Research Article Hybrid Algorithms for Fuzzy …downloads.hindawi.com/journals/tswj/2014/497109.pdf · Research Article Hybrid Algorithms for Fuzzy Reverse Supply ... the planning

Research ArticleHybrid Algorithms for Fuzzy Reverse SupplyChain Network Design

Z H Che1 Tzu-An Chiang2 Y C Kuo1 and Zhihua Cui34

1 Department of Industrial Engineering and Management National Taipei University of Technology Taipei 10608 Taiwan2Department of Business Administration National Taipei College of Business Taipei 10051 Taiwan3 Complex System and Computational Intelligent Laboratory Taiyuan University of Science and Technology Taiyuan 030024 China4 State Key Laboratory for Novel Software Technology Nanjing University Nanjing 210023 China

Correspondence should be addressed to Z H Che zhchentutedutw

Received 11 October 2013 Accepted 23 December 2013 Published 24 April 2014

Academic Editors J Liu and K Matsumoto

Copyright copy 2014 Z H Che et alThis is an open access article distributed under theCreativeCommonsAttribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

In consideration of capacity constraints fuzzy defect ratio and fuzzy transport loss ratio this paper attempted to establishan optimized decision model for production planning and distribution of a multiphase multiproduct reverse supply chainwhich addresses defects returned to original manufacturers and in addition develops hybrid algorithms such as ParticleSwarm Optimization-Genetic Algorithm (PSO-GA) Genetic Algorithm-Simulated Annealing (GA-SA) and Particle SwarmOptimization-SimulatedAnnealing (PSO-SA) for solving the optimizedmodel During a case study of amulti-phasemulti-productreverse supply chain network this paper explained the suitability of the optimized decision model and the applicability of thealgorithms Finally the hybrid algorithms showed excellent solving capability when compared with original GA and PSOmethods

1 Introduction

Many scholars have been devoted to the study of positivesupply chains for instance [1ndash5] however the reverse supplychain has seldom been involved Dowlatshahi [6] pointedout that reserve logistics which is a new concept in logisticsand supply chainmanagement offer efficient reverse logisticsmanagement that could improve the competitive power ofthe enterprises especially when they face fierce competitionwith low-margin profits Notwithstanding price and qualityas important influential marketing factors within a complexproduct path business operations should focus on howto offer improved after-sale services to customer Settingits target on household appliances and computers in 3C(Computers Communications Consumer Electronics)

Shih [7] discussed the reverse logistics system for end-of-life of products viewing reverse logistics systems as acrucial element of future business operations more effortsshould be made in reutilization rework and recycling atend-of-life [8] reverse logistics is a process of recyclingand refabricating materials [9] reverse logistics is helpfulto protect environments and reduce waste of resources

thus providing an opportunity for the reutilization of prod-ucts Ko and Evans [10] proposed a positive and a reversesupply chain network based on a third partyrsquos logisticsand constructed a mixed-integer nonlinear planning modelof a dynamic integrated distribution network taking intoaccount a two-echelon supply chain network and capacityconstraints underlining the significance of returning thedefective products to the suppliersrsquo partners In addition thedefect ratios and transport loss ratios are fuzzy values in thereal-world supply chain environments Fuzzy defect ratiosand fuzzy transport loss ratios thus are included in thisreverse model for meeting actual conditions

Thus this paper focuses on the reverse supply chain andconstructs an optimized decision model for the selection ofsupply chain partners as well as determination of productionand distribution quantities Multiechelon logistics issuescould be regarded as a Knapsack of a multiple selectionportfolio and resource distribution as a NP-hard issue [11]however the reverse supply chain is more complex in thispaper with production defect ratios transport loss ratios anddesignated reprocessing are considered

Hindawi Publishing Corporatione Scientific World JournalVolume 2014 Article ID 497109 16 pageshttpdxdoiorg1011552014497109

2 The Scientific World Journal

GAs have beenwidely used in solving real-world complexoptimization problems [12ndash16] and Min et al [17] Sha andChe [18] Tsai [19] Ko and Evans [10] Min et al [20]Che and Chiang [21] and Che and Chiang [22] appliedGA to solve the planning issues of a supply chain networkMoreover PSOs also have been widely employed for solvingoptimization problems in different fields and some heuristicalgorithms with similar concept of PSO are developed [23ndash30] Yin and Wang [31] Yu and Fang [32] Chen et al[33] Che and Cui [34] and Che [35] employed a PSO tooptimize a resource distribution system with satisfactoryresults Yet no research efforts were made with respect tothe planning of a reverse supply chain with GA and PSOFor this reason these two heuristic algorithms were used tosolve the reverse supply chain in this paper along with otherthree hybrid algorithms PSO-GA PSO-SA and GA-SAThesolving capability of these five algorithms was compared andthe optimum one was selected as a reference for decision-making

2 Fuzzy Theory

Fuzzy theory first proposed by Zaden in 1965 as an extensionof a general set is a numerical control methodology forimitating human thought and addressing the inaccuracy ofall physical systems According to FuzzyTheory the thoughtlogic of human begins as fuzzy and is intended for judgmenteven if conditions and data are uncertain while moderncomputers feature bipolar logic that is 0 or 1 differentfrom the logic of humans However fuzzy logic theory canrepresent the degree of fuzzy concepts with values between 0and 1 namely ldquomembership functionrdquo

Karkowski [36] indicated that triangular is the mostcommonmembership function in solving possibilistic math-ematical programming problems among the various types ofmembership function Other related studies concerning theuse of triangular fuzzy numbers for decision making prob-lems are [37ndash40] Hence in this paper the defect ratios andtransport loss ratios are denoted by triangular fuzzy numbersThe triangular fuzzy numbers are not compulsory if othertypes of fuzzy numbers are more applicable they can beused

The triangular fuzzy number can be represented as119891 = (119891119897 119891119898 119891119906) where 119891119897 119891119898 and 119891119906 are lower boundmode and upper bound values respectively Figure 1 showsthe triangular possibility distribution of fuzzy number119891

In addition it is essential for practical applications that afuzzy number should be transformed to a numerical valueThe transform process is called ldquodefuzzificationrdquo Associatedordinary number (AON) is a simple method in defuzzifi-cation and many researches have employed it directly andeffectively [41ndash43] In this paper hence the AON is used tofind the crisp value for defect and transport loss ratios TheAONmethod can be expressed as

AON (119891) =119891119897 + 2119891119898 + 119891119906

4 (1)

U(f

)

ffl fm fu

Figure 1 Membership functions of a triangular fuzzy number

3 Problem Formulation and Solving

31 Description and Definition This paper analyzed thereverse distribution activities of defective products in acomplex supply chain network and explored a method offeeding these products back to the manufacturing partnerswith consideration of the capacity constraints of suppliersand the demands of multi-phase multi-product productionand planning Moreover the partners shall be selected basedon total objective functions (minimized production trans-port inspection rework costs and optimized productionquality) in addition the fuzzified production defect ratioand transport loss ratio are taken into account Given thefact of numerous suppliers in a supply chain network withdifferent production characteristics and resource allocationcapabilities covering their capacity and yield it is crucial toselect proper suppliers in a complex supply chain network

Positive logistics are highlighted in a traditional supplychain but unavoidable defects arising from production ortransportation processes are overlooked In practice thedefective products must be returned to the manufacturersRelevant original data in this paper were subjected to 119879-treatment for data integration [44ndash46] Equation (2) is a119879-treatment formula (119883 variable 119883 average SD standarddeviation)

119879 =119883 minus 119883

SD10+ 50 (2)

32 Mathematical Model for Multiphase and MultiproductReverse Supply Chain Themathematical symbols of a reversesupply chain one listed in the Symbols ofMathematicalModelsection

The mathematical model of a multi-phase plan of areverse supply chain is detailed as follows

Minimize [

[

119875

sum119901=1

119868minus1

sum119894=1

119869119894

sum119895=1

119870119894+1

sum119896=1

(PrC(119894119895) times 119883119901

((119894119895)(119894+1119896)))

+119875

sum119901=1

119868

sum119894=1

119869119894

sum119895=1

119870119894+1

sum119896=1

(TrC((119894119895)(119894+1119896))

The Scientific World Journal 3

times (119883119901

((119894119895)(119894+1119896))

+119877119883119901

((119894+1119896)(119894119895))))

+119875

sum119901=1

119868

sum119894=119868

119869119894

sum119895=1

119870119894minus1

sum119896=1

(PrC(119894119895) times 119883119901

((119894minus1119896)(119894119895)))

+119875

sum119901=1

119868

sum119894=1

119869119894

sum119895=1

119870119894+1

sum119896=1

(ChC(119894119895) times 119883119901

((119894119895)(119894+1119896)))]

]

times119875

sum119901=1

119868

sum119894=1

119869119894

sum119895=1

119876119901

(119894119895)

(3)

st119870119894+1

sum119896=1

119883119901

((119894119895)(119894+1119896))

= INT119870119894+1

sum119896=1

119883119901

((119894119895)(119894+1119896))

times (1 minus FTR((119894119895)(119894+1119896))

) + 119877119883119901minus1

((119894+1119896)(119894119895))

119894 = 1 119901 = 1 2 3 119875 119895 = 1 2 3 119869

(4)

119870119894minus1

sum119896=1

119883119901

((119894minus1119896)(119894119895))

= INT[119870119894minus1

sum119896=1

119883119901

((119894minus1119896)(119894119895))times119870119894+1

sum119896=1

(1 minus FTR((119894119895)(119894+1119896))

)]

+

119870119894+1

sum119896=1

119877119883119901minus1

((119894+1119896)(119894119895))minus119870119894minus1

sum119896=1

119877119883119901

((119894119895)(119894minus1119896))

119894 = 2 119868 minus 1 119901 = 1 2 3 119875 119895 = 1 2 3 119869

(5)119870119894minus1

sum119896=1

119883119901

((119894minus1119896)(119894119895))

= INT119870119894minus1

sum119896=1

[119883119901

((119894minus1119896)(119894119895))

times (1 minus FTR((119894119895)(119894minus1119896))

)

minus 119877119883119901

((119894119895)(119894minus1119896))]

119894 = 119868 119901 = 1 2 3 119875 119895 = 1 2 3 119869

(6)

119870119894minus1

sum119896=1

119877119883119901

((119894119895)(119894minus1119896))

= INT(119870119894minus1

sum119896=1

119883119901

((119894minus1119896)(119894119895))

+119870119894+1

sum119896=1

119877119883119901minus1

((119894+1119896)(119894119895))) times FDR

(119894119895)

119894 = 2 3 119868 119901 = 2 3 119875 119895 = 1 2 3 119869

(7)

119883(119894119895)

= INT119870119894+1

sum119896=1

119883119901

((119894119895)(119894+1119896))times (1 minus FDR

(119894119895))

times (1 minus FTR((119894119895)(119894+1119896))

)

119894 = 1 119901 = 1 2 3 119875 119895 = 1 2 3 119869

(8)

119883(119894119895)

= INT119870119894minus1

sum119896=1

119883119901

((119894minus1119896)(119894119895))times (1 minus FDR

(119894119895))

times (1 minus FTR((119894119895)(119894+1119896))

)

119894 = 2 3 119868 minus 1 119901 = 1 2 3 119875

119895 = 1 2 3 119869

(9)

MinCAP(119894119895) le119870119894+1

sum119896=1

119883119901

((119894119895)(119894+1119896))le MaxCAP(119894119895)

119894 = 1 2 119868 minus 1 119901 = 1 2 3 119875 119895 = 1 2 3 119869

(10)

119883119901

((119894119895)(119894+1119896))gt 0 and isin integer forall119894 119895 119896 119901

(11)

119877119883119901

((119894119895)(119894minus1119896))= 0

for 119901 = 0 119894 = 1 2 119868

119895 = 1 2 3 119869 119896 = 1 2 3 119870

(12)

Equation (3) shows objective functions involved in mini-mizing production costs transport costs rework costs checkcosts and quality (quality level 1 is defined as optimumquality and 10 as worst quality) (4) (5) and (6) representquantity transported from the first-hierarchy partner to thesecond-hierarchy partner and finally to the partner of lasthierarchy respectively while the fuzzy transport loss ratioand rework quantity of returned defective products are alsoconsidered (7) represents the rework quantity of defectiveproducts to be returned to the partner of previous hierarchy(8) and (9) indicate that limited production quantities ofpartners from first to last hierarchy shall meet customerdemands (10) indicates that the limited transport quantitywill not be bigger than the maximum capacity nor less thanthe minimum capacity of the partner (11) indicates that thelimited transport quantity must be an integer bigger thanzero and (12) indicates that no defective product is producedin the early phase of multi-product multi-phase productionplanning


33 Proposed Algorithms In this paper GA PSO PSO-GAGA-SA and PSO-SA were applied to determine the bestapproximate solution with minimum objective functions ina reverse supply chain

331 GA Solving Model

Step 1 Develop the structure of chromosome (Figure 2) andthe production and transport quantities were real-codedEiben et al [47] argued that real-coding could accelerate thealgorithm convergence and improve consistency In Figure 2119875(11) rarr 119875(21) represents the transport path from the firstpartner of the first hierarchy to the first partner of the secondhierarchy Gene value is an integral number representing thequantity of partner product transported on the distributionpath

Step 2 Generate a random initial population according tothe final customer demands of the partners restrict thepopulation for meeting the demand constraint (4)sim(12) andthen obtain the Fitness value by substituting the chromosomeinto the objective formula (3)

Step 3 Use Roulette Wheel method to select the chromo-somes Calculate selection probability of every chromosomeof which the chromosomes of better fitness function have ahigher probability

Step 4 Randomly select two chromosomes from the popu-lation for crossover and generate random crossover pointsthen exchange the genes of the chromosome as shown inFigure 3 if the crossover rate is 119909119888 the number of chromo-somes is 119910119888 the crossover quantity is 119909119888 times 119910119888 = 119899119888 a betterefficiency could be achieved if crossover rate is 075sim095 [47]

Step 5 Randomly select a chromosome for mutation with itsposition if the mutation rate is 119909119898 and the number of genesis 119910119898 the mutation number is 119909119898 times 119910119898 = 119899119898 as shown inFigure 4 a higher mutation rate means a higher amplitude amutation rate lt 01 is a typical value [48]

Step 6 When the chromosomes of best offspring are superiorto those of worst population this population will be replacedas a new one

Step 7 Repeat Steps 2 to 6 until the stop conditions aresatisfied

332 PSO Solving Model

Step 1 Set the particle number iteration number maximumspeed learning factor and inertia weight

Step 2 Randomly generate the initial speed and position ofevery particle with the range specified in the constraint (4)sim(12)

Step 3 Substitute the particles of population into the objectivefunction equation (3) to obtain the Pbest of each particle andthe Gbest of the population

Step 4 Update the speed and position of particles usingInertia Weight Method [49] as shown in (13) when 119908ranges between 09 and 12 there is a higher opportunity todetermine a global optimal solution [50] as follows

V119899119894= 119908V119888119894+ 1198881 times rand () times (1199041015840

119894minus 119904119888119894) + 1198882 times rand () times (11990410158401015840

119894minus 119904119888119894)

(13)

119904119899119894= 119904119888119894+ V119899119894 (14)

where V119888119894represents the speed when the particle position is

changed V119899119894is the new speed of particle 119894 119904119888

119894is the current

position of particle 1199041015840119894is the memory value of the individual

best position of particle 119894 11990410158401015840119894is thememory value of the global

best position 119904119899119894is the new position of particle 119894 119908 is inertia

weight rand() is a random variable between (0 1) and 1198881 and1198882 are learning factors

Step 5 Substitute the updated particle position into theconstraint (4)sim(12) review if the updated position meets therequirements of constraints if any particle exceeds the rangeupdate again until all particles meet the requirements ofconstraint (4)sim(12)

Step 6 Compare the particlersquos objective function value withupdated particle position and its Pbest If the objectivefunction value is superior to the Pbest the Pbest of thisparticle will be replaced by its objective function value withupdated particle position

Step 7 Compare the Pbest and Gbest If the best value ofparticle is superior to Gbest the Gbest will be replaced by thebest value of the particle

Step 8 Repeat Steps 2 to 7 until meeting the stop conditionsor reaching the set iteration number

333 PSO-GA Solving Model

Steps 1sim3 Perform Steps 1sim3 of PSO solving model

Step 4 Perform Step 3 of GA solving model to select theparticle positions of better fitness functions stored in thelibraryWith this selectionmechanism there is a higher prob-ability that the particle position of better fitness functionswill become Gbest another new Gbest could be obtainedthrough recombination and the particles could be evaluatedand properly deleted of which the worst individuals arereplaced by optimum individuals after sequencing of fitnessfunctions


Gene cell item

Gene value4660

3793

20519114

893

59

1420

215610

1883855

762721

28512895

00

90

5512821

24143

130

16433

105

P(11)darr darr darr darr darr darr darr darr darr darr darr darr darr darr

P(21)

