natural factors andthe equipment operators in reality Therefore the applicationof uncertainty factors in the integratedmanagement problemis a valuable research direction in the future

Competing Interests

The authors declare that they have no competing interests

Authorsrsquo Contributions

All authors contributed equally and significantly to writingthis article

Acknowledgments

This work is sponsored by National Natural Science Founda-tion ofChina (71602114) ldquoChenguangProgramrdquo supported byShanghai Education Development Foundation and ShanghaiMunicipal Education Commission (14CG48) Shanghai Sail-ing Program (14YF1411200) Doctoral Fund of theMinistry ofEducation (20133121110001) Shanghai Municipal EducationCommission Project (14YZ112) Shanghai Science amp Tech-nology Committee Research Project (15590501700) Shang-hai Maritime University Doctoral Innovation Fund Project(2015ycx063) and Shanghai Maritime University DoctoralExcellent Thesis Training Program (2015BXLP006)

References

[1] D Chang Z H JiangW Yan and J He ldquoIntegrating berth allo-cation and quay crane assignmentsrdquo Transportation Research

12 Scientific Programming

Part E LogisticsampTransportation Review vol 46 no 6 pp 975ndash990 2010

[2] J L He D F Chang W J Mi and W Yan ldquoA hybrid parallelgenetic algorithm for yard crane schedulingrdquo TransportationResearch Part E Logistics and Transportation Review vol 46no 1 pp 136ndash155 2010

[3] J G Jin D Lee and J X Cao ldquoStorage yard management inmaritime container terminalsrdquo Transportation Science 2014

[4] C-H Chen and W Yan ldquoEngineering informatics in portoperations and logisticsrdquoAdvanced Engineering Informatics vol25 no 3 pp 401ndash402 2011

[5] C-H Chen L P Khoo Y T Chong and X F Yin ldquoKnowledgediscovery using genetic algorithm for maritime situationalawarenessrdquo Expert Systems with Applications vol 41 no 6 pp2742ndash2753 2014

[6] J He Y Huang and D Chang ldquoSimulation-based heuristicmethod for container supply chain network optimizationrdquoAdvanced Engineering Informatics vol 29 no 3 pp 339ndash3542015

[7] I F A Vis and R De Koster ldquoTransshipment of containersat a container terminal an overviewrdquo European Journal ofOperational Research vol 147 no 1 pp 1ndash16 2003

[8] D Steenken S Voszlig and R Stahlbock ldquoContainer terminaloperation and operations researchmdasha classification and litera-ture reviewrdquo OR Spectrum vol 26 no 1 pp 3ndash49 2004

[9] R Stahlbock and S Voszlig ldquoOperations research at containerterminals a literature updaterdquo Operations Research-Spektrumvol 30 no 1 pp 1ndash52 2008

[10] X Jiang L H Lee E P Chew Y Han and K C Tan ldquoAcontainer yard storage strategy for improving land utilizationand operation efficiency in a transshipment hub portrdquoEuropeanJournal of Operational Research vol 221 no 1 pp 64ndash73 2012

[11] L H Lee E P Chew K C Tan and Y Han ldquoAn optimizationmodel for storage yardmanagement in transshipment hubsrdquoORSpectrum vol 28 no 4 pp 539ndash561 2006

[12] Y Han L H Lee E P Chew and K Tan ldquoA yard storagestrategy forminimizing traffic congestion in amarine containertransshipment hubrdquo OR Spectrum Quantitative Approaches inManagement vol 30 no 4 pp 697ndash720 2008

[13] X Jiang E P Chew L H Lee and K C Tan ldquoFlexible space-sharing strategy for storage yard management in a transship-ment hub portrdquo OR Spectrum vol 35 no 2 pp 417ndash439 2013

[14] L Zhen ldquoContainer yard template planning under uncertainmaritimemarketrdquo Transportation Research Part E Logistics andTransportation Review vol 69 pp 199ndash217 2014

[15] C Zhang Y-W Wan J Liu and R J Linn ldquoDynamiccrane deployment in container storage yardsrdquo TransportationResearch Part B Methodological vol 36 no 6 pp 537ndash5552002

[16] R K Chung C-L Li andW Lin ldquoInterblock crane deploymentin container terminalsrdquoTransportation Science vol 36 no 1 pp79ndash93 2002

[17] R Linn J-Y Liu Y-W Wan C Q Zhang and K G MurtyldquoRubber tired gantry crane deployment for container yardoperationrdquo Computers amp Industrial Engineering vol 45 no 3pp 429ndash442 2003

[18] Z Cao D-H Lee and Q Meng ldquoDeployment strategies ofdouble-rail-mounted gantry crane systems for loading out-bound containers in container terminalsrdquo International Journalof Production Economics vol 115 no 1 pp 221ndash228 2008

[19] K H Kim and H B Kim ldquoThe optimal sizing of the storagespace and handling facilities for import containersrdquoTransporta-tion Research Part B Methodological vol 36 no 9 pp 821ndash8352002

[20] D-H Lee J G Jin and J H Chen ldquoIntegrated bay allocationand yard crane scheduling problem for transshipment contain-ersrdquo Transportation Research Record vol 2222 no 8 pp 63ndash712011

[21] S H Won X Zhang and K H Kim ldquoWorkload-based yard-planning system in container terminalsrdquo Journal of IntelligentManufacturing vol 23 no 6 pp 2193ndash2206 2012

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Scientific Programming 9

Table 3 Results of instances with different coefficient values

Instances119886 = 1 119886 = 08 119886 = 06 119886 = 04 119886 = 02 119886 = 01198911

(TEUs)1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

S W1 880 128800 880 110880 840 108900 800 103820 800 99990 800 99990S W2 880 129380 840 119960 840 110880 800 107910 760 102960 760 99990S W3 880 133340 840 127640 800 118800 760 108900 720 102960 680 99990M W1 1680 293150 1600 268500 1480 241600 1360 228830 1240 222450 1160 221760M W2 1600 286480 1560 261460 1440 239900 1320 228670 1240 224960 1160 221950M W3 1560 282360 1520 264300 1440 241860 1320 230100 1200 225960 1120 222140L W1 2480 468460 2400 432570 2360 403120 2200 387550 2120 380350 2080 376180L W2 2480 467820 2400 432800 2320 405670 2160 387610 2120 380640 2040 377050L W3 2400 468680 2360 433130 2280 405880 2160 388060 2080 381020 2000 378120

Table 4 Results of instances with different YCs

Instances119873119884119873119877 = 3 119873119884119873119877 = 35 119873119884119873119877 = 4 119873119884119873119877 = 45 119873119884119873119877 = 51198911

(TEUs)1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

S1 W1 960 99990 980 98040 980 97160 1000 96500 1000 96320S1 W2 960 99990 960 98630 980 97640 980 96500 1000 96320S1 W3 960 99990 960 99160 980 98420 980 97930 1000 96950M1 W1 1680 221760 1700 217730 1780 214200 1820 211770 1820 210040M1 W2 1600 221950 1640 218780 1700 215980 1760 213530 1760 211690M1 W3 1580 222140 1620 219420 1680 216560 1700 213840 1760 211870L1 W1 2480 376180 2540 367550 2580 360430 2640 354660 2640 351530L1 W2 2480 377050 2520 368580 2540 361910 2580 354960 2600 351600L1 W3 2420 378120 2460 368990 2500 362320 2540 355740 2600 352690

Δf1

Δf2

Sharing space (TEUs)

Tran

spor

tatio

n co

st (yen

)

tan 1205792 =Δf2Δf1

1205791

1205792

1205793

Figure 6 Relationships between yard space and operation cost

the container terminal yard storage is extremely scarce thatcould infect yard operation the operators should create morestorage space and the space-utilizing oriented strategy maybe adopted that is 119886 should take a bigger value otherwisethe cost saving should be the primary selection It is worthnoting that the marginal cost of yard sharing space (tan 120579)grows nonlinearly with the increase of coefficient 11988653 Yard Crane Resource Analysis In this section the effectsof total YCs on yard storage space utilization and yardoperation cost are tested We changed the number of YCs in

95000

96000

97000

98000

99000

100000

101000

940

950

960

970

980

990

1000

1010

Sharing space (TEUs)Transportation cost (yen)

NYN

R=3

NYN

R=45

NYN

R=4

NYN

R=5

NYN

R=35

Figure 7 Yard crane influence of small-scale experiments

the yard and the other parameters are unchanged For thisgroup of experiments consider the yard sharing space andyard operation cost separately so the coefficient 119886 is equal to1 and 0 respectively in the calculation of yard sharing spaceand yard operation cost The detailed results are shown inTable 4

Figures 7 8 and 9 show the effects of YCs on yard sharingspace and yard operation cost intuitively From these figures

10 Scientific Programming

Table 5 Results of instances with different subblock volume

Instances119873119878119873119861 = 3 119873119878119873119861 = 4 119873119878119873119861 = 5 119873119878119873119861 = 61198911

(TEUs)1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

S2 W1 756 106550 880 99990 960 95680 mdash mdashS2 W2 756 106550 880 99990 960 96280 mdash mdashS2 W3 756 106550 880 99990 960 99200 mdash mdashM2 W1 1404 231680 1680 221760 1888 217440 1950 210870M2 W2 1404 231760 1600 221950 1856 215210 mdash mdashM2 W3 1350 235930 1560 222140 1824 218130 mdash mdashL2 W1 2214 394550 2480 376180 2720 366960 2938 359620L2 W2 2214 396640 2480 377050 2688 371090 mdash mdashL2 W3 2160 398150 2400 378120 2656 373210 mdash mdash

208000

210000

212000

214000

216000

218000

224000

222000

220000

1550

1600

1650

1700

1750

1800

Sharing space (TEUs)Transportation cost (yen)

NYN

R=3

NYN

R=45

NYN

R=4

NYN

R=5

NYN

R=35

Figure 8 Yard crane influence of medium-scale experiments

we can find that the sharing space gradually becomes biggerwith the average YCs number in each zone increasing but theyard operation cost has an opposite situation

For the increasing of yard sharing space the mainreason could be that the added YCs relieved the YC loadingpoint constraint and then created more flexible service linespairings among subblocks but this effect is slight only about4