P(12)

P(21)

P(13)

P(21)

P(14)

P(21)

P(11)

P(22)

P(12)

P(22)

P(13)

P(22)

P(14)

P(22)middot middot middot

middot middot middot

P(31)

P(42)

P(32)

P(42)

P(33)

P(42)

P(31)

P(43)

P(32)

P(43)

P(33)

P(43)43

a

24b

49c

Xa product b product Y

c product Z

Figure 2 Structure of chromosome

Parent 1 Cut point

Gene cell item

Gene value1507481

687914

234139

577622

411552

763790

2010138

Parent 2

Gene cell item

Gene value745641

988678

1269380

802135

338870

501398

162981

Ofspring 1 One point crossover

Gene cell item

Gene value157481

687914

234139

802135

338870

501398

162981

Ofspring 2 Gene cell

item

Gene value745641

988678

1269380

577622

411552

763790

2010138

P(11)darr darr darr darr darr darr darr darr

P(21)

P(12)

P(21)

P(13)

P(21)

P(14)

P(21)

P(11)

P(22)

P(12)

P(22)

P(13)

P(22)

P(14)

P(22)


P(21)

P(12)

P(21)

P(13)

P(21)

P(14)

P(21)

P(11)

P(22)

P(12)

P(22)

P(13)

P(22)

P(14)

P(22)


P(21)

P(12)

P(21)

P(13)

P(21)

P(14) P(11)

P(22)

P(12)

P(22)

P(13)

P(22)

P(14)

P(22)


P(21)

P(12)

P(21)

P(13)

P(21)

P(14)

P(22)

P(22)

P(11)

P(22)

P(12)

P(22)

P(13)

P(22)

P(14)

P(22)

11a

25b

66c

11a

25b

66c

20a

44b

48c

20a

44b

48c


c product Z

Figure 3 Single-point crossover

Step 5 Obtain a new group of good populations using theselection mechanism then perform Steps 1sim3 of PSO solvingmodel and obtain the new Pbest and Gbest

Step 6 Perform Step 5 of GA solving model to randomlyselect mutation particles for single-point mutation and gen-erate a new population

Step 7 Perform Steps 4sim7 of PSO solvingmodel to obtain thenew Pbest and Gbest of the new population

Step 8 Repeat Steps 2 to 7 until stop conditions are met

334 PSO-SA Solving Model


Step 7

Substep 71 Set start temperature (119879start) end temperature(119879end) cooling rate (120572) and length of Markov Chain (119872)

Substep 72 Disturb the updated particle under current tem-perature 119879 and generate a neighboring solution 119896

Substep 73 Calculate the objective function perform distur-bance mechanism under current temperature to generate aneighboring solution 119896 and then substitute it into the objec-tive function equation (5) and calculate its fitness function119891(119883) and the difference of the fitness function Δ119891(119899) =119891(1198831015840)minus119891(119883) Obtain initial solution119883 and through iterationof random disturbances neighboring reasonable solutionsobtain a new solution1198831015840 every particle runs across the lengthof Markov Chain119872 several times at start temperature 119879starta fitness is obtained every time (energy function Δ119891(119899))

Substep 74 Judge if this neighboring solution is acceptedthrough probability function using probability function(15) as shown below and then randomly generate randomnumber 119903 from 0 to 1 as follows

119875 (119899) =

1 if Δ119891 (119899) le 0

exp(minusΔ119891 (119899)

119879) if Δ119891 (119899) gt 0

(15)


Old

Gene cell item

Gene value 115687 1505397 176876 234283 871688 412025 469175 923048

New Mutation operator

Gene cell item

Gene value 207964 1505397 176876 234283 573775 412025 287439 923048


P(21)

P(12)

P(21)

P(13)

P(21)

P(14)

P(21)

P(11)

P(22)

P(12)

P(22)

P(13)

P(22)

P(14)

P(22)


P(21)

P(12)

P(21)

P(13)

P(21)

P(14)

P(21)

P(11)

P(22)

P(12)

P(22)

P(13)

P(22)

P(14)

P(22)

Figure 4 Mutation

Substep 75 Compare random number 119903 with probabilitynumber 119875(119899) if 119903 le 119875(119899) it will disturb the neighboringsolution 119896 replace the particle and its fitness function if119903 gt 119875(119899) it will not replace the particle A new disturbancesolution will generate if not accepted until the termination ofset search times

Substep 76 Repeat Substeps 72ndash75 through Markov Chain(119872) until119872 times and then perform the cooling steps indi-cating that a stable state is reached under this temperature

Substep 77 Implement the cooling procedure at the set-cooling rate of 120572 through a cooling mechanism 119879 = 119879 times 120572

Substep 78 Judge if the cycling is finished through the set endtemperature 119879end if 119879 le 119879end perform the next step if 119879 gt119879end repeat Substeps 72 to 77 until 119879 le 119879end

Step 8 Repeat Steps 2 to 7 until reaching the desired iterationnumber

335 GA-SA Solving Model

Steps 1sim5 Perform Steps 1 to 5 of GA solving model

Step 6 Perform Substeps 71 to 78 of PSO-SA solving model

Step 7 Generate new offspring through genetic evolution ifoptimumfitness function of offspring is superior to that of thepopulation will be replaced as a new one otherwise maintainthe chromosomes of original population for next-generationevolution

Step 8 Repeat Steps 3 to 7 until the set stop conditions aremet

4 Illustrative Example and Results Analysis

41 Case Description In a complex supply chain networkeven a leading manufacturer cannot guarantee 100 yieldduring the production process or prevent any defect duringthe transport process However the defect ratio and loss ratioare not fixed thus fuzzy defect ratio and fuzzy transport lossratio are applied in this paper

Based on a supply chain network of 4-4-3-3 thispaper simulated rework activity of returned defective prod-ucts through a multi-product multi-phase production planAssuming that the initial inventory is zero the defectiveproducts arising from the production process of upstreammanufacturers and from the transport process are returnedto original manufacturers for rework the suppliers of 1stndash4th hierarchy have no fixed production defect ratio ortransport loss ratio meanwhile the multi-product multi-phase production is planned into three phases with defectiveproducts only returned during the second phase Moreoverassuming that the production defect ratio and check costsof the first-hierarchy suppliers are not considered only thedefective products from the partners of 2nd to the 4th arereturned for rework in addition assume that the reworkprocess is the same as the production process then therework costs and production costs are the same Accordingto first-phase production planning 119883 products for finalcustomer requirements amount to 400 350 450 and 119884products amount to 250 150 200 and 119885 products amountto 100 200 and 250 Figure 5 depicts the framework ofa reverse supply chain and relevant parameters includingproduction costs (PrC) transport costs (TrC) check costs(ChC) quality (119876) fuzzy defect ratio (FDR) fuzzy transportloss ratio (FTR) and maximum and minimum capacity(Max CAP andMin CAP) Since the production defect ratioand transport loss ratio are fuzzy sets with triangular fuzzynumber (1) is used for defuzzification For partner 119875(21)its fuzzy number of defect ratio is (06 22 3) then itsFDR is 2 according to (1) For the conciseness of this paperthe detail calculating processes of the production defect andtransport loss ratios for all partners and transport paths arenot presented and their defuzzified values are shown inFigure 5

42 Experimental Results and Analysis PSO GA PSO-GAGA-SA and PSO-SAwere applied for solving the distributionissues of a reverse supply chain network the experimentaldesign was conducted under the parameters of solvingperformance of which every combination of parameters wasimplemented 20 times to determine an optimal combinationas listed in Table 1

It is learnt from Table 1 that the optimal combination ofPSO parameters is particle number 10 generation number1000 maximum speed 125 inertia weight 215 and learningfactor 205 the optimal combination of GA parameters is


Table 1 Combination of experimental parameters

PSO

Population size 10 10 10 10 20 20 20 20Generations 500 500 1000 1000 500 500 1000 1000Max velocity 095 125 095 125 095 125 095 125Initial weight 125 215 125 215 125 215 125 215

1198881 1198882 205 205 205 205 205 205 205 205Avg fitness 24462289 24461153 24460103 24458116 24459087 24460841 24458923 24457531

Avg execution time (sec) 6731 6896 12468 12391 12842 12546 21391 21016Avg convergence time (sec) 4766 4275 8791 8437 7986 8311 17694 16972

GA

Population size 5 5 5 5 10 10 10 10Generations 500 500 1000 1000 500 500 1000 1000Crossover rate 075 08 075 08 075 08 075 08Mutation rate 008 007 008 007 008 007 008 007Avg fitness 24465387 24464085 24462752 24461924 24463297 24463159 244603191 24459450


PSO-GA


1198881 1198882 205 205 205 205 205 205 205 205Mutation rate 008 007 008 007 008 007 008 007Avg fitness 24790482 24692938 24662117 24579829 24507556 24453060 24697893 24662084


GA-SA

Population size 5 5 5 5 10 10 10 10Generations 500 500 1000 1000 500 500 1000 1000Crossover rate 075 08 075 08 075 08 075 08Mutation rate 008 007 008 007 008 007 008 007

Initial temperature 300 300 400 400 300 300 400 400Markov Chain Length 50 50 100 100 50 50 100 100

Cooling rate 09 09 099 099 09 09 099 099Final temperature 1 1 5 5 1 1 5 5

Avg fitness 24459076 24458365 24458351 24458067 24457247 24456391 24457425 24457544Avg execution time (sec) 27477 26041 81462 79039 68671 66993 279145 274338

Avg convergence time (sec) 22374 20768 74744 73412 63467 62522 265074 263862

PSO-SA


1198881 1198882 205 205 205 205 205 205 205 205Initial temperature 300 300 400 400 300 300 400 400

Markov Chain Length 50 50 100 100 50 50 100 100Cooling rate 09 09 099 099 09 09 099 099

Final temperature 1 1 5 5 1 1 5 5Avg fitness 24457588 24457887 24455842 24455147 24455895 24456068 24456457 24456778



First echelon Second echelon Third echelon Fourth echelon

Q 1 Demand

Demand

Demand

LogisticsReverse logistics

723612414134221413312614425222323521422124722621

843222924322112453511641722235133322

Production cost (PrC)

Quality (Q)

Transportation cost (TrC)

Check cost (ChC)

415542653634242414325423322

Fuzzy defective rate (FDR)

MinCAP lt X lt maxCAP

Fuzzy transportation loss ratio (FTR)

PrC 15

50 lt X lt 3500

Q 1PrC 24

70 lt X lt 3300

Q 3PrC 32

40 lt X lt 3400

Q 5PrC 41

30 lt X lt 3300

Q 4

PrC 35

70 lt X lt 4000

Q 1

PrC 18

50 lt X lt 3500

Q 2

PrC 22

80 lt X lt 3300

Q 4

PrC 34

60 lt X lt 3400

Q 4

PrC 30

40 lt X lt 3200

Q 3

PrC 20

30 lt X lt 3600

Q 2

PrC 27

40 lt X lt 3400

Q 3

PrC 45

30 lt X lt 3700

Q 1

PrC 13

50 lt X lt 3600

Q 2

PrC 36

30 lt X lt 3300

P(31) rarr P(41)

P(31) rarr P(42)

P(31) rarr P(43)

P(32) rarr P(41)

P(32) rarr P(42)

P(32) rarr P(43)

P(33) rarr P(41)

P(33) rarr P(42)

P(33) rarr P(43)

P(21) rarr P(31)

P(21) rarr P(32)

P(21) rarr P(33)

P(22) rarr P(31)

P(22) rarr P(32)

P(22) rarr P(33)

P(23) rarr P(31)

P(23) rarr P(32)

P(23) rarr P(33)

P(24) rarr P(31)

P(24) rarr P(32)

P(24) rarr P(33)

P(14) rarr P(21)

P(14) rarr P(22)

P(14) rarr P(23)

P(14) rarr P(24)

P(11) rarr P(21)

P(11) rarr P(22)

P(11) rarr P(23)

P(11) rarr P(23)

P(12) rarr P(21)

P(12) rarr P(22)

P(12) rarr P(23)

P(12) rarr P(24)

P(13) rarr P(21)

P(13) rarr P(22)

P(13) rarr P(23)

P(13) rarr P(24)

TrCFTRChCTrCFTRChCTrCFTRChC

P(41)P(31)P(21)

P(42)P(32)P(22)

P(43)P(33)P(23)

P(24)

P(11)

P(12)

P(13)

P(14)

FDR 2 FDR 5 FDR 1

FDR 3FDR 3FDR 1

FDR 2 FDR 1 FDR 2

FDR 4

Figure 5 4-4-3-3 reverse supply chain network

population number 10 generation number 1000 crossoverrate 08 and mutation rate 007 the optimal combinationof PSO-GA parameters is particle number 20 generationnumber 500 maximum speed 125 inertia weight 215learning factor 205 and mutation rate 007 the optimalcombination of GA-SA parameters is population number 10generation number 500 crossover rate 08mutation rate 007start temperature 300 Markov Chain 50 cooling rate 09

and end temperature 1 the optimal combination of PSO-SAparameters is particle number 10 generation number 1000maximum speed 125 inertia weight 215 learning factor 205start temperature 400 Markov Chain 100 cooling rate 099end temperature 5

To compare the advantages and disadvantages of thesealgorithms ANOVA was used to judge if convergence valueexecution time and convergence time differed considerably


Table 2 ANOVA verification of fitness values

HypothesizeH0

Fitness120583PSO = Fitness120583GA = Fitness120583PSO-GA = Fitness120583GA-SA = Fitness120583PSO-SA

H1 otherwiseAlgorithm Numbers Sum Average VariancePSO 30 734139577 2447131923 1120394034GA 30 734406462 244802154 910941494PSO-GA 30 733498321 2444994403 1372449396GA-SA 30 733929774 244643258 752499584PSO-SA 30 733666393 2445554643 3467767352Source SS Freedom MS 119865 119875 value Critical valueIntergroup 176119864 + 10 4 4389633912 287880644 002486 2434065Intragroup 221119864 + 11 145 1524810372Sum 239119864 + 11 149

Result reject H0

Table 3 ANOVA verification of execution time

HypothesizeH0

ET120583PSO = ET120583GA = ET120583PSO-GA = ET120583GA-SA = ET120583PSO-SA

H1 otherwiseAlgorithm Numbers Sum Average VariancePSO 30 372022 1240073 0076341375GA 30 6524661 2174887 0165604217PSO-GA 30 380424 126808 0076438303GA-SA 30 2004847 6682823 0187643495PSO-SA 30 775495 2584983 0192059868Source SS Freedom MS 119865 119875 value Critical valueIntergroup 9081557 4 2270389 1626150094 000000 2434065Intragroup 2024453 145 0139617Sum 908176 149

Result reject H0

Table 4 ANOVA verification of convergence time

HypothesizeH0

CT120583PSO = CT120583GA = CT120583PSO-GA = CT120583GA-SA = CT120583PSO-SA

H1 otherwiseAlgorithm Numbers Sum Average VariancePSO 30 246605 8220167 00913266GA 30 6375408 2125136 07256669PSO-GA 30 171189 57063 0014925GA-SA 30 1863747 621249 04336888PSO-SA 30 326895 108965 02385541Source SS Freedom MS 119865 119875 value Critical valueIntergroup 939149 4 2347872 78045896 000000 2434065Intragroup 4362068 145 0300832Sum 123119864 + 09 89

Result reject H0


Table 5 Multiple comparison on fitness valueFitness120583PSO

Fitness120583GAFitness120583PSO-GA

Fitness120583GA-SAFitness120583GA (minus +)Fitness120583PSO-GA (+ +) (+ +)Fitness120583GA-SA (+ +) (+ +) (minus +)Fitness120583PSO-SA (+ +) (+ +) (minus +) (minus +)

Table 6 Multiple comparison on execution timeET120583PSO

ET120583GAET120583PSO-GA

ET120583GA-SAET120583GA (minus minus)ET120583PSO-GA (minus minus) (+ +)ET120583GA-SA (minus minus) (+ +) (minus minus)ET120583PSO-SA (minus minus) (+ +) (minus minus) (+ +)

Table 7 Multiple comparison on convergence timeCT120583PSO

CT120583GACT120583PSO-GA

CT120583GA-SACT120583GA (minus minus)CT120583PSO-GA (+ +) (+ +)CT120583GA-SA (minus minus) (+ +) (minus minus)CT120583PSO-SA (minus minus) (+ +) (minus minus) (+ +)

then the algorithms were compared using Scheffersquos multiplecomparison method [51] one-way ANOVA was used tocheck the difference of characteristics and variables [52]Scheffersquos multiple comparison method was then used tocheck the differences of the various groups and whether thedifferences reached a significant level Tables 2 3 and 4 listthe comparative check data of the five algorithms which weresourced from 30 occasions of independent calculations forthe optimal combination of parameters

In Tables 2ndash4 the results of ANOVA verification areshown that all H0 are rejected (119875 value lt 120572 = 005)Then the fitness value execution time and convergence timeof the algorithms were compared using Scheffersquos multiplecomparison method with Scheffersquos equation as follows

119909119894 minus 119909119895 minus radic(119896 minus 1) 119865120572(119896minus1)(119899minus119896)radicMSE( 1

119899119894+1

119899119895)

119909119894 minus 119909119895 + radic(119896 minus 1) 119865120572(119896minus1)(119899minus119896)radicMSE( 1

119899119894+1

119899119895)

(16)

where 119909119894 119909119895 are the mean values of algorithms compared 119896 isgroup freedom119865120572(119896minus1)(119899minus119896) is critical valueMSE is intergroupMS 119899119894 119899119895 is number of samples

Table 5 shows Fitness120583PSO-GA = Fitness120583GA-SA =Fitness120583PSO-SA lt Fitness120583PSO = Fitness120583GA that is PSO-GA GA-SA and PSO-SA are all better than PSO andGA and there are no clear differences in the fitnessvalues of the three algorithms The comparative resultof system execution time is shown in Table 6 and

ET120583PSO lt ET120583PSO-GA lt ET120583PSO-SA lt ET120583GA-SA lt ET120583GAis the PSO is superior to other solving models Theconvergence times of the algorithms are shown in Table 7and CT120583PSO-GA lt CT120583PSO lt CT120583PSO-SA lt CT120583GA-SA lt CT120583GAPSO-GA lt PSO lt PSO-SA lt GA-SA lt GA that is PSO-GAhas faster convergence speed than PSO PSO-SA GA-SAand GA The results show that PSO-GA performs better infitness value execution time and convergence time Thenthe PSO-GA is employed to make the distribution plan ofthree periods reverse supply chain and the results are shownin Tables 8 9 and 10

5 Conclusions

This paper focused on analyzing the issues of returningdefective products to original manufacturers in a reversesupply chain system Fuzzy defect and fuzzy transport lossratios were considered and an optimized mathematicalmodel was developedThis model combined cost and qualitywithT-technology and described how to plan a reverse supplychain on the precondition of meeting customer demandsand realizing the capacity of partners To solve the problemsefficiently three hybrid algorithms were applied to thisreverse model including PSO-GA PSO-SA and GA-SAthen the performances of these algorithms were comparedThe experimental results show that if the fitness valueexecution time and convergence time are considered PSO-GA has the minimal value which means that PSO-GA hasthe qualities and capabilities for dealing with the productionplanning and distribution of a multi-phase multi-productreverse supply chain


Table8Distrib

utionplan

byPS

O-G

A(firstp

eriod)

From

ToEchelon2

Echelon3

Echelon4

119875(21)

119875(22)

119875(23)

119875(24)

119875(31)

119875(32)

119875(33)

119875(41)

119875(42)

119875(43)

Echelon1

119875(11)

10a 6b49c

7336

4211059

242535

119875(12)

142474

1742633

34182

10210234

119875(13)

1572457

256381

72956

221155

119875(14)

74396

761721

31813

74141

Echelon2

119875(21)

177383

11680

8210325

119875(22)

458237

1091417

8676

119875(23)

5310060

4133

175865

119875(24)

1112369

1029244

921130

Echelon3

119875(31)

17000

1000174

910255

119875(32)

9500

4700

12300

119875(33)

139253101

21315532

2452040

a Produ

ctX

b produ

ctY

c produ

ctZ


Table9Distrib

utionplan

byPS

O-G

A(secon

dperio

d)

From

ToEchelon1

Echelon2

Echelon3

Echelon4

119875(11)

119875(12)

119875(13)

119875(14)

119875(21)

119875(22)

119875(23)

119875(24)

119875(31)

119875(32)

119875(33)

119875(41)

119875(42)

119875(43)

Echelon1

119875(11)

1007612

694880

6134947

18550

119875(12)

341922

0270

2145047

911014

119875(13)

9533495

1311351

81740

285126

119875(14)

111110

1215100

9910

125215

Reverse

Echelon2

119875(21)

000

300

300

122

13032067

1892759

10850

119875(22)

200

400

600

221

15537213

523817

0290

119875(23)

100

100

000

122

82344

12

12362108

819410

119875(24)

000

100

000

183

55051

13970

556390

Reverse

Echelon3119875(31)

600

1500

200

4137

413030

1343610

11700

119875(32)

300

300

100

013

13000

12100

603960

119875(33)

200

000

000

26

32260151

1430304

646150

Reverse

Echelon4119875(41)

300

200

231

119875(42)

400

200

885

119875(43)

300

400

76

3Dem

and

400300150

400350300

25040

0150


Table10D

istrib

utionplan

byPS

O-G

A(th

irdperio

d)

From

ToEchelon1

Echelon2

Echelon3

Echelon4

119875(11)

119875(12)

119875(13)

119875(14)

119875(21)

119875(22)

119875(23)

119875(24)

119875(31)

119875(32)

119875(33)

119875(41)

119875(42)

119875(43)

Echelon1

119875(11)

86184

40615108

301253

248313

119875(12)

346036

137628

1651376

3515930

119875(13)

2724

301217

471160

278285

119875(14)

56010

7831

8610222

174698

Reverse

Echelon2

119875(21)

200

100

200

293

26915

332349

1135511

119875(22)

200

000

400

014

430362

3727318

10504

119875(23)

100

300

000

092

21728238

82238

93646

119875(24)

000

100

000

223

216061

2218348

9910412

Reverse

Echelon3119875(31)

500

600

300

22712

1900354

21300

580193

119875(32)

500

100

300

357

932530

16500

11300

119875(33)

000

000

200

272

16600

12330287

230246

Reverse

Echelon4119875(41)

100

200

36

2119875(42)

500

400

5716

119875(43)

300

200

2175

Dem

and

450250350

500300100

400200200


Symbols of Mathematical Model

119899 Number of products 119899 = 1 2 3 119873119873 Total number119894 Hierarchy of supply chain 119894 = 1 2 3 119868119868 Total number of hierarchy of supply chain119901 Production phase 119905 = 1 2 3 119879119875 Total production phase119869119894 Serial number of partner of 119894th hierarchy119870119894 Serial number of partner of 119894th hierarchy

designated to original manufacturerChC(119894119895) Check cost of 119895th partner of 119894th hierarchyPrC(119894119895) Production cost of 119895th partner of 119894th

hierarchyTrC((119894119895)(119894+1119896)) Transport cost from 119895th partner of 119894th

hierarchy to original (designated) partner119896 of 119894 + 1 hierarchy

FTR((119894119895)(119894+1119896))

Fuzzy transport loss ratio from 119895th partnerof 119894th hierarchy to original (designated)partner of 119894 + 1 hierarchy

FDR(119894119895)

Fuzzy defect ratio of 119895th partner of 119894thhierarchy

119883119901

(119894119895) Production quantity of 119895th partner of 119894th

hierarchy at phase 119901119883119875((119894119895)(119894+1119896))

Transport quantity from 119895th partner of 119894thhierarchy at phase 119901 to original(designated) partner of 119894 + 1 hierarchy

119877119883119875minus1((119894+1119896)(119894119895))

Quantity of defective products transportedfrom 119895th partner of 119894th hierarchy at phase119901 minus 1 back to original (designated) partnerof 119894 + 1 hierarchy

MaxCAP(119894119895) Maximum capacity of 119895th partner of 119894thhierarchy

MinCAP(119894119895) Minimum capacity of 119895th partner of 119894thhierarchy

119876119901

(119894119895) Quality level of 119895th partner of 119894th

hierarchy at phase 119901ChC(119894119895) Check cost of 119895th partner of 119894th hierarchyPrC(119894119895) Production cost of 119895th partner of 119894th



SD119876(119894119895)

Standard deviation of quality of 119895thpartner of 119894th hierarchy

SDChC(119894119895)

Standard deviation of check cost of 119895thpartner of 119894th hierarchy

SDPrC(119894119895)

Standard deviation of production cost of119895th partner of 119894th hierarchy

SDTrC((119894119895)(119894+1119896))

Standard deviation of transport cost from119895th partner of 119894th hierarchy to original(designated) partner 119896 of 119894 + 1 hierarchy

INT Integer

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors would like to thank Mr K Hsiao for supportingwriting programs and theNational ScienceCouncil of Taiwanfor their partial financial support (Grants nos NSC 102-2410-H-027-009 and NSC 101-2410-H-027-006) The authorswould also like to acknowledge the editors and anonymousreviewers for their helpful comments and suggestions whichgreatly improved the presentation of this paper

References

[1] G Desbarats ldquoThe innovation supply chainrdquo Supply ChainManagement vol 4 no 1 pp 7ndash10 1999

[2] S M Disney M M Naim and A Potter ldquoAssessing the impactof e-business on supply chain dynamicsrdquo International Journalof Production Economics vol 89 no 2 pp 109ndash118 2004

[3] T M Simatupang and R Sridharan ldquoThe collaboration indexa measure for supply chain collaborationrdquo International Journalof Physical Distribution and Logistics Management vol 35 no 1pp 44ndash62 2005

[4] D Y Sha and Z H Che ldquoVirtual integration with a multi-criteria partner selectionmodel for themulti-echelonmanufac-turing systemrdquo International Journal of Advanced Manufactur-ing Technology vol 25 no 7-8 pp 793ndash802 2005

[5] M Tuominen and M Anttila ldquoStrategising for innovationand inter-firm collaboration capability analysis in assessingcompetitive superiorityrdquo International Journal of TechnologyManagement vol 33 no 2-3 pp 214ndash233 2006

[6] S Dowlatshahi ldquoDeveloping a theory of reverse logisticsrdquoInterfaces vol 30 no 3 pp 143ndash155 2000

[7] L-H Shih ldquoReverse logistics system planning for recyclingelectrical appliances and computers in Taiwanrdquo ResourcesConservation and Recycling vol 32 no 1 pp 55ndash72 2001

[8] ADesai andAMital ldquoEvaluation of disassemblability to enabledesign for disassembly in mass productionrdquo International Jour-nal of Industrial Ergonomics vol 32 no 4 pp 265ndash281 2003

[9] I Dobos ldquoOptimal production-inventory strategies for aHMMS-type reverse logistics systemrdquo International Journal ofProduction Economics vol 81-82 pp 351ndash360 2003

[10] H J Ko and G W Evans ldquoA genetic algorithm-based heuristicfor the dynamic integrated forwardreverse logistics networkfor 3PLsrdquoComputers and Operations Research vol 34 no 2 pp346ndash366 2007

[11] M Gen and R Cheng Genetic Algorithms and EngineeringDesign John Wiley amp Sons New York NY USA 1997

[12] B Stojanovic M Milivojevic M Ivanovic N Milivojevicand D Divac ldquoAdaptive system for dam behavior modelingbased on linear regression and genetic algorithmsrdquo Advances inEngineering Software vol 65 pp 182ndash190 2013

[13] R Belevicius D Jatulis and D Sesok ldquoOptimization of tallguyed masts using genetic algorithmsrdquo Engineering Structuresvol 56 pp 239ndash245 2013

[14] D S Hong andH S Cho ldquoA genetic-algorithm-based approachto the generation of robotic assembly sequencesrdquo ControlEngineering Practice vol 7 no 2 pp 151ndash159 1999

[15] L Ozdamar ldquoA genetic algorithm approach to a generalcategory project scheduling problemrdquo IEEE Transactions onSystems Man and Cybernetics C vol 29 no 1 pp 44ndash59 1999

[16] M F Sebaaly and H Fujimoto ldquoGenetic planner for assemblyautomationrdquo inProceedings of the IEEE International Conference


on Evolutionary Computation (ICECrsquo96) pp 401ndash406 May1996

[17] H Min C S Ko and H J Ko ldquoThe spatial and temporalconsolidation of returned products in a closed-loop supplychain networkrdquo Computers and Industrial Engineering vol 51no 2 pp 309ndash320 2006

[18] D Y Sha and Z H Che ldquoSupply chain network designpartner selection and productiondistribution planning using asystematic modelrdquo Journal of the Operational Research Societyvol 57 no 1 pp 52ndash62 2006

[19] C-F Tsai ldquoAn intelligent adaptive system for the optimalvariable selections of RampD and quality supply chainsrdquo ExpertSystems with Applications vol 31 no 4 pp 808ndash825 2006

[20] H Min H J Ko and C S Ko ldquoA genetic algorithm approachto developing the multi-echelon reverse logistics network forproduct returnsrdquo Omega vol 34 no 1 pp 56ndash69 2006

[21] Z H Che and C J Chiang ldquoA modified Pareto genetic algo-rithm for multi-objective build-to-order supply chain planningwith product assemblyrdquo Advances in Engineering Software vol41 no 7-8 pp 1011ndash1022 2010

[22] Z H Che and T A Chiang ldquoDesigning a collaborative supplychain plan using the analytic hierarchy process and geneticalgorithm with cycle time estimationrdquo International Journal ofProduction Research vol 50 no 16 pp 4426ndash4443 2012

[23] Z H Che ldquoPSO-based back-propagation artificial neural net-work for product and mold cost estimation of plastic injectionmoldingrdquo Computers and Industrial Engineering vol 58 no 4pp 625ndash637 2010

[24] E Garcıa-Gonzalo and J L Fernandez-Martınez ldquoA briefhistorical review of particle swarmoptimization (PSO)rdquo Journalof Bioinformatics and Intelligent Control vol 1 no 1 pp 3ndash162012

[25] L Ali and S L Sabat ldquoParticle swarm optimization based uni-versal solver for global optimizationrdquo Journal of Bioinformaticsand Intelligent Control vol 1 no 1 pp 95ndash105 2012

[26] R K Sahu S Panda U K Rout and P Raul ldquoApplicationof gravitational search algorithm for load frequency controlof multi area power systemrdquo Journal of Bioinformatics andIntelligent Control vol 2 no 3 pp 200ndash210 2013

[27] A S Reddy and K Vaisakh ldquoEnvironmental constrained eco-nomic dispatch by modified shuffled frog leaping algorithmrdquoJournal of Bioinformatics and Intelligent Control vol 2 no 3pp 216ndash222 2013

[28] L P Xie J C Zeng and R A Formato ldquoSelection strategies forgravitational constant G in artificial physics optimisation basedon analysis of convergence propertiesrdquo International Journal ofBio-Inspired Computation vol 4 no 6 pp 380ndash391 2012

[29] X J Cai S J Fan and Y Tan ldquoLight responsive curve selectionfor photosynthesis operator of APOArdquo International Journal ofBio-Inspired Computation vol 4 no 6 pp 373ndash379 2012

[30] K Agarwal M Goyal and P R Srivastava ldquoCode coverageusing intelligent water drop (IWD)rdquo International Journal ofBio-Inspired Computation vol 4 no 6 pp 392ndash402 2012

[31] P-Y Yin and J-Y Wang ldquoA particle swarm optimizationapproach to the nonlinear resource allocation problemrdquoAppliedMathematics and Computation vol 183 no 1 pp 232ndash2422006

[32] J X Yu and X Y Fang ldquoDynamic reactive power optimizationbased on particle swam optimization algorithmrdquo East ChinaElectric Power vol 34 no 11 pp 21ndash25 2006

[33] Y H Chen W J Wang and C H Chiu ldquoParticle swarmoptimization algorithm and its application to power systemrdquoHenan Science vol 25 no 1 pp 29ndash32 2007

[34] Z H Che and Z Cui ldquoUnbalanced supply chain design usingthe analytic network process and a hybrid heuristic-basedalgorithm with balance modulating mechanismrdquo InternationalJournal of Bio-Inspired Computation vol 3 no 1 pp 56ndash662011

[35] Z H Che ldquoA particle swarm optimization algorithm for solvingunbalanced supply chain planning problemsrdquo Applied SoftComputing Journal vol 12 no 4 pp 1279ndash1287 2012

[36] I Karkowski ldquoArchitectural synthesis with possibilistic pro-grammingrdquo in Proceedings of the 28th Annual Hawaii Interna-tional Conference on System Sciences vol 1 pp 14ndash22 1995

[37] R E Giachetti and R E Young ldquoA parametric representation offuzzy numbers and their arithmetic operatorsrdquo Fuzzy Sets andSystems vol 91 no 2 pp 185ndash202 1997

[38] J H Moon and C S Kang ldquoApplication of fuzzy decisionmaking method to the evaluation of spent fuel storage optionsrdquoProgress in Nuclear Energy vol 39 no 3-4 pp 345ndash351 2001

[39] J K Cochran and H-N Chen ldquoFuzzy multi-criteria selectionof object-oriented simulation software for production systemanalysisrdquo Computers and Operations Research vol 32 no 1 pp153ndash168 2005

[40] H K Chiou and G H Tzeng ldquoFuzzy hierarchical evaluationwith grey relation model of green engineering for industryrdquoInternational of Fuzzy System vol 3 pp 466ndash475 2001