However generally speaking the increase of YCs shoulddecrease the yard operation cost considerably because it canavoid yard crane interzone movement as far as possible Butthese results shown in the figures could not express thisphenomenon obviously there is still only 6 cost decreaseA significant cause of this phenomenon is that the operationcost we considered is on the situation that the objectivefunction is cost-saving pattern (the coefficient 120572 equal to 0)so the yard operation cost we compared has been optimizedIt means that the amount of YCs interzone movements hasbeen decreased to an optimal level and this phenomenoncould be directly identified by Table 3 in Section 51

54 Subblock Volume Analysis The authors are also inter-ested in how the volume of subblock infects the yard space

335000340000345000350000355000360000365000370000375000380000

2350

2400

2450

2500

2550

2600

2650

Sharing space (TEUs)Transportation cost (yen)

NYN

R=3

NYN

R=45

NYN

R=4

NYN

R=5

NYN

R=35

Figure 9 Yard crane influence of large-scale experiments

utilization and yard operation cost In this subsection thenumber of subblocks in each block is divided into 3 4 5and 6 thus the volume of each subblock is equal to 270 200160 and 130 TEUs respectively and the other parameters areunchanged Similar to Section 53 the coefficient 119886 is equal to1 and 0 respectively in the calculation of yard sharing spaceand yard operation cost The detailed results are shown inTable 5

As showed in Figures 10 11 and 12 with the volumeof subblock decreasing and the subblocks in the yard blockincreasing gradually that the pairing of service lines becamemore flexible Consequently the space sharing opportunityincreased and the yard operation cost decreased as wellHowever with the decreasing of yard subblocks volume theyard crane service range is limited and such trends willlimit the increase of the yard crane resource demand in theyard When the number of subblocks in the block reaches acertain value the whole container terminal yard area cannotrun normally Accordingly the volume of yard subblock alsoplays an important role in yard management If the value istoo large the sharing space opportunity will decrease andoperation cost will increase However if the value is too smallthe whole system operation pattern will be broken up

Scientific Programming 11

9000092000940009600098000

100000102000104000106000108000

60065070075080085090095010001050

Sharing space (TEUs)Transportation cost (yen)

NSNB=3

NSNB=6

NSNB=5

NSNB=4

Figure 10 Yard subblock size influence of small-scale experiments

1200

1300

1400

1500

1600

1700

1800

1900

2000

200000

205000

210000

215000

220000

225000

230000

235000

Sharing space (TEUs)Transportation cost (yen)

NSNB=3

NSNB=6

NSNB=5

NSNB=4

Figure 11 Yard subblock size influence of medium-scale experi-ments

6 Conclusions

Motivated by the requirement to relieve the operationdilemma for resource-limited container terminal this paperaddressed the integrated yard space allocation and yard cranedeployment problem Two corresponding counterstrategiesare introduced and then an integrated mathematical modelis formulated to solve the problem Numerical experimentsverified the correctness and accuracy of the proposed modelThis study found that space sharing strategy can increase yardspace utilization and yard crane interzone movement strategycan effectively relieve the shortage of YCs In addition aninteresting phenomenon is discovered that there exists atrade-off between yard space utilization and yard operationcost and the volume of yard subblock also plays a significantrole in container port yard management

340000

350000

360000

370000

380000

390000

400000

2000

2200

2400

2600

2800

2900

2100

2300

2500

2700

Sharing space (TEUs)Transportation cost (yen)

NSNB=3

NSNB=6

NSNB=5

NSNB=4

Figure 12 Yard subblock size influence of large-scale experiments

This research can be extended in many relative areas Inthis paper the service line working windows and yard craneefficiency are determined However these parameters mayfluctuate with the factors associated with natural factors andthe equipment operators in reality Therefore the applicationof uncertainty factors in the integratedmanagement problemis a valuable research direction in the future

Competing Interests

The authors declare that they have no competing interests

Authorsrsquo Contributions

All authors contributed equally and significantly to writingthis article

Acknowledgments

This work is sponsored by National Natural Science Founda-tion ofChina (71602114) ldquoChenguangProgramrdquo supported byShanghai Education Development Foundation and ShanghaiMunicipal Education Commission (14CG48) Shanghai Sail-ing Program (14YF1411200) Doctoral Fund of theMinistry ofEducation (20133121110001) Shanghai Municipal EducationCommission Project (14YZ112) Shanghai Science amp Tech-nology Committee Research Project (15590501700) Shang-hai Maritime University Doctoral Innovation Fund Project(2015ycx063) and Shanghai Maritime University DoctoralExcellent Thesis Training Program (2015BXLP006)

References

[1] D Chang Z H JiangW Yan and J He ldquoIntegrating berth allo-cation and quay crane assignmentsrdquo Transportation Research

12 Scientific Programming

Part E LogisticsampTransportation Review vol 46 no 6 pp 975ndash990 2010

[2] J L He D F Chang W J Mi and W Yan ldquoA hybrid parallelgenetic algorithm for yard crane schedulingrdquo TransportationResearch Part E Logistics and Transportation Review vol 46no 1 pp 136ndash155 2010

[3] J G Jin D Lee and J X Cao ldquoStorage yard management inmaritime container terminalsrdquo Transportation Science 2014