[41] Y Tsujimura S Chang andM Gen ldquoEffectivemethod for largescale project planning with multiple fuzzy activity timesrdquo inProceedings of the 2nd IEEE International Conference on FuzzySystems pp 1009ndash1015 April 1993

[42] J G Greenhut G Norman and C Temponi ldquoToward afuzzy theory of oligopolistic competitionrdquo in Proceedings ofthe 3rd International Symposium on Uncertainty Modeling andAnalysis and Annual Conference of the North American FuzzyInformation Processing Society (ISUMA-NAFIPSrsquo95) pp 286ndash291 September 1995

[43] S Petrovic andC Fayad ldquoA fuzzy shifting bottleneck hybridisedwith genetic algorithm for real-world job shop schedulingrdquo inProceedings of the Mini-EURO Conference Managing Uncer-tainty in Decision SupportModels C H Antunes and L C DiasEds pp 1ndash6 Coimbra Portugal 2004

[44] G C Huang and P k Wu ldquoThe Development of a standard-ized mathematics Achievement test for seventh graders andits related study analyzed with IRTrdquo Journal of EducationalResearch and Development vol 2 pp 109ndash142 2006

[45] H S Wang and Z H Che ldquoAn integrated model for supplierselection decisions in configuration changesrdquo Expert Systemswith Applications vol 32 no 4 pp 1132ndash1140 2007

[46] M Y Liou and C M Lu ldquoApplication of the transtheoreticalmodel to smoking behavior among freshmenrdquo Journal of HealthEducation vol 24 pp 47ndash70 2005

[47] A E Eiben R Hinterding and Z Michalewicz ldquoParametercontrol in evolutionary algorithmsrdquo IEEE Transactions onEvolutionary Computation vol 3 no 2 pp 124ndash141 1999

[48] W D Kelton R P Sadowski and D A Sadowski Simulationwith ARENA McGraw-Hill New York NY USA 1998

[49] Y Shi and R C Eberhart ldquoComparison between geneticalgorithms and particle swarm optimizationrdquo in Proceedings ofthe 7th International Conference on Evolutionary ProgrammingVII vol 1447 pp 611ndash616 1998


[50] Y Shi and R Eberhart ldquoModified particle swarm optimizerrdquoin Proceedings of the 1998 IEEE International Conference onEvolutionary Computation (ICECrsquo98) pp 69ndash73 May 1998

[51] H Schee ldquoA method for judging all contrasts in the analysis ofvariancerdquo Biometrica vol 40 no 1-2 pp 87ndash104 1953

[52] C C Shen and C Y Hsieh ldquoA study on the relationship amongattraction tourist satisfaction and loyalty of religious tourisma case of Fo Guang Shan in Kaohsiungrdquo Tourism ManagementResearch vol 3 no 1 pp 79ndash95 2003

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

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Distributed Sensor Networks


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ReconfigurableComputing

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Applied Computational Intelligence and Soft Computing

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Artificial Intelligence

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Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014


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Advances in

Computer EngineeringAdvances in



GAs have beenwidely used in solving real-world complexoptimization problems [12ndash16] and Min et al [17] Sha andChe [18] Tsai [19] Ko and Evans [10] Min et al [20]Che and Chiang [21] and Che and Chiang [22] appliedGA to solve the planning issues of a supply chain networkMoreover PSOs also have been widely employed for solvingoptimization problems in different fields and some heuristicalgorithms with similar concept of PSO are developed [23ndash30] Yin and Wang [31] Yu and Fang [32] Chen et al[33] Che and Cui [34] and Che [35] employed a PSO tooptimize a resource distribution system with satisfactoryresults Yet no research efforts were made with respect tothe planning of a reverse supply chain with GA and PSOFor this reason these two heuristic algorithms were used tosolve the reverse supply chain in this paper along with otherthree hybrid algorithms PSO-GA PSO-SA and GA-SAThesolving capability of these five algorithms was compared andthe optimum one was selected as a reference for decision-making

2 Fuzzy Theory

Fuzzy theory first proposed by Zaden in 1965 as an extensionof a general set is a numerical control methodology forimitating human thought and addressing the inaccuracy ofall physical systems According to FuzzyTheory the thoughtlogic of human begins as fuzzy and is intended for judgmenteven if conditions and data are uncertain while moderncomputers feature bipolar logic that is 0 or 1 differentfrom the logic of humans However fuzzy logic theory canrepresent the degree of fuzzy concepts with values between 0and 1 namely ldquomembership functionrdquo

Karkowski [36] indicated that triangular is the mostcommonmembership function in solving possibilistic math-ematical programming problems among the various types ofmembership function Other related studies concerning theuse of triangular fuzzy numbers for decision making prob-lems are [37ndash40] Hence in this paper the defect ratios andtransport loss ratios are denoted by triangular fuzzy numbersThe triangular fuzzy numbers are not compulsory if othertypes of fuzzy numbers are more applicable they can beused

The triangular fuzzy number can be represented as119891 = (119891119897 119891119898 119891119906) where 119891119897 119891119898 and 119891119906 are lower boundmode and upper bound values respectively Figure 1 showsthe triangular possibility distribution of fuzzy number119891

In addition it is essential for practical applications that afuzzy number should be transformed to a numerical valueThe transform process is called ldquodefuzzificationrdquo Associatedordinary number (AON) is a simple method in defuzzifi-cation and many researches have employed it directly andeffectively [41ndash43] In this paper hence the AON is used tofind the crisp value for defect and transport loss ratios TheAONmethod can be expressed as

AON (119891) =119891119897 + 2119891119898 + 119891119906

4 (1)

U(f

)

ffl fm fu

Figure 1 Membership functions of a triangular fuzzy number

3 Problem Formulation and Solving

31 Description and Definition This paper analyzed thereverse distribution activities of defective products in acomplex supply chain network and explored a method offeeding these products back to the manufacturing partnerswith consideration of the capacity constraints of suppliersand the demands of multi-phase multi-product productionand planning Moreover the partners shall be selected basedon total objective functions (minimized production trans-port inspection rework costs and optimized productionquality) in addition the fuzzified production defect ratioand transport loss ratio are taken into account Given thefact of numerous suppliers in a supply chain network withdifferent production characteristics and resource allocationcapabilities covering their capacity and yield it is crucial toselect proper suppliers in a complex supply chain network

Positive logistics are highlighted in a traditional supplychain but unavoidable defects arising from production ortransportation processes are overlooked In practice thedefective products must be returned to the manufacturersRelevant original data in this paper were subjected to 119879-treatment for data integration [44ndash46] Equation (2) is a119879-treatment formula (119883 variable 119883 average SD standarddeviation)

119879 =119883 minus 119883

SD10+ 50 (2)

32 Mathematical Model for Multiphase and MultiproductReverse Supply Chain Themathematical symbols of a reversesupply chain one listed in the Symbols ofMathematicalModelsection

The mathematical model of a multi-phase plan of areverse supply chain is detailed as follows

Minimize [

[

119875

sum119901=1

119868minus1

sum119894=1

119869119894

sum119895=1

119870119894+1

sum119896=1

(PrC(119894119895) times 119883119901

((119894119895)(119894+1119896)))

+119875

sum119901=1

119868

sum119894=1

119869119894

sum119895=1

119870119894+1

sum119896=1

(TrC((119894119895)(119894+1119896))


times (119883119901

((119894119895)(119894+1119896))

+119877119883119901

((119894+1119896)(119894119895))))

+119875

sum119901=1

119868

sum119894=119868

119869119894

sum119895=1

119870119894minus1

sum119896=1

(PrC(119894119895) times 119883119901

((119894minus1119896)(119894119895)))

+119875

sum119901=1

119868

sum119894=1

119869119894

sum119895=1

119870119894+1

sum119896=1

(ChC(119894119895) times 119883119901

((119894119895)(119894+1119896)))]

]

times119875

sum119901=1

119868

sum119894=1

119869119894

sum119895=1

119876119901

(119894119895)

(3)

st119870119894+1

sum119896=1

119883119901

((119894119895)(119894+1119896))

= INT119870119894+1

sum119896=1

119883119901

((119894119895)(119894+1119896))

times (1 minus FTR((119894119895)(119894+1119896))

) + 119877119883119901minus1

((119894+1119896)(119894119895))

119894 = 1 119901 = 1 2 3 119875 119895 = 1 2 3 119869

(4)

119870119894minus1

sum119896=1

119883119901

((119894minus1119896)(119894119895))

= INT[119870119894minus1

sum119896=1

119883119901

((119894minus1119896)(119894119895))times119870119894+1

sum119896=1

(1 minus FTR((119894119895)(119894+1119896))

)]

+

119870119894+1

sum119896=1

119877119883119901minus1

((119894+1119896)(119894119895))minus119870119894minus1

sum119896=1

119877119883119901

((119894119895)(119894minus1119896))

119894 = 2 119868 minus 1 119901 = 1 2 3 119875 119895 = 1 2 3 119869

(5)119870119894minus1

sum119896=1

119883119901

((119894minus1119896)(119894119895))

= INT119870119894minus1

sum119896=1

[119883119901

((119894minus1119896)(119894119895))


)

minus 119877119883119901

((119894119895)(119894minus1119896))]

119894 = 119868 119901 = 1 2 3 119875 119895 = 1 2 3 119869

(6)

119870119894minus1

sum119896=1

119877119883119901

((119894119895)(119894minus1119896))

= INT(119870119894minus1

sum119896=1

119883119901

((119894minus1119896)(119894119895))

+119870119894+1

sum119896=1

119877119883119901minus1

((119894+1119896)(119894119895))) times FDR

(119894119895)

119894 = 2 3 119868 119901 = 2 3 119875 119895 = 1 2 3 119869

(7)

119883(119894119895)

= INT119870119894+1

sum119896=1

119883119901

((119894119895)(119894+1119896))times (1 minus FDR

(119894119895))

times (1 minus FTR((119894119895)(119894+1119896))

)

119894 = 1 119901 = 1 2 3 119875 119895 = 1 2 3 119869

(8)

119883(119894119895)

= INT119870119894minus1

sum119896=1

119883119901


(119894119895))

times (1 minus FTR((119894119895)(119894+1119896))

)

119894 = 2 3 119868 minus 1 119901 = 1 2 3 119875

119895 = 1 2 3 119869

(9)

MinCAP(119894119895) le119870119894+1

sum119896=1

119883119901

((119894119895)(119894+1119896))le MaxCAP(119894119895)

119894 = 1 2 119868 minus 1 119901 = 1 2 3 119875 119895 = 1 2 3 119869

(10)

119883119901


(11)

119877119883119901

((119894119895)(119894minus1119896))= 0

for 119901 = 0 119894 = 1 2 119868

119895 = 1 2 3 119869 119896 = 1 2 3 119870

(12)



















119894minus 119904119888119894)

(13)

119904119899119894= 119904119888119894+ V119899119894 (14)
















Gene cell item

Gene value4660

3793

20519114

893

59

1420

215610

1883855

762721

28512895

00

90

5512821

24143

130

16433

105


P(21)

P(12)

P(21)

P(13)

P(21)

P(14)

P(21)

P(11)

P(22)

P(12)

P(22)

P(13)

P(22)

P(14)



P(31)

P(42)

P(32)

P(42)

P(33)

P(42)

P(31)

P(43)

P(32)

P(43)

P(33)

P(43)43

a

24b

49c


c product Z


Parent 1 Cut point

Gene cell item

Gene value1507481

687914

234139

577622

411552

763790

2010138

Parent 2

Gene cell item

Gene value745641

988678

1269380

802135

338870

501398

162981


Gene cell item

Gene value157481

687914

234139

802135

338870

501398

162981


item

Gene value745641

988678

1269380

577622

411552

763790

2010138


P(21)

P(12)

P(21)

P(13)

P(21)

P(14)

P(21)

P(11)

P(22)

P(12)

P(22)

P(13)

P(22)

P(14)

P(22)


P(21)

P(12)

P(21)

P(13)

P(21)

P(14)

P(21)

P(11)

P(22)

P(12)

P(22)

P(13)

P(22)

P(14)

P(22)


P(21)

P(12)

P(21)

P(13)

P(21)

P(14) P(11)

P(22)

P(12)

P(22)

P(13)

P(22)

P(14)

P(22)


P(21)

P(12)

P(21)

P(13)

P(21)

P(14)

P(22)

P(22)

P(11)

P(22)

P(12)

P(22)

P(13)

P(22)

P(14)

P(22)

11a

25b

66c

11a

25b

66c

20a

44b

48c

20a

44b

48c


c product Z








Step 7





119875 (119899) =

1 if Δ119891 (119899) le 0

exp(minusΔ119891 (119899)

119879) if Δ119891 (119899) gt 0

(15)


Old

Gene cell item

Gene value 115687 1505397 176876 234283 871688 412025 469175 923048


Gene cell item

Gene value 207964 1505397 176876 234283 573775 412025 287439 923048


P(21)

P(12)

P(21)

P(13)

P(21)

P(14)

P(21)

P(11)

P(22)

P(12)

P(22)

P(13)

P(22)

P(14)

P(22)


P(21)

P(12)

P(21)

P(13)

P(21)

P(14)

P(21)

P(11)

P(22)

P(12)

P(22)

P(13)

P(22)

P(14)

P(22)

Figure 4 Mutation


















PSO


1198881 1198882 205 205 205 205 205 205 205 205Avg fitness 24462289 24461153 24460103 24458116 24459087 24460841 24458923 24457531


GA



PSO-GA




GA-SA






PSO-SA








Q 1 Demand

Demand

Demand


723612414134221413312614425222323521422124722621

843222924322112453511641722235133322


Quality (Q)


Check cost (ChC)

415542653634242414325423322




PrC 15

50 lt X lt 3500

Q 1PrC 24

70 lt X lt 3300

Q 3PrC 32

40 lt X lt 3400

Q 5PrC 41

30 lt X lt 3300

Q 4

PrC 35

70 lt X lt 4000

Q 1

PrC 18

50 lt X lt 3500

Q 2

PrC 22

80 lt X lt 3300

Q 4

PrC 34

60 lt X lt 3400

Q 4

PrC 30

40 lt X lt 3200

Q 3

PrC 20

30 lt X lt 3600

Q 2

PrC 27

40 lt X lt 3400

Q 3

PrC 45

30 lt X lt 3700

Q 1

PrC 13

50 lt X lt 3600

Q 2

PrC 36

30 lt X lt 3300

P(31) rarr P(41)

P(31) rarr P(42)

P(31) rarr P(43)

P(32) rarr P(41)

P(32) rarr P(42)

P(32) rarr P(43)

P(33) rarr P(41)

P(33) rarr P(42)

P(33) rarr P(43)

P(21) rarr P(31)

P(21) rarr P(32)

P(21) rarr P(33)

P(22) rarr P(31)

P(22) rarr P(32)

P(22) rarr P(33)

P(23) rarr P(31)

P(23) rarr P(32)

P(23) rarr P(33)

P(24) rarr P(31)

P(24) rarr P(32)

P(24) rarr P(33)

P(14) rarr P(21)

P(14) rarr P(22)

P(14) rarr P(23)

P(14) rarr P(24)

P(11) rarr P(21)

P(11) rarr P(22)

P(11) rarr P(23)

P(11) rarr P(23)

P(12) rarr P(21)

P(12) rarr P(22)

P(12) rarr P(23)

P(12) rarr P(24)

P(13) rarr P(21)

P(13) rarr P(22)

P(13) rarr P(23)

P(13) rarr P(24)


P(41)P(31)P(21)

P(42)P(32)P(22)

P(43)P(33)P(23)

P(24)

P(11)

P(12)

P(13)

P(14)

FDR 2 FDR 5 FDR 1

FDR 3FDR 3FDR 1

FDR 2 FDR 1 FDR 2

FDR 4







HypothesizeH0



Result reject H0


HypothesizeH0



Result reject H0


HypothesizeH0



Result reject H0














119899119894+1

119899119895)


119899119894+1

119899119895)

(16)




5 Conclusions



Table8Distrib

utionplan

byPS

O-G

A(firstp

eriod)

From

ToEchelon2

Echelon3

Echelon4

119875(21)

119875(22)

119875(23)

119875(24)

119875(31)

119875(32)

119875(33)

119875(41)

119875(42)

119875(43)

Echelon1

119875(11)

10a 6b49c

7336

4211059

242535

119875(12)

142474

1742633

34182

10210234

119875(13)

1572457

256381

72956

221155

119875(14)

74396

761721

31813

74141

Echelon2

119875(21)

177383

11680

8210325

119875(22)

458237

1091417

8676

119875(23)

5310060

4133

175865

119875(24)

1112369

1029244

921130

Echelon3

119875(31)

17000

1000174

910255

119875(32)

9500

4700

12300

119875(33)

139253101

21315532

2452040

a Produ

ctX

b produ

ctY

c produ

ctZ


Table9Distrib

utionplan

byPS

O-G

A(secon

dperio

d)

From

ToEchelon1

Echelon2

Echelon3

Echelon4

119875(11)