[4] C-H Chen and W Yan ldquoEngineering informatics in portoperations and logisticsrdquoAdvanced Engineering Informatics vol25 no 3 pp 401ndash402 2011

[5] C-H Chen L P Khoo Y T Chong and X F Yin ldquoKnowledgediscovery using genetic algorithm for maritime situationalawarenessrdquo Expert Systems with Applications vol 41 no 6 pp2742ndash2753 2014

[6] J He Y Huang and D Chang ldquoSimulation-based heuristicmethod for container supply chain network optimizationrdquoAdvanced Engineering Informatics vol 29 no 3 pp 339ndash3542015

[7] I F A Vis and R De Koster ldquoTransshipment of containersat a container terminal an overviewrdquo European Journal ofOperational Research vol 147 no 1 pp 1ndash16 2003

[8] D Steenken S Voszlig and R Stahlbock ldquoContainer terminaloperation and operations researchmdasha classification and litera-ture reviewrdquo OR Spectrum vol 26 no 1 pp 3ndash49 2004

[9] R Stahlbock and S Voszlig ldquoOperations research at containerterminals a literature updaterdquo Operations Research-Spektrumvol 30 no 1 pp 1ndash52 2008

[10] X Jiang L H Lee E P Chew Y Han and K C Tan ldquoAcontainer yard storage strategy for improving land utilizationand operation efficiency in a transshipment hub portrdquoEuropeanJournal of Operational Research vol 221 no 1 pp 64ndash73 2012

[11] L H Lee E P Chew K C Tan and Y Han ldquoAn optimizationmodel for storage yardmanagement in transshipment hubsrdquoORSpectrum vol 28 no 4 pp 539ndash561 2006

[12] Y Han L H Lee E P Chew and K Tan ldquoA yard storagestrategy forminimizing traffic congestion in amarine containertransshipment hubrdquo OR Spectrum Quantitative Approaches inManagement vol 30 no 4 pp 697ndash720 2008

[13] X Jiang E P Chew L H Lee and K C Tan ldquoFlexible space-sharing strategy for storage yard management in a transship-ment hub portrdquo OR Spectrum vol 35 no 2 pp 417ndash439 2013

[14] L Zhen ldquoContainer yard template planning under uncertainmaritimemarketrdquo Transportation Research Part E Logistics andTransportation Review vol 69 pp 199ndash217 2014

[15] C Zhang Y-W Wan J Liu and R J Linn ldquoDynamiccrane deployment in container storage yardsrdquo TransportationResearch Part B Methodological vol 36 no 6 pp 537ndash5552002

[16] R K Chung C-L Li andW Lin ldquoInterblock crane deploymentin container terminalsrdquoTransportation Science vol 36 no 1 pp79ndash93 2002

[17] R Linn J-Y Liu Y-W Wan C Q Zhang and K G MurtyldquoRubber tired gantry crane deployment for container yardoperationrdquo Computers amp Industrial Engineering vol 45 no 3pp 429ndash442 2003

[18] Z Cao D-H Lee and Q Meng ldquoDeployment strategies ofdouble-rail-mounted gantry crane systems for loading out-bound containers in container terminalsrdquo International Journalof Production Economics vol 115 no 1 pp 221ndash228 2008

[19] K H Kim and H B Kim ldquoThe optimal sizing of the storagespace and handling facilities for import containersrdquoTransporta-tion Research Part B Methodological vol 36 no 9 pp 821ndash8352002

[20] D-H Lee J G Jin and J H Chen ldquoIntegrated bay allocationand yard crane scheduling problem for transshipment contain-ersrdquo Transportation Research Record vol 2222 no 8 pp 63ndash712011

[21] S H Won X Zhang and K H Kim ldquoWorkload-based yard-planning system in container terminalsrdquo Journal of IntelligentManufacturing vol 23 no 6 pp 2193ndash2206 2012

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

10 Scientific Programming

Table 5 Results of instances with different subblock volume

Instances119873119878119873119861 = 3 119873119878119873119861 = 4 119873119878119873119861 = 5 119873119878119873119861 = 61198911

(TEUs)1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

1198911(TEUs)

1198912(yen)

S2 W1 756 106550 880 99990 960 95680 mdash mdashS2 W2 756 106550 880 99990 960 96280 mdash mdashS2 W3 756 106550 880 99990 960 99200 mdash mdashM2 W1 1404 231680 1680 221760 1888 217440 1950 210870M2 W2 1404 231760 1600 221950 1856 215210 mdash mdashM2 W3 1350 235930 1560 222140 1824 218130 mdash mdashL2 W1 2214 394550 2480 376180 2720 366960 2938 359620L2 W2 2214 396640 2480 377050 2688 371090 mdash mdashL2 W3 2160 398150 2400 378120 2656 373210 mdash mdash

208000

210000

212000

214000

216000

218000

224000

222000

220000

1550

1600

1650

1700

1750

1800

Sharing space (TEUs)Transportation cost (yen)

NYN

R=3

NYN

R=45

NYN

R=4

NYN

R=5

NYN

R=35

Figure 8 Yard crane influence of medium-scale experiments

we can find that the sharing space gradually becomes biggerwith the average YCs number in each zone increasing but theyard operation cost has an opposite situation

For the increasing of yard sharing space the mainreason could be that the added YCs relieved the YC loadingpoint constraint and then created more flexible service linespairings among subblocks but this effect is slight only about4

However generally speaking the increase of YCs shoulddecrease the yard operation cost considerably because it canavoid yard crane interzone movement as far as possible Butthese results shown in the figures could not express thisphenomenon obviously there is still only 6 cost decreaseA significant cause of this phenomenon is that the operationcost we considered is on the situation that the objectivefunction is cost-saving pattern (the coefficient 120572 equal to 0)so the yard operation cost we compared has been optimizedIt means that the amount of YCs interzone movements hasbeen decreased to an optimal level and this phenomenoncould be directly identified by Table 3 in Section 51

54 Subblock Volume Analysis The authors are also inter-ested in how the volume of subblock infects the yard space

335000340000345000350000355000360000365000370000375000380000

2350

2400

2450

2500

2550

2600

2650

Sharing space (TEUs)Transportation cost (yen)

NYN

R=3

NYN

R=45

NYN

R=4

NYN

R=5

NYN

R=35

Figure 9 Yard crane influence of large-scale experiments

utilization and yard operation cost In this subsection thenumber of subblocks in each block is divided into 3 4 5and 6 thus the volume of each subblock is equal to 270 200160 and 130 TEUs respectively and the other parameters areunchanged Similar to Section 53 the coefficient 119886 is equal to1 and 0 respectively in the calculation of yard sharing spaceand yard operation cost The detailed results are shown inTable 5

As showed in Figures 10 11 and 12 with the volumeof subblock decreasing and the subblocks in the yard blockincreasing gradually that the pairing of service lines becamemore flexible Consequently the space sharing opportunityincreased and the yard operation cost decreased as wellHowever with the decreasing of yard subblocks volume theyard crane service range is limited and such trends willlimit the increase of the yard crane resource demand in theyard When the number of subblocks in the block reaches acertain value the whole container terminal yard area cannotrun normally Accordingly the volume of yard subblock alsoplays an important role in yard management If the value istoo large the sharing space opportunity will decrease andoperation cost will increase However if the value is too smallthe whole system operation pattern will be broken up

Scientific Programming 11

9000092000940009600098000

100000102000104000106000108000

60065070075080085090095010001050

Sharing space (TEUs)Transportation cost (yen)

NSNB=3

NSNB=6

NSNB=5

NSNB=4

Figure 10 Yard subblock size influence of small-scale experiments

1200

1300

1400

1500

1600

1700

1800

1900

2000

200000

205000

210000

215000

220000

225000

230000

235000

Sharing space (TEUs)Transportation cost (yen)

NSNB=3

NSNB=6

NSNB=5

NSNB=4

Figure 11 Yard subblock size influence of medium-scale experi-ments

6 Conclusions

Motivated by the requirement to relieve the operationdilemma for resource-limited container terminal this paperaddressed the integrated yard space allocation and yard cranedeployment problem Two corresponding counterstrategiesare introduced and then an integrated mathematical modelis formulated to solve the problem Numerical experimentsverified the correctness and accuracy of the proposed modelThis study found that space sharing strategy can increase yardspace utilization and yard crane interzone movement strategycan effectively relieve the shortage of YCs In addition aninteresting phenomenon is discovered that there exists atrade-off between yard space utilization and yard operationcost and the volume of yard subblock also plays a significantrole in container port yard management

340000

350000

360000

370000

380000

390000

400000

2000

2200

2400

2600

2800

2900

2100

2300

2500

2700

Sharing space (TEUs)Transportation cost (yen)

NSNB=3

NSNB=6

NSNB=5

NSNB=4

Figure 12 Yard subblock size influence of large-scale experiments

This research can be extended in many relative areas Inthis paper the service line working windows and yard craneefficiency are determined However these parameters mayfluctuate with the factors associated with natural factors andthe equipment operators in reality Therefore the applicationof uncertainty factors in the integratedmanagement problemis a valuable research direction in the future

Competing Interests

The authors declare that they have no competing interests

Authorsrsquo Contributions

All authors contributed equally and significantly to writingthis article

Acknowledgments

This work is sponsored by National Natural Science Founda-tion ofChina (71602114) ldquoChenguangProgramrdquo supported byShanghai Education Development Foundation and ShanghaiMunicipal Education Commission (14CG48) Shanghai Sail-ing Program (14YF1411200) Doctoral Fund of theMinistry ofEducation (20133121110001) Shanghai Municipal EducationCommission Project (14YZ112) Shanghai Science amp Tech-nology Committee Research Project (15590501700) Shang-hai Maritime University Doctoral Innovation Fund Project(2015ycx063) and Shanghai Maritime University DoctoralExcellent Thesis Training Program (2015BXLP006)

References

[1] D Chang Z H JiangW Yan and J He ldquoIntegrating berth allo-cation and quay crane assignmentsrdquo Transportation Research

12 Scientific Programming

Part E LogisticsampTransportation Review vol 46 no 6 pp 975ndash990 2010

[2] J L He D F Chang W J Mi and W Yan ldquoA hybrid parallelgenetic algorithm for yard crane schedulingrdquo TransportationResearch Part E Logistics and Transportation Review vol 46no 1 pp 136ndash155 2010