119875(12)

119875(13)

119875(14)

119875(21)

119875(22)

119875(23)

119875(24)

119875(31)

119875(32)

119875(33)

119875(41)

119875(42)

119875(43)

Echelon1

119875(11)

1007612

694880

6134947

18550

119875(12)

341922

0270

2145047

911014

119875(13)

9533495

1311351

81740

285126

119875(14)

111110

1215100

9910

125215

Reverse

Echelon2

119875(21)

000

300

300

122

13032067

1892759

10850

119875(22)

200

400

600

221

15537213

523817

0290

119875(23)

100

100

000

122

82344

12

12362108

819410

119875(24)

000

100

000

183

55051

13970

556390

Reverse

Echelon3119875(31)

600

1500

200

4137

413030

1343610

11700

119875(32)

300

300

100

013

13000

12100

603960

119875(33)

200

000

000

26

32260151

1430304

646150

Reverse

Echelon4119875(41)

300

200

231

119875(42)

400

200

885

119875(43)

300

400

76

3Dem

and

400300150

400350300

25040

0150


Table10D

istrib

utionplan

byPS

O-G

A(th

irdperio

d)

From

ToEchelon1

Echelon2

Echelon3

Echelon4

119875(11)

119875(12)

119875(13)

119875(14)

119875(21)

119875(22)

119875(23)

119875(24)

119875(31)

119875(32)

119875(33)

119875(41)

119875(42)

119875(43)

Echelon1

119875(11)

86184

40615108

301253

248313

119875(12)

346036

137628

1651376

3515930

119875(13)

2724

301217

471160

278285

119875(14)

56010

7831

8610222

174698

Reverse

Echelon2

119875(21)

200

100

200

293

26915

332349

1135511

119875(22)

200

000

400

014

430362

3727318

10504

119875(23)

100

300

000

092

21728238

82238

93646

119875(24)

000

100

000

223

216061

2218348

9910412

Reverse

Echelon3119875(31)

500

600

300

22712

1900354

21300

580193

119875(32)

500

100

300

357

932530

16500

11300

119875(33)

000

000

200

272

16600

12330287

230246

Reverse

Echelon4119875(41)

100

200

36

2119875(42)

500

400

5716

119875(43)

300

200

2175

Dem

and

450250350

500300100

400200200







FTR((119894119895)(119894+1119896))


FDR(119894119895)


119883119901




119877119883119875minus1((119894+1119896)(119894119895))




119876119901





SD119876(119894119895)


SDChC(119894119895)


SDPrC(119894119895)


SDTrC((119894119895)(119894+1119896))


INT Integer



Acknowledgments


References































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




times (119883119901

((119894119895)(119894+1119896))

+119877119883119901

((119894+1119896)(119894119895))))

+119875

sum119901=1

119868

sum119894=119868

119869119894

sum119895=1

119870119894minus1

sum119896=1

(PrC(119894119895) times 119883119901

((119894minus1119896)(119894119895)))

+119875

sum119901=1

119868

sum119894=1

119869119894

sum119895=1

119870119894+1

sum119896=1

(ChC(119894119895) times 119883119901

((119894119895)(119894+1119896)))]

]

times119875

sum119901=1

119868

sum119894=1

119869119894

sum119895=1

119876119901

(119894119895)

(3)

st119870119894+1

sum119896=1

119883119901

((119894119895)(119894+1119896))

= INT119870119894+1

sum119896=1

119883119901

((119894119895)(119894+1119896))

times (1 minus FTR((119894119895)(119894+1119896))

) + 119877119883119901minus1

((119894+1119896)(119894119895))

119894 = 1 119901 = 1 2 3 119875 119895 = 1 2 3 119869

(4)

119870119894minus1

sum119896=1

119883119901

((119894minus1119896)(119894119895))

= INT[119870119894minus1

sum119896=1

119883119901

((119894minus1119896)(119894119895))times119870119894+1

sum119896=1

(1 minus FTR((119894119895)(119894+1119896))

)]

+

119870119894+1

sum119896=1

119877119883119901minus1

((119894+1119896)(119894119895))minus119870119894minus1

sum119896=1

119877119883119901

((119894119895)(119894minus1119896))

119894 = 2 119868 minus 1 119901 = 1 2 3 119875 119895 = 1 2 3 119869

(5)119870119894minus1

sum119896=1

119883119901

((119894minus1119896)(119894119895))

= INT119870119894minus1

sum119896=1

[119883119901

((119894minus1119896)(119894119895))


)

minus 119877119883119901

((119894119895)(119894minus1119896))]

119894 = 119868 119901 = 1 2 3 119875 119895 = 1 2 3 119869

(6)

119870119894minus1

sum119896=1

119877119883119901

((119894119895)(119894minus1119896))

= INT(119870119894minus1

sum119896=1

119883119901

((119894minus1119896)(119894119895))

+119870119894+1

sum119896=1

119877119883119901minus1

((119894+1119896)(119894119895))) times FDR

(119894119895)

119894 = 2 3 119868 119901 = 2 3 119875 119895 = 1 2 3 119869

(7)

119883(119894119895)

= INT119870119894+1

sum119896=1

119883119901

((119894119895)(119894+1119896))times (1 minus FDR

(119894119895))

times (1 minus FTR((119894119895)(119894+1119896))

)

119894 = 1 119901 = 1 2 3 119875 119895 = 1 2 3 119869

(8)

119883(119894119895)

= INT119870119894minus1

sum119896=1

119883119901


(119894119895))

times (1 minus FTR((119894119895)(119894+1119896))

)

119894 = 2 3 119868 minus 1 119901 = 1 2 3 119875

119895 = 1 2 3 119869

(9)

MinCAP(119894119895) le119870119894+1

sum119896=1

119883119901

((119894119895)(119894+1119896))le MaxCAP(119894119895)

119894 = 1 2 119868 minus 1 119901 = 1 2 3 119875 119895 = 1 2 3 119869

(10)

119883119901


(11)

119877119883119901

((119894119895)(119894minus1119896))= 0

for 119901 = 0 119894 = 1 2 119868

119895 = 1 2 3 119869 119896 = 1 2 3 119870

(12)



















119894minus 119904119888119894)

(13)

119904119899119894= 119904119888119894+ V119899119894 (14)
















Gene cell item

Gene value4660

3793

20519114

893

59

1420

215610

1883855

762721

28512895

00

90

5512821

24143

130

16433

105


P(21)

P(12)

P(21)

P(13)

P(21)

P(14)

P(21)

P(11)

P(22)

P(12)

P(22)

P(13)

P(22)

P(14)



P(31)

P(42)

P(32)

P(42)

P(33)

P(42)

P(31)

P(43)

P(32)

P(43)

P(33)

P(43)43

a

24b

49c


c product Z


Parent 1 Cut point

Gene cell item

Gene value1507481

687914

234139

577622

411552

763790

2010138

Parent 2

Gene cell item

Gene value745641

988678

1269380

802135

338870

501398

162981


Gene cell item

Gene value157481

687914

234139

802135

338870

501398

162981


item

Gene value745641

988678

1269380

577622

411552

763790

2010138


P(21)

P(12)

P(21)

P(13)

P(21)

P(14)

P(21)

P(11)

P(22)

P(12)

P(22)

P(13)

P(22)

P(14)

P(22)


P(21)

P(12)

P(21)

P(13)

P(21)

P(14)

P(21)

P(11)

P(22)

P(12)

P(22)

P(13)

P(22)

P(14)

P(22)


P(21)

P(12)

P(21)

P(13)

P(21)

P(14) P(11)

P(22)

P(12)

P(22)

P(13)

P(22)

P(14)

P(22)


P(21)

P(12)

P(21)

P(13)

P(21)

P(14)

P(22)

P(22)

P(11)

P(22)

P(12)

P(22)

P(13)

P(22)

P(14)

P(22)

11a

25b

66c

11a

25b

66c

20a

44b

48c

20a

44b

48c


c product Z








Step 7





119875 (119899) =

1 if Δ119891 (119899) le 0

exp(minusΔ119891 (119899)

119879) if Δ119891 (119899) gt 0

(15)


Old

Gene cell item

Gene value 115687 1505397 176876 234283 871688 412025 469175 923048


Gene cell item

Gene value 207964 1505397 176876 234283 573775 412025 287439 923048


P(21)

P(12)

P(21)

P(13)

P(21)

P(14)

P(21)

P(11)

P(22)

P(12)

P(22)

P(13)

P(22)

P(14)

P(22)


P(21)

P(12)

P(21)

P(13)

P(21)

P(14)

P(21)

P(11)

P(22)

P(12)

P(22)

P(13)

P(22)

P(14)

P(22)

Figure 4 Mutation


















PSO


1198881 1198882 205 205 205 205 205 205 205 205Avg fitness 24462289 24461153 24460103 24458116 24459087 24460841 24458923 24457531


GA



PSO-GA




GA-SA






PSO-SA








Q 1 Demand

Demand

Demand


723612414134221413312614425222323521422124722621

843222924322112453511641722235133322


Quality (Q)


Check cost (ChC)

415542653634242414325423322




PrC 15

50 lt X lt 3500

Q 1PrC 24

70 lt X lt 3300

Q 3PrC 32

40 lt X lt 3400

Q 5PrC 41

30 lt X lt 3300

Q 4

PrC 35

70 lt X lt 4000

Q 1

PrC 18

50 lt X lt 3500

Q 2

PrC 22

80 lt X lt 3300

Q 4

PrC 34

60 lt X lt 3400

Q 4

PrC 30

40 lt X lt 3200

Q 3

PrC 20

30 lt X lt 3600

Q 2

PrC 27

40 lt X lt 3400

Q 3

PrC 45

30 lt X lt 3700

Q 1

PrC 13

50 lt X lt 3600

Q 2

PrC 36

30 lt X lt 3300

P(31) rarr P(41)

P(31) rarr P(42)

P(31) rarr P(43)

P(32) rarr P(41)

P(32) rarr P(42)

P(32) rarr P(43)

P(33) rarr P(41)

P(33) rarr P(42)

P(33) rarr P(43)

P(21) rarr P(31)

P(21) rarr P(32)

P(21) rarr P(33)

P(22) rarr P(31)

P(22) rarr P(32)

P(22) rarr P(33)

P(23) rarr P(31)

P(23) rarr P(32)

P(23) rarr P(33)

P(24) rarr P(31)

P(24) rarr P(32)

P(24) rarr P(33)

P(14) rarr P(21)

P(14) rarr P(22)

P(14) rarr P(23)

P(14) rarr P(24)

P(11) rarr P(21)

P(11) rarr P(22)

P(11) rarr P(23)

P(11) rarr P(23)

P(12) rarr P(21)

P(12) rarr P(22)

P(12) rarr P(23)

P(12) rarr P(24)

P(13) rarr P(21)

P(13) rarr P(22)

P(13) rarr P(23)

P(13) rarr P(24)


P(41)P(31)P(21)

P(42)P(32)P(22)

P(43)P(33)P(23)

P(24)

P(11)

P(12)

P(13)

P(14)

FDR 2 FDR 5 FDR 1

FDR 3FDR 3FDR 1

FDR 2 FDR 1 FDR 2

FDR 4







HypothesizeH0



Result reject H0


HypothesizeH0



Result reject H0


HypothesizeH0



Result reject H0














119899119894+1

119899119895)


119899119894+1

119899119895)

(16)




5 Conclusions



Table8Distrib

utionplan

byPS

O-G

A(firstp

eriod)

From

ToEchelon2

Echelon3

Echelon4

119875(21)

119875(22)

119875(23)

119875(24)

119875(31)

119875(32)

119875(33)

119875(41)

119875(42)

119875(43)

Echelon1

119875(11)

10a 6b49c

7336

4211059

242535

119875(12)

142474

1742633

34182

10210234

119875(13)

1572457

256381

72956

221155

119875(14)

74396

761721

31813

74141

Echelon2

119875(21)

177383

11680

8210325

119875(22)

458237

1091417

8676

119875(23)

5310060

4133

175865

119875(24)

1112369

1029244

921130

Echelon3

119875(31)

17000

1000174

910255

119875(32)

9500

4700

12300

119875(33)

139253101

21315532

2452040

a Produ

ctX

b produ

ctY

c produ

ctZ


Table9Distrib

utionplan

byPS

O-G

A(secon

dperio

d)

From

ToEchelon1

Echelon2

Echelon3

Echelon4

119875(11)

119875(12)

119875(13)

119875(14)

119875(21)

119875(22)

119875(23)

119875(24)

119875(31)

119875(32)

119875(33)

119875(41)

119875(42)

119875(43)

Echelon1

119875(11)

1007612

694880

6134947

18550

119875(12)

341922

0270

2145047

911014

119875(13)

9533495

1311351

81740

285126

119875(14)

111110

1215100

9910

125215

Reverse

Echelon2

119875(21)

000

300

300

122

13032067

1892759

10850

119875(22)

200

400

600

221

15537213

523817

0290

119875(23)

100

100

000

122

82344

12

12362108

819410

119875(24)

000

100

000

183

55051

13970

556390

Reverse

Echelon3119875(31)

600

1500

200

4137

413030

1343610

11700

119875(32)

300

300

100

013

13000

12100

603960

119875(33)

200

000

000

26

32260151

1430304

646150

Reverse

Echelon4119875(41)

300

200

231

119875(42)

400

200

885

119875(43)

300

400

76

3Dem

and

400300150

400350300

25040

0150


Table10D

istrib

utionplan

byPS

O-G

A(th

irdperio

d)

From

ToEchelon1

Echelon2

Echelon3

Echelon4

119875(11)

119875(12)

119875(13)

119875(14)

119875(21)

119875(22)

119875(23)

119875(24)

119875(31)

119875(32)

119875(33)

119875(41)

119875(42)

119875(43)

Echelon1

119875(11)

86184

40615108

301253

248313

119875(12)

346036

137628

1651376

3515930

119875(13)

2724

301217

471160

278285

119875(14)

56010

7831

8610222

174698

Reverse

Echelon2

119875(21)

200

100

200

293

26915

332349

1135511

119875(22)

200

000

400

014

430362

3727318

10504

119875(23)

100

300

000

092

21728238

82238

93646

119875(24)

000

100

000

223

216061

2218348

9910412

Reverse

Echelon3119875(31)

500

600

300

22712

1900354

21300

580193

119875(32)

500

100

300

357

932530

16500

11300

119875(33)

000

000

200

272

16600

12330287

230246

Reverse

Echelon4119875(41)

100

200

36

2119875(42)

500

400

5716

119875(43)

300

200

2175

Dem

and

450250350

500300100

400200200







FTR((119894119895)(119894+1119896))


FDR(119894119895)


119883119901




119877119883119875minus1((119894+1119896)(119894119895))




119876119901





SD119876(119894119895)


SDChC(119894119895)


SDPrC(119894119895)


SDTrC((119894119895)(119894+1119896))


INT Integer



Acknowledgments


References































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




















119894minus 119904119888119894)

(13)

119904119899119894= 119904119888119894+ V119899119894 (14)
















Gene cell item

Gene value4660

3793

20519114

893

59

1420

215610

1883855

762721

28512895

00

90

5512821

24143

130

16433

105


P(21)

P(12)

P(21)

P(13)

P(21)

P(14)

P(21)

P(11)

P(22)

P(12)

P(22)

P(13)

P(22)

P(14)



P(31)

P(42)

P(32)

P(42)

P(33)

P(42)

P(31)

P(43)

P(32)

P(43)

P(33)

P(43)43

a

24b

49c


c product Z


Parent 1 Cut point

Gene cell item

Gene value1507481

687914

234139

577622

411552

763790

2010138

Parent 2

Gene cell item

Gene value745641

988678

1269380

802135

338870

501398

162981


Gene cell item

Gene value157481

687914

234139

802135

338870

501398

162981


item

Gene value745641

988678

1269380

577622

411552

763790

2010138


P(21)

P(12)

P(21)

P(13)

P(21)

P(14)

P(21)

P(11)

P(22)

P(12)

P(22)

P(13)

P(22)

P(14)

P(22)


P(21)

P(12)

P(21)

P(13)

P(21)

P(14)

P(21)

P(11)

P(22)

P(12)

P(22)

P(13)

P(22)

P(14)

P(22)


P(21)

P(12)

P(21)

P(13)

P(21)

P(14) P(11)

P(22)

P(12)

P(22)

P(13)

P(22)

P(14)

P(22)


P(21)

P(12)

P(21)

P(13)

P(21)

P(14)

P(22)

P(22)

P(11)

P(22)

P(12)

P(22)

P(13)

P(22)

P(14)

P(22)

11a

25b

66c

11a

25b

66c

20a

44b

48c

20a

44b

48c


c product Z








Step 7





119875 (119899) =

1 if Δ119891 (119899) le 0

exp(minusΔ119891 (119899)

119879) if Δ119891 (119899) gt 0

(15)