[3] J G Jin D Lee and J X Cao ldquoStorage yard management inmaritime container terminalsrdquo Transportation Science 2014

[4] C-H Chen and W Yan ldquoEngineering informatics in portoperations and logisticsrdquoAdvanced Engineering Informatics vol25 no 3 pp 401ndash402 2011

[5] C-H Chen L P Khoo Y T Chong and X F Yin ldquoKnowledgediscovery using genetic algorithm for maritime situationalawarenessrdquo Expert Systems with Applications vol 41 no 6 pp2742ndash2753 2014

[6] J He Y Huang and D Chang ldquoSimulation-based heuristicmethod for container supply chain network optimizationrdquoAdvanced Engineering Informatics vol 29 no 3 pp 339ndash3542015

[7] I F A Vis and R De Koster ldquoTransshipment of containersat a container terminal an overviewrdquo European Journal ofOperational Research vol 147 no 1 pp 1ndash16 2003

[8] D Steenken S Voszlig and R Stahlbock ldquoContainer terminaloperation and operations researchmdasha classification and litera-ture reviewrdquo OR Spectrum vol 26 no 1 pp 3ndash49 2004

[9] R Stahlbock and S Voszlig ldquoOperations research at containerterminals a literature updaterdquo Operations Research-Spektrumvol 30 no 1 pp 1ndash52 2008

[10] X Jiang L H Lee E P Chew Y Han and K C Tan ldquoAcontainer yard storage strategy for improving land utilizationand operation efficiency in a transshipment hub portrdquoEuropeanJournal of Operational Research vol 221 no 1 pp 64ndash73 2012

[11] L H Lee E P Chew K C Tan and Y Han ldquoAn optimizationmodel for storage yardmanagement in transshipment hubsrdquoORSpectrum vol 28 no 4 pp 539ndash561 2006

[12] Y Han L H Lee E P Chew and K Tan ldquoA yard storagestrategy forminimizing traffic congestion in amarine containertransshipment hubrdquo OR Spectrum Quantitative Approaches inManagement vol 30 no 4 pp 697ndash720 2008

[13] X Jiang E P Chew L H Lee and K C Tan ldquoFlexible space-sharing strategy for storage yard management in a transship-ment hub portrdquo OR Spectrum vol 35 no 2 pp 417ndash439 2013

[14] L Zhen ldquoContainer yard template planning under uncertainmaritimemarketrdquo Transportation Research Part E Logistics andTransportation Review vol 69 pp 199ndash217 2014

[15] C Zhang Y-W Wan J Liu and R J Linn ldquoDynamiccrane deployment in container storage yardsrdquo TransportationResearch Part B Methodological vol 36 no 6 pp 537ndash5552002

[16] R K Chung C-L Li andW Lin ldquoInterblock crane deploymentin container terminalsrdquoTransportation Science vol 36 no 1 pp79ndash93 2002

[17] R Linn J-Y Liu Y-W Wan C Q Zhang and K G MurtyldquoRubber tired gantry crane deployment for container yardoperationrdquo Computers amp Industrial Engineering vol 45 no 3pp 429ndash442 2003

[18] Z Cao D-H Lee and Q Meng ldquoDeployment strategies ofdouble-rail-mounted gantry crane systems for loading out-bound containers in container terminalsrdquo International Journalof Production Economics vol 115 no 1 pp 221ndash228 2008

[19] K H Kim and H B Kim ldquoThe optimal sizing of the storagespace and handling facilities for import containersrdquoTransporta-tion Research Part B Methodological vol 36 no 9 pp 821ndash8352002

[20] D-H Lee J G Jin and J H Chen ldquoIntegrated bay allocationand yard crane scheduling problem for transshipment contain-ersrdquo Transportation Research Record vol 2222 no 8 pp 63ndash712011

[21] S H Won X Zhang and K H Kim ldquoWorkload-based yard-planning system in container terminalsrdquo Journal of IntelligentManufacturing vol 23 no 6 pp 2193ndash2206 2012

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Scientific Programming 11

9000092000940009600098000

100000102000104000106000108000

60065070075080085090095010001050

Sharing space (TEUs)Transportation cost (yen)

NSNB=3

NSNB=6

NSNB=5

NSNB=4

Figure 10 Yard subblock size influence of small-scale experiments

1200

1300

1400

1500

1600

1700

1800

1900

2000

200000

205000

210000

215000

220000

225000

230000

235000

Sharing space (TEUs)Transportation cost (yen)

NSNB=3

NSNB=6

NSNB=5

NSNB=4

Figure 11 Yard subblock size influence of medium-scale experi-ments

6 Conclusions

Motivated by the requirement to relieve the operationdilemma for resource-limited container terminal this paperaddressed the integrated yard space allocation and yard cranedeployment problem Two corresponding counterstrategiesare introduced and then an integrated mathematical modelis formulated to solve the problem Numerical experimentsverified the correctness and accuracy of the proposed modelThis study found that space sharing strategy can increase yardspace utilization and yard crane interzone movement strategycan effectively relieve the shortage of YCs In addition aninteresting phenomenon is discovered that there exists atrade-off between yard space utilization and yard operationcost and the volume of yard subblock also plays a significantrole in container port yard management

340000

350000

360000

370000

380000

390000

400000

2000

2200

2400

2600

2800

2900

2100

2300

2500

2700

Sharing space (TEUs)Transportation cost (yen)

NSNB=3

NSNB=6

NSNB=5

NSNB=4

Figure 12 Yard subblock size influence of large-scale experiments

This research can be extended in many relative areas Inthis paper the service line working windows and yard craneefficiency are determined However these parameters mayfluctuate with the factors associated with natural factors andthe equipment operators in reality Therefore the applicationof uncertainty factors in the integratedmanagement problemis a valuable research direction in the future

Competing Interests

The authors declare that they have no competing interests

Authorsrsquo Contributions

All authors contributed equally and significantly to writingthis article

Acknowledgments

This work is sponsored by National Natural Science Founda-tion ofChina (71602114) ldquoChenguangProgramrdquo supported byShanghai Education Development Foundation and ShanghaiMunicipal Education Commission (14CG48) Shanghai Sail-ing Program (14YF1411200) Doctoral Fund of theMinistry ofEducation (20133121110001) Shanghai Municipal EducationCommission Project (14YZ112) Shanghai Science amp Tech-nology Committee Research Project (15590501700) Shang-hai Maritime University Doctoral Innovation Fund Project(2015ycx063) and Shanghai Maritime University DoctoralExcellent Thesis Training Program (2015BXLP006)

References

[1] D Chang Z H JiangW Yan and J He ldquoIntegrating berth allo-cation and quay crane assignmentsrdquo Transportation Research

12 Scientific Programming

Part E LogisticsampTransportation Review vol 46 no 6 pp 975ndash990 2010

[2] J L He D F Chang W J Mi and W Yan ldquoA hybrid parallelgenetic algorithm for yard crane schedulingrdquo TransportationResearch Part E Logistics and Transportation Review vol 46no 1 pp 136ndash155 2010

[3] J G Jin D Lee and J X Cao ldquoStorage yard management inmaritime container terminalsrdquo Transportation Science 2014

[4] C-H Chen and W Yan ldquoEngineering informatics in portoperations and logisticsrdquoAdvanced Engineering Informatics vol25 no 3 pp 401ndash402 2011

[5] C-H Chen L P Khoo Y T Chong and X F Yin ldquoKnowledgediscovery using genetic algorithm for maritime situationalawarenessrdquo Expert Systems with Applications vol 41 no 6 pp2742ndash2753 2014

[6] J He Y Huang and D Chang ldquoSimulation-based heuristicmethod for container supply chain network optimizationrdquoAdvanced Engineering Informatics vol 29 no 3 pp 339ndash3542015

[7] I F A Vis and R De Koster ldquoTransshipment of containersat a container terminal an overviewrdquo European Journal ofOperational Research vol 147 no 1 pp 1ndash16 2003

[8] D Steenken S Voszlig and R Stahlbock ldquoContainer terminaloperation and operations researchmdasha classification and litera-ture reviewrdquo OR Spectrum vol 26 no 1 pp 3ndash49 2004

[9] R Stahlbock and S Voszlig ldquoOperations research at containerterminals a literature updaterdquo Operations Research-Spektrumvol 30 no 1 pp 1ndash52 2008

[10] X Jiang L H Lee E P Chew Y Han and K C Tan ldquoAcontainer yard storage strategy for improving land utilizationand operation efficiency in a transshipment hub portrdquoEuropeanJournal of Operational Research vol 221 no 1 pp 64ndash73 2012

[11] L H Lee E P Chew K C Tan and Y Han ldquoAn optimizationmodel for storage yardmanagement in transshipment hubsrdquoORSpectrum vol 28 no 4 pp 539ndash561 2006

[12] Y Han L H Lee E P Chew and K Tan ldquoA yard storagestrategy forminimizing traffic congestion in amarine containertransshipment hubrdquo OR Spectrum Quantitative Approaches inManagement vol 30 no 4 pp 697ndash720 2008

[13] X Jiang E P Chew L H Lee and K C Tan ldquoFlexible space-sharing strategy for storage yard management in a transship-ment hub portrdquo OR Spectrum vol 35 no 2 pp 417ndash439 2013

[14] L Zhen ldquoContainer yard template planning under uncertainmaritimemarketrdquo Transportation Research Part E Logistics andTransportation Review vol 69 pp 199ndash217 2014

[15] C Zhang Y-W Wan J Liu and R J Linn ldquoDynamiccrane deployment in container storage yardsrdquo TransportationResearch Part B Methodological vol 36 no 6 pp 537ndash5552002

[16] R K Chung C-L Li andW Lin ldquoInterblock crane deploymentin container terminalsrdquoTransportation Science vol 36 no 1 pp79ndash93 2002

[17] R Linn J-Y Liu Y-W Wan C Q Zhang and K G MurtyldquoRubber tired gantry crane deployment for container yardoperationrdquo Computers amp Industrial Engineering vol 45 no 3pp 429ndash442 2003