Old

Gene cell item

Gene value 115687 1505397 176876 234283 871688 412025 469175 923048


Gene cell item

Gene value 207964 1505397 176876 234283 573775 412025 287439 923048


P(21)

P(12)

P(21)

P(13)

P(21)

P(14)

P(21)

P(11)

P(22)

P(12)

P(22)

P(13)

P(22)

P(14)

P(22)


P(21)

P(12)

P(21)

P(13)

P(21)

P(14)

P(21)

P(11)

P(22)

P(12)

P(22)

P(13)

P(22)

P(14)

P(22)

Figure 4 Mutation


















PSO


1198881 1198882 205 205 205 205 205 205 205 205Avg fitness 24462289 24461153 24460103 24458116 24459087 24460841 24458923 24457531


GA



PSO-GA




GA-SA






PSO-SA








Q 1 Demand

Demand

Demand


723612414134221413312614425222323521422124722621

843222924322112453511641722235133322


Quality (Q)


Check cost (ChC)

415542653634242414325423322




PrC 15

50 lt X lt 3500

Q 1PrC 24

70 lt X lt 3300

Q 3PrC 32

40 lt X lt 3400

Q 5PrC 41

30 lt X lt 3300

Q 4

PrC 35

70 lt X lt 4000

Q 1

PrC 18

50 lt X lt 3500

Q 2

PrC 22

80 lt X lt 3300

Q 4

PrC 34

60 lt X lt 3400

Q 4

PrC 30

40 lt X lt 3200

Q 3

PrC 20

30 lt X lt 3600

Q 2

PrC 27

40 lt X lt 3400

Q 3

PrC 45

30 lt X lt 3700

Q 1

PrC 13

50 lt X lt 3600

Q 2

PrC 36

30 lt X lt 3300

P(31) rarr P(41)

P(31) rarr P(42)

P(31) rarr P(43)

P(32) rarr P(41)

P(32) rarr P(42)

P(32) rarr P(43)

P(33) rarr P(41)

P(33) rarr P(42)

P(33) rarr P(43)

P(21) rarr P(31)

P(21) rarr P(32)

P(21) rarr P(33)

P(22) rarr P(31)

P(22) rarr P(32)

P(22) rarr P(33)

P(23) rarr P(31)

P(23) rarr P(32)

P(23) rarr P(33)

P(24) rarr P(31)

P(24) rarr P(32)

P(24) rarr P(33)

P(14) rarr P(21)

P(14) rarr P(22)

P(14) rarr P(23)

P(14) rarr P(24)

P(11) rarr P(21)

P(11) rarr P(22)

P(11) rarr P(23)

P(11) rarr P(23)

P(12) rarr P(21)

P(12) rarr P(22)

P(12) rarr P(23)

P(12) rarr P(24)

P(13) rarr P(21)

P(13) rarr P(22)

P(13) rarr P(23)

P(13) rarr P(24)


P(41)P(31)P(21)

P(42)P(32)P(22)

P(43)P(33)P(23)

P(24)

P(11)

P(12)

P(13)

P(14)

FDR 2 FDR 5 FDR 1

FDR 3FDR 3FDR 1

FDR 2 FDR 1 FDR 2

FDR 4







HypothesizeH0



Result reject H0


HypothesizeH0



Result reject H0


HypothesizeH0



Result reject H0














119899119894+1

119899119895)


119899119894+1

119899119895)

(16)




5 Conclusions



Table8Distrib

utionplan

byPS

O-G

A(firstp

eriod)

From

ToEchelon2

Echelon3

Echelon4

119875(21)

119875(22)

119875(23)

119875(24)

119875(31)

119875(32)

119875(33)

119875(41)

119875(42)

119875(43)

Echelon1

119875(11)

10a 6b49c

7336

4211059

242535

119875(12)

142474

1742633

34182

10210234

119875(13)

1572457

256381

72956

221155

119875(14)

74396

761721

31813

74141

Echelon2

119875(21)

177383

11680

8210325

119875(22)

458237

1091417

8676

119875(23)

5310060

4133

175865

119875(24)

1112369

1029244

921130

Echelon3

119875(31)

17000

1000174

910255

119875(32)

9500

4700

12300

119875(33)

139253101

21315532

2452040

a Produ

ctX

b produ

ctY

c produ

ctZ


Table9Distrib

utionplan

byPS

O-G

A(secon

dperio

d)

From

ToEchelon1

Echelon2

Echelon3

Echelon4

119875(11)

119875(12)

119875(13)

119875(14)

119875(21)

119875(22)

119875(23)

119875(24)

119875(31)

119875(32)

119875(33)

119875(41)

119875(42)

119875(43)

Echelon1

119875(11)

1007612

694880

6134947

18550

119875(12)

341922

0270

2145047

911014

119875(13)

9533495

1311351

81740

285126

119875(14)

111110

1215100

9910

125215

Reverse

Echelon2

119875(21)

000

300

300

122

13032067

1892759

10850

119875(22)

200

400

600

221

15537213

523817

0290

119875(23)

100

100

000

122

82344

12

12362108

819410

119875(24)

000

100

000

183

55051

13970

556390

Reverse

Echelon3119875(31)

600

1500

200

4137

413030

1343610

11700

119875(32)

300

300

100

013

13000

12100

603960

119875(33)

200

000

000

26

32260151

1430304

646150

Reverse

Echelon4119875(41)

300

200

231

119875(42)

400

200

885

119875(43)

300

400

76

3Dem

and

400300150

400350300

25040

0150


Table10D

istrib

utionplan

byPS

O-G

A(th

irdperio

d)

From

ToEchelon1

Echelon2

Echelon3

Echelon4

119875(11)

119875(12)

119875(13)

119875(14)

119875(21)

119875(22)

119875(23)

119875(24)

119875(31)

119875(32)

119875(33)

119875(41)

119875(42)

119875(43)

Echelon1

119875(11)

86184

40615108

301253

248313

119875(12)

346036

137628

1651376

3515930

119875(13)

2724

301217

471160

278285

119875(14)

56010

7831

8610222

174698

Reverse

Echelon2

119875(21)

200

100

200

293

26915

332349

1135511

119875(22)

200

000

400

014

430362

3727318

10504

119875(23)

100

300

000

092

21728238

82238

93646

119875(24)

000

100

000

223

216061

2218348

9910412

Reverse

Echelon3119875(31)

500

600

300

22712

1900354

21300

580193

119875(32)

500

100

300

357

932530

16500

11300

119875(33)

000

000

200

272

16600

12330287

230246

Reverse

Echelon4119875(41)

100

200

36

2119875(42)

500

400

5716

119875(43)

300

200

2175

Dem

and

450250350

500300100

400200200







FTR((119894119895)(119894+1119896))


FDR(119894119895)


119883119901




119877119883119875minus1((119894+1119896)(119894119895))




119876119901





SD119876(119894119895)


SDChC(119894119895)


SDPrC(119894119895)


SDTrC((119894119895)(119894+1119896))


INT Integer



Acknowledgments


References































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




Gene cell item

Gene value4660

3793

20519114

893

59

1420

215610

1883855

762721

28512895

00

90

5512821

24143

130

16433

105


P(21)

P(12)

P(21)

P(13)

P(21)

P(14)

P(21)

P(11)

P(22)

P(12)

P(22)

P(13)

P(22)

P(14)



P(31)

P(42)

P(32)

P(42)

P(33)

P(42)

P(31)

P(43)

P(32)

P(43)

P(33)

P(43)43

a

24b

49c


c product Z


Parent 1 Cut point

Gene cell item

Gene value1507481

687914

234139

577622

411552

763790

2010138

Parent 2

Gene cell item

Gene value745641

988678

1269380

802135

338870

501398

162981


Gene cell item

Gene value157481

687914

234139

802135

338870

501398

162981


item

Gene value745641

988678

1269380

577622

411552

763790

2010138


P(21)

P(12)

P(21)

P(13)

P(21)

P(14)

P(21)

P(11)

P(22)

P(12)

P(22)

P(13)

P(22)

P(14)

P(22)


P(21)

P(12)

P(21)

P(13)

P(21)

P(14)

P(21)

P(11)

P(22)

P(12)

P(22)

P(13)

P(22)

P(14)

P(22)


P(21)

P(12)

P(21)

P(13)

P(21)

P(14) P(11)

P(22)

P(12)

P(22)

P(13)

P(22)

P(14)

P(22)


P(21)

P(12)

P(21)

P(13)

P(21)

P(14)

P(22)

P(22)

P(11)

P(22)

P(12)

P(22)

P(13)

P(22)

P(14)

P(22)

11a

25b

66c

11a

25b

66c

20a

44b

48c

20a

44b

48c


c product Z








Step 7





119875 (119899) =

1 if Δ119891 (119899) le 0

exp(minusΔ119891 (119899)

119879) if Δ119891 (119899) gt 0

(15)


Old

Gene cell item

Gene value 115687 1505397 176876 234283 871688 412025 469175 923048


Gene cell item

Gene value 207964 1505397 176876 234283 573775 412025 287439 923048


P(21)

P(12)

P(21)

P(13)

P(21)

P(14)

P(21)

P(11)

P(22)

P(12)

P(22)

P(13)

P(22)

P(14)

P(22)


P(21)

P(12)

P(21)

P(13)

P(21)

P(14)

P(21)

P(11)

P(22)

P(12)

P(22)

P(13)

P(22)

P(14)

P(22)

Figure 4 Mutation


















PSO


1198881 1198882 205 205 205 205 205 205 205 205Avg fitness 24462289 24461153 24460103 24458116 24459087 24460841 24458923 24457531


GA



PSO-GA




GA-SA






PSO-SA








Q 1 Demand

Demand

Demand


723612414134221413312614425222323521422124722621

843222924322112453511641722235133322


Quality (Q)


Check cost (ChC)

415542653634242414325423322




PrC 15

50 lt X lt 3500

Q 1PrC 24

70 lt X lt 3300

Q 3PrC 32

40 lt X lt 3400

Q 5PrC 41

30 lt X lt 3300

Q 4

PrC 35

70 lt X lt 4000

Q 1

PrC 18

50 lt X lt 3500

Q 2

PrC 22

80 lt X lt 3300

Q 4

PrC 34

60 lt X lt 3400

Q 4

PrC 30

40 lt X lt 3200

Q 3

PrC 20

30 lt X lt 3600

Q 2

PrC 27

40 lt X lt 3400

Q 3

PrC 45

30 lt X lt 3700

Q 1

PrC 13

50 lt X lt 3600

Q 2

PrC 36

30 lt X lt 3300

P(31) rarr P(41)

P(31) rarr P(42)

P(31) rarr P(43)

P(32) rarr P(41)

P(32) rarr P(42)

P(32) rarr P(43)

P(33) rarr P(41)

P(33) rarr P(42)

P(33) rarr P(43)

P(21) rarr P(31)

P(21) rarr P(32)

P(21) rarr P(33)

P(22) rarr P(31)

P(22) rarr P(32)

P(22) rarr P(33)

P(23) rarr P(31)

P(23) rarr P(32)

P(23) rarr P(33)

P(24) rarr P(31)

P(24) rarr P(32)

P(24) rarr P(33)

P(14) rarr P(21)

P(14) rarr P(22)

P(14) rarr P(23)

P(14) rarr P(24)

P(11) rarr P(21)

P(11) rarr P(22)

P(11) rarr P(23)

P(11) rarr P(23)

P(12) rarr P(21)

P(12) rarr P(22)

P(12) rarr P(23)

P(12) rarr P(24)

P(13) rarr P(21)

P(13) rarr P(22)

P(13) rarr P(23)

P(13) rarr P(24)


P(41)P(31)P(21)

P(42)P(32)P(22)

P(43)P(33)P(23)

P(24)

P(11)

P(12)

P(13)

P(14)

FDR 2 FDR 5 FDR 1

FDR 3FDR 3FDR 1

FDR 2 FDR 1 FDR 2

FDR 4







HypothesizeH0



Result reject H0


HypothesizeH0



Result reject H0


HypothesizeH0



Result reject H0














119899119894+1

119899119895)


119899119894+1

119899119895)

(16)




5 Conclusions



Table8Distrib

utionplan

byPS

O-G

A(firstp

eriod)

From

ToEchelon2

Echelon3

Echelon4

119875(21)

119875(22)

119875(23)

119875(24)

119875(31)

119875(32)

119875(33)

119875(41)

119875(42)

119875(43)

Echelon1

119875(11)

10a 6b49c

7336

4211059

242535

119875(12)

142474

1742633

34182

10210234

119875(13)

1572457

256381

72956

221155

119875(14)

74396

761721

31813

74141

Echelon2

119875(21)

177383

11680

8210325

119875(22)

458237

1091417

8676

119875(23)

5310060

4133

175865

119875(24)

1112369

1029244

921130

Echelon3

119875(31)

17000

1000174

910255

119875(32)

9500

4700

12300

119875(33)

139253101

21315532

2452040

a Produ

ctX

b produ

ctY

c produ

ctZ


Table9Distrib

utionplan

byPS

O-G

A(secon

dperio

d)

From

ToEchelon1

Echelon2

Echelon3

Echelon4

119875(11)

119875(12)

119875(13)

119875(14)

119875(21)

119875(22)

119875(23)

119875(24)

119875(31)

119875(32)

119875(33)

119875(41)

119875(42)

119875(43)

Echelon1

119875(11)

1007612

694880

6134947

18550

119875(12)

341922

0270

2145047

911014

119875(13)

9533495

1311351

81740

285126

119875(14)

111110

1215100

9910

125215

Reverse

Echelon2

119875(21)

000

300

300

122

13032067

1892759

10850

119875(22)

200

400

600

221

15537213

523817

0290

119875(23)

100

100

000

122

82344

12

12362108

819410

119875(24)

000

100

000

183

55051

13970

556390

Reverse

Echelon3119875(31)

600

1500

200

4137

413030

1343610

11700

119875(32)

300

300

100

013

13000

12100

603960

119875(33)

200

000

000

26

32260151

1430304

646150

Reverse

Echelon4119875(41)

300

200

231

119875(42)

400

200

885

119875(43)

300

400

76

3Dem

and

400300150

400350300

25040

0150


Table10D

istrib

utionplan

byPS

O-G

A(th

irdperio

d)

From

ToEchelon1

Echelon2

Echelon3

Echelon4

119875(11)

119875(12)

119875(13)

119875(14)

119875(21)

119875(22)

119875(23)

119875(24)

119875(31)

119875(32)

119875(33)

119875(41)

119875(42)

119875(43)

Echelon1

119875(11)

86184

40615108

301253

248313

119875(12)

346036

137628

1651376

3515930

119875(13)

2724

301217

471160

278285

119875(14)

56010

7831

8610222

174698

Reverse

Echelon2

119875(21)

200

100

200

293

26915

332349

1135511

119875(22)

200

000

400

014

430362

3727318

10504

119875(23)

100

300

000

092

21728238

82238

93646

119875(24)

000

100

000

223

216061

2218348

9910412

Reverse

Echelon3119875(31)

500

600

300

22712

1900354

21300

580193

119875(32)

500

100

300

357

932530

16500

11300

119875(33)

000

000

200

272

16600

12330287

230246

Reverse

Echelon4119875(41)

100

200

36

2119875(42)

500

400

5716

119875(43)

300

200

2175

Dem

and

450250350

500300100

400200200







FTR((119894119895)(119894+1119896))


FDR(119894119895)


119883119901




119877119883119875minus1((119894+1119896)(119894119895))




119876119901





SD119876(119894119895)


SDChC(119894119895)


SDPrC(119894119895)


SDTrC((119894119895)(119894+1119896))


INT Integer



Acknowledgments


References































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




Old

Gene cell item

Gene value 115687 1505397 176876 234283 871688 412025 469175 923048


Gene cell item

Gene value 207964 1505397 176876 234283 573775 412025 287439 923048


P(21)

P(12)

P(21)

P(13)

P(21)

P(14)

P(21)

P(11)

P(22)

P(12)

P(22)

P(13)

P(22)

P(14)

P(22)


P(21)

P(12)

P(21)

P(13)

P(21)

P(14)

P(21)

P(11)

P(22)

P(12)

P(22)

P(13)

P(22)

P(14)

P(22)

Figure 4 Mutation


















PSO


1198881 1198882 205 205 205 205 205 205 205 205Avg fitness 24462289 24461153 24460103 24458116 24459087 24460841 24458923 24457531


GA



PSO-GA




GA-SA






PSO-SA








Q 1 Demand

Demand

Demand


723612414134221413312614425222323521422124722621

843222924322112453511641722235133322


Quality (Q)


Check cost (ChC)