[18] Z Cao D-H Lee and Q Meng ldquoDeployment strategies ofdouble-rail-mounted gantry crane systems for loading out-bound containers in container terminalsrdquo International Journalof Production Economics vol 115 no 1 pp 221ndash228 2008

[19] K H Kim and H B Kim ldquoThe optimal sizing of the storagespace and handling facilities for import containersrdquoTransporta-tion Research Part B Methodological vol 36 no 9 pp 821ndash8352002

[20] D-H Lee J G Jin and J H Chen ldquoIntegrated bay allocationand yard crane scheduling problem for transshipment contain-ersrdquo Transportation Research Record vol 2222 no 8 pp 63ndash712011

[21] S H Won X Zhang and K H Kim ldquoWorkload-based yard-planning system in container terminalsrdquo Journal of IntelligentManufacturing vol 23 no 6 pp 2193ndash2206 2012

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

12 Scientific Programming

Part E LogisticsampTransportation Review vol 46 no 6 pp 975ndash990 2010

[2] J L He D F Chang W J Mi and W Yan ldquoA hybrid parallelgenetic algorithm for yard crane schedulingrdquo TransportationResearch Part E Logistics and Transportation Review vol 46no 1 pp 136ndash155 2010

[3] J G Jin D Lee and J X Cao ldquoStorage yard management inmaritime container terminalsrdquo Transportation Science 2014

[4] C-H Chen and W Yan ldquoEngineering informatics in portoperations and logisticsrdquoAdvanced Engineering Informatics vol25 no 3 pp 401ndash402 2011

[5] C-H Chen L P Khoo Y T Chong and X F Yin ldquoKnowledgediscovery using genetic algorithm for maritime situationalawarenessrdquo Expert Systems with Applications vol 41 no 6 pp2742ndash2753 2014

[6] J He Y Huang and D Chang ldquoSimulation-based heuristicmethod for container supply chain network optimizationrdquoAdvanced Engineering Informatics vol 29 no 3 pp 339ndash3542015

[7] I F A Vis and R De Koster ldquoTransshipment of containersat a container terminal an overviewrdquo European Journal ofOperational Research vol 147 no 1 pp 1ndash16 2003

[8] D Steenken S Voszlig and R Stahlbock ldquoContainer terminaloperation and operations researchmdasha classification and litera-ture reviewrdquo OR Spectrum vol 26 no 1 pp 3ndash49 2004

[9] R Stahlbock and S Voszlig ldquoOperations research at containerterminals a literature updaterdquo Operations Research-Spektrumvol 30 no 1 pp 1ndash52 2008

[10] X Jiang L H Lee E P Chew Y Han and K C Tan ldquoAcontainer yard storage strategy for improving land utilizationand operation efficiency in a transshipment hub portrdquoEuropeanJournal of Operational Research vol 221 no 1 pp 64ndash73 2012

[11] L H Lee E P Chew K C Tan and Y Han ldquoAn optimizationmodel for storage yardmanagement in transshipment hubsrdquoORSpectrum vol 28 no 4 pp 539ndash561 2006

[12] Y Han L H Lee E P Chew and K Tan ldquoA yard storagestrategy forminimizing traffic congestion in amarine containertransshipment hubrdquo OR Spectrum Quantitative Approaches inManagement vol 30 no 4 pp 697ndash720 2008

[13] X Jiang E P Chew L H Lee and K C Tan ldquoFlexible space-sharing strategy for storage yard management in a transship-ment hub portrdquo OR Spectrum vol 35 no 2 pp 417ndash439 2013

[14] L Zhen ldquoContainer yard template planning under uncertainmaritimemarketrdquo Transportation Research Part E Logistics andTransportation Review vol 69 pp 199ndash217 2014

[15] C Zhang Y-W Wan J Liu and R J Linn ldquoDynamiccrane deployment in container storage yardsrdquo TransportationResearch Part B Methodological vol 36 no 6 pp 537ndash5552002

[16] R K Chung C-L Li andW Lin ldquoInterblock crane deploymentin container terminalsrdquoTransportation Science vol 36 no 1 pp79ndash93 2002

[17] R Linn J-Y Liu Y-W Wan C Q Zhang and K G MurtyldquoRubber tired gantry crane deployment for container yardoperationrdquo Computers amp Industrial Engineering vol 45 no 3pp 429ndash442 2003

[18] Z Cao D-H Lee and Q Meng ldquoDeployment strategies ofdouble-rail-mounted gantry crane systems for loading out-bound containers in container terminalsrdquo International Journalof Production Economics vol 115 no 1 pp 221ndash228 2008

[19] K H Kim and H B Kim ldquoThe optimal sizing of the storagespace and handling facilities for import containersrdquoTransporta-tion Research Part B Methodological vol 36 no 9 pp 821ndash8352002

[20] D-H Lee J G Jin and J H Chen ldquoIntegrated bay allocationand yard crane scheduling problem for transshipment contain-ersrdquo Transportation Research Record vol 2222 no 8 pp 63ndash712011

[21] S H Won X Zhang and K H Kim ldquoWorkload-based yard-planning system in container terminalsrdquo Journal of IntelligentManufacturing vol 23 no 6 pp 2193ndash2206 2012

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014