415542653634242414325423322




PrC 15

50 lt X lt 3500

Q 1PrC 24

70 lt X lt 3300

Q 3PrC 32

40 lt X lt 3400

Q 5PrC 41

30 lt X lt 3300

Q 4

PrC 35

70 lt X lt 4000

Q 1

PrC 18

50 lt X lt 3500

Q 2

PrC 22

80 lt X lt 3300

Q 4

PrC 34

60 lt X lt 3400

Q 4

PrC 30

40 lt X lt 3200

Q 3

PrC 20

30 lt X lt 3600

Q 2

PrC 27

40 lt X lt 3400

Q 3

PrC 45

30 lt X lt 3700

Q 1

PrC 13

50 lt X lt 3600

Q 2

PrC 36

30 lt X lt 3300

P(31) rarr P(41)

P(31) rarr P(42)

P(31) rarr P(43)

P(32) rarr P(41)

P(32) rarr P(42)

P(32) rarr P(43)

P(33) rarr P(41)

P(33) rarr P(42)

P(33) rarr P(43)

P(21) rarr P(31)

P(21) rarr P(32)

P(21) rarr P(33)

P(22) rarr P(31)

P(22) rarr P(32)

P(22) rarr P(33)

P(23) rarr P(31)

P(23) rarr P(32)

P(23) rarr P(33)

P(24) rarr P(31)

P(24) rarr P(32)

P(24) rarr P(33)

P(14) rarr P(21)

P(14) rarr P(22)

P(14) rarr P(23)

P(14) rarr P(24)

P(11) rarr P(21)

P(11) rarr P(22)

P(11) rarr P(23)

P(11) rarr P(23)

P(12) rarr P(21)

P(12) rarr P(22)

P(12) rarr P(23)

P(12) rarr P(24)

P(13) rarr P(21)

P(13) rarr P(22)

P(13) rarr P(23)

P(13) rarr P(24)


P(41)P(31)P(21)

P(42)P(32)P(22)

P(43)P(33)P(23)

P(24)

P(11)

P(12)

P(13)

P(14)

FDR 2 FDR 5 FDR 1

FDR 3FDR 3FDR 1

FDR 2 FDR 1 FDR 2

FDR 4







HypothesizeH0



Result reject H0


HypothesizeH0



Result reject H0


HypothesizeH0



Result reject H0














119899119894+1

119899119895)


119899119894+1

119899119895)

(16)




5 Conclusions



Table8Distrib

utionplan

byPS

O-G

A(firstp

eriod)

From

ToEchelon2

Echelon3

Echelon4

119875(21)

119875(22)

119875(23)

119875(24)

119875(31)

119875(32)

119875(33)

119875(41)

119875(42)

119875(43)

Echelon1

119875(11)

10a 6b49c

7336

4211059

242535

119875(12)

142474

1742633

34182

10210234

119875(13)

1572457

256381

72956

221155

119875(14)

74396

761721

31813

74141

Echelon2

119875(21)

177383

11680

8210325

119875(22)

458237

1091417

8676

119875(23)

5310060

4133

175865

119875(24)

1112369

1029244

921130

Echelon3

119875(31)

17000

1000174

910255

119875(32)

9500

4700

12300

119875(33)

139253101

21315532

2452040

a Produ

ctX

b produ

ctY

c produ

ctZ


Table9Distrib

utionplan

byPS

O-G

A(secon

dperio

d)

From

ToEchelon1

Echelon2

Echelon3

Echelon4

119875(11)

119875(12)

119875(13)

119875(14)

119875(21)

119875(22)

119875(23)

119875(24)

119875(31)

119875(32)

119875(33)

119875(41)

119875(42)

119875(43)

Echelon1

119875(11)

1007612

694880

6134947

18550

119875(12)

341922

0270

2145047

911014

119875(13)

9533495

1311351

81740

285126

119875(14)

111110

1215100

9910

125215

Reverse

Echelon2

119875(21)

000

300

300

122

13032067

1892759

10850

119875(22)

200

400

600

221

15537213

523817

0290

119875(23)

100

100

000

122

82344

12

12362108

819410

119875(24)

000

100

000

183

55051

13970

556390

Reverse

Echelon3119875(31)

600

1500

200

4137

413030

1343610

11700

119875(32)

300

300

100

013

13000

12100

603960

119875(33)

200

000

000

26

32260151

1430304

646150

Reverse

Echelon4119875(41)

300

200

231

119875(42)

400

200

885

119875(43)

300

400

76

3Dem

and

400300150

400350300

25040

0150


Table10D

istrib

utionplan

byPS

O-G

A(th

irdperio

d)

From

ToEchelon1

Echelon2

Echelon3

Echelon4

119875(11)

119875(12)

119875(13)

119875(14)

119875(21)

119875(22)

119875(23)

119875(24)

119875(31)

119875(32)

119875(33)

119875(41)

119875(42)

119875(43)

Echelon1

119875(11)

86184

40615108

301253

248313

119875(12)

346036

137628

1651376

3515930

119875(13)

2724

301217

471160

278285

119875(14)

56010

7831

8610222

174698

Reverse

Echelon2

119875(21)

200

100

200

293

26915

332349

1135511

119875(22)

200

000

400

014

430362

3727318

10504

119875(23)

100

300

000

092

21728238

82238

93646

119875(24)

000

100

000

223

216061

2218348

9910412

Reverse

Echelon3119875(31)

500

600

300

22712

1900354

21300

580193

119875(32)

500

100

300

357

932530

16500

11300

119875(33)

000

000

200

272

16600

12330287

230246

Reverse

Echelon4119875(41)

100

200

36

2119875(42)

500

400

5716

119875(43)

300

200

2175

Dem

and

450250350

500300100

400200200







FTR((119894119895)(119894+1119896))


FDR(119894119895)


119883119901




119877119883119875minus1((119894+1119896)(119894119895))




119876119901





SD119876(119894119895)


SDChC(119894119895)


SDPrC(119894119895)


SDTrC((119894119895)(119894+1119896))


INT Integer



Acknowledgments


References































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in





PSO


1198881 1198882 205 205 205 205 205 205 205 205Avg fitness 24462289 24461153 24460103 24458116 24459087 24460841 24458923 24457531


GA



PSO-GA




GA-SA






PSO-SA








Q 1 Demand

Demand

Demand


723612414134221413312614425222323521422124722621

843222924322112453511641722235133322


Quality (Q)


Check cost (ChC)

415542653634242414325423322




PrC 15

50 lt X lt 3500

Q 1PrC 24

70 lt X lt 3300

Q 3PrC 32

40 lt X lt 3400

Q 5PrC 41

30 lt X lt 3300

Q 4

PrC 35

70 lt X lt 4000

Q 1

PrC 18

50 lt X lt 3500

Q 2

PrC 22

80 lt X lt 3300

Q 4

PrC 34

60 lt X lt 3400

Q 4

PrC 30

40 lt X lt 3200

Q 3

PrC 20

30 lt X lt 3600

Q 2

PrC 27

40 lt X lt 3400

Q 3

PrC 45

30 lt X lt 3700

Q 1

PrC 13

50 lt X lt 3600

Q 2

PrC 36

30 lt X lt 3300

P(31) rarr P(41)

P(31) rarr P(42)

P(31) rarr P(43)

P(32) rarr P(41)

P(32) rarr P(42)

P(32) rarr P(43)

P(33) rarr P(41)

P(33) rarr P(42)

P(33) rarr P(43)

P(21) rarr P(31)

P(21) rarr P(32)

P(21) rarr P(33)

P(22) rarr P(31)

P(22) rarr P(32)

P(22) rarr P(33)

P(23) rarr P(31)

P(23) rarr P(32)

P(23) rarr P(33)

P(24) rarr P(31)

P(24) rarr P(32)

P(24) rarr P(33)

P(14) rarr P(21)

P(14) rarr P(22)

P(14) rarr P(23)

P(14) rarr P(24)

P(11) rarr P(21)

P(11) rarr P(22)

P(11) rarr P(23)

P(11) rarr P(23)

P(12) rarr P(21)

P(12) rarr P(22)

P(12) rarr P(23)

P(12) rarr P(24)

P(13) rarr P(21)

P(13) rarr P(22)

P(13) rarr P(23)

P(13) rarr P(24)


P(41)P(31)P(21)

P(42)P(32)P(22)

P(43)P(33)P(23)

P(24)

P(11)

P(12)

P(13)

P(14)

FDR 2 FDR 5 FDR 1

FDR 3FDR 3FDR 1

FDR 2 FDR 1 FDR 2

FDR 4







HypothesizeH0



Result reject H0


HypothesizeH0



Result reject H0


HypothesizeH0



Result reject H0














119899119894+1

119899119895)


119899119894+1

119899119895)

(16)




5 Conclusions



Table8Distrib

utionplan

byPS

O-G

A(firstp

eriod)

From

ToEchelon2

Echelon3

Echelon4

119875(21)

119875(22)

119875(23)

119875(24)

119875(31)

119875(32)

119875(33)

119875(41)

119875(42)

119875(43)

Echelon1

119875(11)

10a 6b49c

7336

4211059

242535

119875(12)

142474

1742633

34182

10210234

119875(13)

1572457

256381

72956

221155

119875(14)

74396

761721

31813

74141

Echelon2

119875(21)

177383

11680

8210325

119875(22)

458237

1091417

8676

119875(23)

5310060

4133

175865

119875(24)

1112369

1029244

921130

Echelon3

119875(31)

17000

1000174

910255

119875(32)

9500

4700

12300

119875(33)

139253101

21315532

2452040

a Produ

ctX

b produ

ctY

c produ

ctZ


Table9Distrib

utionplan

byPS

O-G

A(secon

dperio

d)

From

ToEchelon1

Echelon2

Echelon3

Echelon4

119875(11)

119875(12)

119875(13)

119875(14)

119875(21)

119875(22)

119875(23)

119875(24)

119875(31)

119875(32)

119875(33)

119875(41)

119875(42)

119875(43)

Echelon1

119875(11)

1007612

694880

6134947

18550

119875(12)

341922

0270

2145047

911014

119875(13)

9533495

1311351

81740

285126

119875(14)

111110

1215100

9910

125215

Reverse

Echelon2

119875(21)

000

300

300

122

13032067

1892759

10850

119875(22)

200

400

600

221

15537213

523817

0290

119875(23)

100

100

000

122

82344

12

12362108

819410

119875(24)

000

100

000

183

55051

13970

556390

Reverse

Echelon3119875(31)

600

1500

200

4137

413030

1343610

11700

119875(32)

300

300

100

013

13000

12100

603960

119875(33)

200

000

000

26

32260151

1430304

646150

Reverse

Echelon4119875(41)

300

200

231

119875(42)

400

200

885

119875(43)

300

400

76

3Dem

and

400300150

400350300

25040

0150


Table10D

istrib

utionplan

byPS

O-G

A(th

irdperio

d)

From

ToEchelon1

Echelon2

Echelon3

Echelon4

119875(11)

119875(12)

119875(13)

119875(14)

119875(21)

119875(22)

119875(23)

119875(24)

119875(31)

119875(32)

119875(33)

119875(41)

119875(42)

119875(43)

Echelon1

119875(11)

86184

40615108

301253

248313

119875(12)

346036

137628

1651376

3515930

119875(13)

2724

301217

471160

278285

119875(14)

56010

7831

8610222

174698

Reverse

Echelon2

119875(21)

200

100

200

293

26915

332349

1135511

119875(22)

200

000

400

014

430362

3727318

10504

119875(23)

100

300

000

092

21728238

82238

93646

119875(24)

000

100

000

223

216061

2218348

9910412

Reverse

Echelon3119875(31)

500

600

300

22712

1900354

21300

580193

119875(32)

500

100

300

357

932530

16500

11300

119875(33)

000

000

200

272

16600

12330287

230246

Reverse

Echelon4119875(41)

100

200

36

2119875(42)

500

400

5716

119875(43)

300

200

2175

Dem

and

450250350

500300100

400200200







FTR((119894119895)(119894+1119896))


FDR(119894119895)


119883119901




119877119883119875minus1((119894+1119896)(119894119895))




119876119901





SD119876(119894119895)


SDChC(119894119895)


SDPrC(119894119895)


SDTrC((119894119895)(119894+1119896))


INT Integer



Acknowledgments


References































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in





Q 1 Demand

Demand

Demand


723612414134221413312614425222323521422124722621

843222924322112453511641722235133322


Quality (Q)


Check cost (ChC)

415542653634242414325423322




PrC 15

50 lt X lt 3500

Q 1PrC 24

70 lt X lt 3300

Q 3PrC 32

40 lt X lt 3400

Q 5PrC 41

30 lt X lt 3300

Q 4

PrC 35

70 lt X lt 4000

Q 1

PrC 18

50 lt X lt 3500

Q 2

PrC 22

80 lt X lt 3300

Q 4

PrC 34

60 lt X lt 3400

Q 4

PrC 30

40 lt X lt 3200

Q 3

PrC 20

30 lt X lt 3600

Q 2

PrC 27

40 lt X lt 3400

Q 3

PrC 45

30 lt X lt 3700

Q 1

PrC 13

50 lt X lt 3600

Q 2

PrC 36

30 lt X lt 3300

P(31) rarr P(41)

P(31) rarr P(42)

P(31) rarr P(43)

P(32) rarr P(41)

P(32) rarr P(42)

P(32) rarr P(43)

P(33) rarr P(41)

P(33) rarr P(42)

P(33) rarr P(43)

P(21) rarr P(31)

P(21) rarr P(32)

P(21) rarr P(33)

P(22) rarr P(31)

P(22) rarr P(32)

P(22) rarr P(33)

P(23) rarr P(31)

P(23) rarr P(32)

P(23) rarr P(33)

P(24) rarr P(31)

P(24) rarr P(32)

P(24) rarr P(33)

P(14) rarr P(21)

P(14) rarr P(22)

P(14) rarr P(23)

P(14) rarr P(24)

P(11) rarr P(21)

P(11) rarr P(22)

P(11) rarr P(23)

P(11) rarr P(23)

P(12) rarr P(21)

P(12) rarr P(22)

P(12) rarr P(23)

P(12) rarr P(24)

P(13) rarr P(21)

P(13) rarr P(22)

P(13) rarr P(23)

P(13) rarr P(24)


P(41)P(31)P(21)

P(42)P(32)P(22)

P(43)P(33)P(23)

P(24)

P(11)

P(12)

P(13)

P(14)

FDR 2 FDR 5 FDR 1

FDR 3FDR 3FDR 1

FDR 2 FDR 1 FDR 2

FDR 4







HypothesizeH0



Result reject H0


HypothesizeH0



Result reject H0


HypothesizeH0



Result reject H0














119899119894+1

119899119895)


119899119894+1

119899119895)

(16)




5 Conclusions



Table8Distrib

utionplan

byPS

O-G

A(firstp

eriod)

From

ToEchelon2

Echelon3

Echelon4

119875(21)

119875(22)

119875(23)

119875(24)

119875(31)

119875(32)

119875(33)

119875(41)

119875(42)

119875(43)

Echelon1

119875(11)

10a 6b49c

7336

4211059

242535

119875(12)

142474

1742633

34182

10210234

119875(13)

1572457

256381

72956

221155

119875(14)

74396

761721

31813

74141

Echelon2

119875(21)

177383

11680

8210325

119875(22)

458237

1091417

8676

119875(23)

5310060

4133

175865

119875(24)

1112369

1029244

921130

Echelon3

119875(31)

17000

1000174

910255

119875(32)

9500

4700

12300

119875(33)

139253101

21315532

2452040

a Produ

ctX

b produ

ctY

c produ

ctZ


Table9Distrib

utionplan

byPS

O-G

A(secon

dperio

d)

From

ToEchelon1

Echelon2

Echelon3

Echelon4

119875(11)

119875(12)

119875(13)

119875(14)

119875(21)

119875(22)

119875(23)

119875(24)

119875(31)

119875(32)

119875(33)

119875(41)

119875(42)

119875(43)

Echelon1

119875(11)

1007612

694880

6134947

18550

119875(12)

341922

0270

2145047

911014

119875(13)

9533495

1311351

81740

285126

119875(14)

111110

1215100

9910

125215

Reverse

Echelon2

119875(21)

000

300

300

122

13032067

1892759

10850

119875(22)

200

400

600

221

15537213

523817

0290

119875(23)

100

100

000

122

82344

12

12362108

819410

119875(24)

000

100

000

183

55051

13970

556390

Reverse

Echelon3119875(31)

600

1500

200

4137

413030

1343610

11700

119875(32)

300

300

100

013

13000

12100

603960

119875(33)

200

000

000

26

32260151

1430304

646150

Reverse

Echelon4119875(41)

300

200

231

119875(42)

400

200

885

119875(43)

300

400

76

3Dem

and

400300150

400350300

25040

0150


Table10D

istrib

utionplan

byPS

O-G

A(th

irdperio

d)

From

ToEchelon1

Echelon2

Echelon3

Echelon4

119875(11)

119875(12)

119875(13)

119875(14)

119875(21)

119875(22)

119875(23)

119875(24)

119875(31)

119875(32)

119875(33)

119875(41)

119875(42)

119875(43)

Echelon1

119875(11)

86184

40615108

301253

248313

119875(12)

346036

137628

1651376

3515930

119875(13)

2724

301217

471160

278285

119875(14)

56010

7831

8610222

174698

Reverse

Echelon2

119875(21)

200

100

200

293

26915

332349

1135511

119875(22)

200

000

400

014

430362

3727318

10504

119875(23)

100

300

000

092

21728238

82238

93646

119875(24)

000

100

000

223

216061

2218348

9910412

Reverse

Echelon3119875(31)

500

600

300

22712

1900354

21300

580193

119875(32)

500

100

300

357

932530

16500

11300

119875(33)

000

000

200

272

16600

12330287

230246

Reverse

Echelon4119875(41)

100

200

36

2119875(42)

500

400

5716

119875(43)

300

200

2175

Dem

and

450250350

500300100

400200200







FTR((119894119895)(119894+1119896))


FDR(119894119895)


119883119901




119877119883119875minus1((119894+1119896)(119894119895))




119876119901





SD119876(119894119895)


SDChC(119894119895)


SDPrC(119894119895)


SDTrC((119894119895)(119894+1119896))


INT Integer



Acknowledgments


References































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in





HypothesizeH0



Result reject H0


HypothesizeH0



Result reject H0


HypothesizeH0



Result reject H0














119899119894+1

119899119895)


119899119894+1

119899119895)

(16)




5 Conclusions



Table8Distrib

utionplan

byPS

O-G

A(firstp

eriod)

From

ToEchelon2

Echelon3

Echelon4

119875(21)

119875(22)

119875(23)

119875(24)

119875(31)

119875(32)

119875(33)

119875(41)

119875(42)

119875(43)

Echelon1

119875(11)

10a 6b49c

7336

4211059

242535

119875(12)

142474

1742633

34182

10210234

119875(13)

1572457

256381

72956

221155

119875(14)

74396

761721

31813

74141

Echelon2

119875(21)

177383

11680

8210325

119875(22)

458237

1091417

8676

119875(23)

5310060

4133

175865

119875(24)

1112369

1029244

921130

Echelon3

119875(31)

17000

1000174

910255

119875(32)

9500

4700

12300

119875(33)

139253101

21315532

2452040

a Produ

ctX

b produ

ctY

c produ

ctZ


Table9Distrib

utionplan

byPS

O-G

A(secon

dperio

d)

From

ToEchelon1

Echelon2

Echelon3

Echelon4

119875(11)

119875(12)

119875(13)

119875(14)

119875(21)

119875(22)

119875(23)

119875(24)

119875(31)

119875(32)

119875(33)

119875(41)

119875(42)

119875(43)

Echelon1

119875(11)

1007612

694880

6134947

18550

119875(12)

341922

0270

2145047

911014

119875(13)

9533495

1311351

81740

285126

119875(14)

111110

1215100

9910

125215

Reverse

Echelon2

119875(21)

000

300

300

122

13032067

1892759

10850

119875(22)

200

400

600

221

15537213

523817

0290

119875(23)

100

100

000

122

82344

12

12362108

819410

119875(24)

000

100

000

183

55051

13970

556390

Reverse

Echelon3119875(31)

600

1500

200

4137

413030

1343610

11700

119875(32)

300

300

100

013

13000

12100

603960

119875(33)

200

000

000

26

32260151

1430304

646150

Reverse

Echelon4119875(41)

300

200

231

119875(42)

400

200

885

119875(43)

300

400

76

3Dem

and

400300150

400350300

25040

0150


Table10D

istrib

utionplan

byPS

O-G

A(th

irdperio

d)

From

ToEchelon1

Echelon2

Echelon3

Echelon4

119875(11)

119875(12)

119875(13)

119875(14)

119875(21)

119875(22)

119875(23)

119875(24)

119875(31)

119875(32)

119875(33)

119875(41)

119875(42)

119875(43)

Echelon1

119875(11)

86184

40615108

301253

248313

119875(12)

346036

137628

1651376

3515930

119875(13)

2724

301217

471160

278285

119875(14)

56010

7831

8610222

174698

Reverse

Echelon2

119875(21)

200

100

200

293

26915

332349

1135511

119875(22)

200

000

400

014

430362

3727318

10504

119875(23)

100

300

000

092

21728238

82238

93646

119875(24)

000

100

000

223

216061

2218348

9910412

Reverse

Echelon3119875(31)

500

600

300

22712

1900354

21300

580193

119875(32)

500

100

300

357

932530

16500

11300

119875(33)

000

000

200

272

16600

12330287

230246

Reverse

Echelon4119875(41)

100

200

36

2119875(42)

500

400

5716

119875(43)

300

200

2175

Dem

and

450250350

500300100

400200200







FTR((119894119895)(119894+1119896))


FDR(119894119895)


119883119901




119877119883119875minus1((119894+1119896)(119894119895))




119876119901





SD119876(119894119895)


SDChC(119894119895)


SDPrC(119894119895)


SDTrC((119894119895)(119894+1119896))


INT Integer



Acknowledgments


References































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in
















119899119894+1

119899119895)


119899119894+1

119899119895)

(16)




5 Conclusions



Table8Distrib

utionplan

byPS

O-G

A(firstp

eriod)

From

ToEchelon2

Echelon3

Echelon4

119875(21)

119875(22)

119875(23)

119875(24)

119875(31)

119875(32)

119875(33)

119875(41)

119875(42)

119875(43)

Echelon1

119875(11)

10a 6b49c

7336

4211059

242535

119875(12)

142474

1742633

34182

10210234

119875(13)

1572457

256381

72956

221155

119875(14)

74396

761721

31813

74141

Echelon2

119875(21)

177383

11680

8210325

119875(22)

458237

1091417

8676

119875(23)

5310060

4133

175865

119875(24)

1112369

1029244

921130

Echelon3

119875(31)

17000

1000174

910255

119875(32)

9500

4700

12300

119875(33)

139253101

21315532

2452040

a Produ

ctX

b produ

ctY

c produ

ctZ


Table9Distrib

utionplan

byPS

O-G

A(secon

dperio

d)

From

ToEchelon1

Echelon2

Echelon3

Echelon4

119875(11)

119875(12)

119875(13)

119875(14)

119875(21)

119875(22)

119875(23)

119875(24)

119875(31)

119875(32)

119875(33)

119875(41)

119875(42)

119875(43)

Echelon1

119875(11)

1007612

694880

6134947

18550

119875(12)

341922

0270

2145047

911014

119875(13)

9533495

1311351

81740

285126

119875(14)

111110

1215100

9910

125215

Reverse

Echelon2

119875(21)

000

300

300

122

13032067

1892759

10850

119875(22)

200

400

600

221

15537213

523817

0290

119875(23)

100

100

000

122

82344

12

12362108

819410

119875(24)

000

100

000

183

55051

13970

556390

Reverse

Echelon3119875(31)

600

1500

200

4137

413030

1343610

11700

119875(32)

300

300

100

013

13000

12100

603960

119875(33)

200

000

000

26

32260151

1430304

646150

Reverse

Echelon4119875(41)

300

200

231

119875(42)

400

200

885

119875(43)

300

400

76

3Dem

and

400300150

400350300

25040

0150


Table10D

istrib

utionplan

byPS

O-G

A(th

irdperio

d)

From

ToEchelon1

Echelon2

Echelon3

Echelon4

119875(11)

119875(12)

119875(13)

119875(14)

119875(21)

119875(22)

119875(23)

119875(24)

119875(31)

119875(32)

119875(33)

119875(41)

119875(42)

119875(43)

Echelon1

119875(11)

86184

40615108

301253

248313

119875(12)

346036

137628

1651376

3515930

119875(13)

2724

301217

471160

278285

119875(14)

56010

7831

8610222

174698

Reverse

Echelon2

119875(21)

200

100

200

293

26915

332349

1135511

119875(22)

200

000

400

014

430362

3727318

10504

119875(23)

100

300

000

092

21728238

82238

93646

119875(24)

000

100

000

223

216061

2218348

9910412

Reverse

Echelon3119875(31)

500

600

300

22712

1900354

21300

580193

119875(32)

500

100

300

357

932530

16500

11300

119875(33)

000

000

200

272

16600

12330287

230246

Reverse

Echelon4119875(41)

100

200

36

2119875(42)

500

400

5716

119875(43)

300

200

2175

Dem

and

450250350

500300100

400200200







FTR((119894119895)(119894+1119896))


FDR(119894119895)


119883119901




119877119883119875minus1((119894+1119896)(119894119895))




119876119901





SD119876(119894119895)


SDChC(119894119895)


SDPrC(119894119895)


SDTrC((119894119895)(119894+1119896))


INT Integer



Acknowledgments


References































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




Table8Distrib

utionplan

byPS

O-G

A(firstp

eriod)

From

ToEchelon2

Echelon3

Echelon4

119875(21)

119875(22)

119875(23)

119875(24)

119875(31)

119875(32)

119875(33)

119875(41)

119875(42)

119875(43)

Echelon1

119875(11)

10a 6b49c

7336

4211059

242535

119875(12)

142474

1742633

34182

10210234

119875(13)

1572457

256381

72956

221155

119875(14)

74396

761721

31813

74141

Echelon2

119875(21)

177383

11680

8210325

119875(22)

458237

1091417

8676

119875(23)

5310060

4133

175865

119875(24)

1112369

1029244

921130

Echelon3

119875(31)

17000

1000174

910255

119875(32)

9500

4700

12300

119875(33)

139253101

21315532

2452040

a Produ

ctX

b produ

ctY

c produ

ctZ


Table9Distrib

utionplan

byPS

O-G

A(secon

dperio

d)

From

ToEchelon1

Echelon2

Echelon3

Echelon4

119875(11)

119875(12)

119875(13)

119875(14)

119875(21)

119875(22)

119875(23)

119875(24)

119875(31)

119875(32)

119875(33)

119875(41)

119875(42)

119875(43)

Echelon1

119875(11)

1007612

694880

6134947

18550

119875(12)

341922

0270

2145047

911014

119875(13)

9533495

1311351

81740

285126

119875(14)

111110

1215100

9910

125215

Reverse

Echelon2

119875(21)

000

300

300

122

13032067

1892759

10850

119875(22)

200

400

600

221

15537213

523817

0290

119875(23)

100

100

000

122

82344

12

12362108

819410

119875(24)

000

100

000

183

55051

13970

556390

Reverse

Echelon3119875(31)

600

1500

200

4137

413030

1343610

11700

119875(32)

300

300

100

013

13000

12100

603960

119875(33)

200

000

000

26

32260151

1430304

646150

Reverse

Echelon4119875(41)

300

200

231

119875(42)

400

200

885

119875(43)

300

400

76

3Dem

and

400300150

400350300

25040

0150


Table10D

istrib

utionplan

byPS

O-G

A(th

irdperio

d)

From

ToEchelon1

Echelon2

Echelon3

Echelon4

119875(11)

119875(12)

119875(13)

119875(14)

119875(21)

119875(22)

119875(23)

119875(24)

119875(31)

119875(32)

119875(33)

119875(41)

119875(42)

119875(43)

Echelon1

119875(11)

86184

40615108

301253

248313

119875(12)

346036

137628

1651376

3515930

119875(13)

2724

301217

471160

278285

119875(14)

56010

7831

8610222

174698

Reverse

Echelon2

119875(21)

200

100

200

293

26915

332349

1135511

119875(22)

200

000

400

014

430362

3727318

10504

119875(23)

100

300

000

092

21728238

82238

93646

119875(24)

000

100

000

223

216061

2218348

9910412

Reverse

Echelon3119875(31)

500

600

300

22712

1900354

21300

580193

119875(32)

500

100

300

357

932530

16500

11300

119875(33)

000

000

200

272

16600

12330287

230246

Reverse

Echelon4119875(41)

100

200

36

2119875(42)

500

400

5716

119875(43)

300

200

2175

Dem

and

450250350

500300100

400200200







FTR((119894119895)(119894+1119896))


FDR(119894119895)


119883119901




119877119883119875minus1((119894+1119896)(119894119895))




119876119901





SD119876(119894119895)


SDChC(119894119895)


SDPrC(119894119895)


SDTrC((119894119895)(119894+1119896))


INT Integer



Acknowledgments


References































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




Table9Distrib

utionplan

byPS

O-G

A(secon

dperio

d)

From

ToEchelon1

Echelon2

Echelon3

Echelon4

119875(11)

119875(12)

119875(13)

119875(14)

119875(21)

119875(22)

119875(23)

119875(24)

119875(31)

119875(32)

119875(33)

119875(41)

119875(42)

119875(43)

Echelon1

119875(11)

1007612

694880

6134947

18550

119875(12)

341922

0270

2145047

911014

119875(13)

9533495

1311351

81740

285126

119875(14)

111110

1215100

9910

125215

Reverse

Echelon2

119875(21)

000

300

300

122

13032067

1892759

10850

119875(22)

200

400

600

221

15537213

523817

0290

119875(23)

100

100

000

122

82344

12

12362108

819410

119875(24)

000

100

000

183

55051

13970

556390

Reverse

Echelon3119875(31)

600

1500

200

4137

413030

1343610

11700

119875(32)

300

300

100

013

13000

12100

603960

119875(33)

200

000

000

26

32260151

1430304

646150

Reverse

Echelon4119875(41)

300

200

231

119875(42)

400

200

885

119875(43)

300

400

76

3Dem

and

400300150

400350300

25040

0150


Table10D

istrib

utionplan

byPS

O-G

A(th

irdperio

d)

From

ToEchelon1

Echelon2

Echelon3

Echelon4

119875(11)

119875(12)

119875(13)

119875(14)

119875(21)

119875(22)

119875(23)

119875(24)

119875(31)

119875(32)

119875(33)

119875(41)

119875(42)

119875(43)

Echelon1

119875(11)

86184

40615108

301253

248313

119875(12)

346036

137628

1651376

3515930

119875(13)

2724

301217

471160

278285

119875(14)

56010

7831

8610222

174698

Reverse

Echelon2

119875(21)

200

100

200

293

26915

332349

1135511

119875(22)

200

000

400

014

430362

3727318

10504

119875(23)

100

300

000

092

21728238

82238

93646

119875(24)

000

100

000

223

216061

2218348

9910412

Reverse

Echelon3119875(31)

500

600

300

22712

1900354

21300

580193

119875(32)

500

100

300

357

932530

16500

11300

119875(33)

000

000

200

272

16600

12330287

230246

Reverse

Echelon4119875(41)

100

200

36

2119875(42)

500

400

5716

119875(43)

300

200

2175

Dem

and

450250350

500300100

400200200







FTR((119894119895)(119894+1119896))


FDR(119894119895)


119883119901




119877119883119875minus1((119894+1119896)(119894119895))




119876119901





SD119876(119894119895)


SDChC(119894119895)


SDPrC(119894119895)


SDTrC((119894119895)(119894+1119896))


INT Integer



Acknowledgments


References































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




Table10D

istrib

utionplan

byPS

O-G

A(th

irdperio

d)

From

ToEchelon1

Echelon2

Echelon3

Echelon4

119875(11)

119875(12)

119875(13)

119875(14)

119875(21)

119875(22)

119875(23)

119875(24)

119875(31)

119875(32)

119875(33)

119875(41)

119875(42)

119875(43)

Echelon1

119875(11)

86184

40615108

301253

248313

119875(12)

346036

137628

1651376

3515930

119875(13)

2724

301217

471160

278285

119875(14)

56010

7831

8610222

174698

Reverse

Echelon2

119875(21)

200

100

200

293

26915

332349

1135511

119875(22)

200

000

400

014

430362

3727318

10504

119875(23)

100

300

000

092

21728238

82238

93646

119875(24)

000

100

000

223

216061

2218348

9910412

Reverse

Echelon3119875(31)

500

600

300

22712

1900354

21300

580193

119875(32)

500

100

300

357

932530

16500

11300

119875(33)

000

000

200

272

16600

12330287

230246

Reverse

Echelon4119875(41)

100

200

36

2119875(42)

500

400

5716

119875(43)

300

200

2175

Dem

and

450250350

500300100

400200200







FTR((119894119895)(119894+1119896))


FDR(119894119895)


119883119901




119877119883119875minus1((119894+1119896)(119894119895))




119876119901





SD119876(119894119895)


SDChC(119894119895)


SDPrC(119894119895)


SDTrC((119894119895)(119894+1119896))


INT Integer



Acknowledgments


References































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in









FTR((119894119895)(119894+1119896))


FDR(119894119895)


119883119901




119877119883119875minus1((119894+1119896)(119894119895))




119876119901





SD119876(119894119895)


SDChC(119894119895)


SDPrC(119894119895)


SDTrC((119894119895)(119894+1119896))


INT Integer



Acknowledgments


References































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in

















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in














Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in










Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in



Documents

Research Article Hybrid Algorithms for Fuzzy …downloads.hindawi.com/journals/tswj/2014/497109.pdf · Research Article Hybrid Algorithms for Fuzzy Reverse Supply ... the planning