Manual Fabric-cutting Process in Apparel Manufacture

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  • DOI 10.1007/s00170-004-2161-0

    O R I G I N A L A R T I C L E

    Int J Adv Manuf Technol (2005) 27: 152158

    W.K. Wong C.K. Kwong P.Y. Mok W.H. Ip C.K. Chan

    Optimization of manual fabric-cutting process in apparel manufactureusing genetic algorithms

    Received: 28 November 2003 / Accepted: 1 March 2004 / Published online: 26 January 2005 Springer-Verlag London Limited 2005

    Abstract In apparel manufacturing, experience and subjectiveassessment of production planners are used quite often to planthe production schedules in their fabric-cutting departments. Thequantities of cut-pieces produced by fabric-cutting departmentsbased on these non-systematic schedules cannot fulfil the cut-piece requirements of the downstream sewing lines and mini-mize the makespan. This paper proposes a genetic algorithms(GAs) approach to optimize both the cut-piece requirementsand the makespan of the conventional fabric-cutting departmentsusing manual spreading and cutting methods. An optimizationmodel for the manual fabric cutting process based on GAs wasdeveloped. Two sets of production data were collected to vali-date the performance of the model and the experimental resultswere obtained. From the results, it can be found that both themakespan and cut-piece fulfilment rates are improved in whichthe latter is improved significantly.

    Keywords Fabric-cutting Genetic algorithms Production scheduling

    Nomenclature

    X Job (fabric lay)N Maximum number of jobsi Job setup (spreading) order and i = 1, 2, . . ., Nj Job processing (cutting) order and j = 1, 2, . . ., Ni, j Setup and processing sequence of jobs Production order of job X and = 1, 2, . . ., PO

    W.K. Wong () C.K. ChanInstitute of Textiles and Clothing,The Hong Kong Polytechnic University,Hunghom, Kowloon, Hong KongE-mail: [email protected].: +852-27666471Fax: +852-27731432

    C.K. Kwong P.Y. Mok W.H. IpDepartment of Industrial System and Engineering,The Hong Kong Polytechnic University,Hunghom, Kowloon, Hong Kong

    Quantity of garments of job X Length of fabric lay of job Xs(Xi) Setup (spreading) time of job Xic(Xj ) Processing (cutting) time of job Xjm Number of spreading tables in the fabric-cutting

    department

    1 Introduction

    In apparel manufacturing, fabric cutting is done before assembly.The performance of the cutting department, which is generallyneglected by manufacturers, is a critical factor on the smoothnessof downstream operations in sewing lines and hence the overallefficiency of the apparel manufacturing plant. Since the late 80s,some apparel manufacturers have implemented the computerizedfabric-cutting systems in their apparel manufacturing process.The demands on fabric-cutting departments for greater accuracy,faster throughput, larger fabric and labour savings have driventhe adoption of computerized cutting systems.

    However, many manufacturers still rely on the manualmethod for the fabric-spreading and cutting operations in theirfabric-cutting department. Before daily spreading and cuttingoperations start, the production planners of cutting departmentsneed to plan the production (spreading and cutting) schedule soas to minimize the idle time of operatives and fulfil the fabriccut-piece requirements from different sewing production lines.The production planning is normally based on their experienceand subjective assessment which is not a systematic methodand an optimal schedule cannot be obtained. As a result, idletimes occur on the spreading and cutting operatives which in turnincreases the overall makespan of cutting departments. The cut-piece quantities produced cannot fulfil the different requirementsof each downstream sewing production line.

    As most of the apparel manufacturers and researchers em-phasize the importance of sewing process, research has beendone to improve the operation of sewing lines. However, the pro-ductivity of cutting departments, which plays a significant role

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    on the smooth flow of work in the sewing lines and thus thewhole manufacturing plant, is often neglected. Jones [1] inves-tigated a table loading system to which a rough spread/cut ratiowas proposed by comparing the estimated total spreading timeto the estimated total cutting time so as to assist management inhandling balancing problems. The further the spread/cut ratio fora specific spread was from the optimum ratio, the more dramaticthe effect of this spread would be on balancing the tables. How-ever, the determination of operative assignments relied on theexperiences and subjective assessment of the production plan-ners of cutting departments. Another limitation is that decisionsare made on an as-needed basis without planning.

    Hui et al. [2] attempted to solve the problem of fabricroll planning in spreading using genetic algorithms. The opti-mal combinations of the fabric roll sequences for each fabriclay were derived in order to minimize fabric wastage duringspreading. Though the fabric roll sequence for each fabric laywas studied, the spreading sequence for all fabric lays, whichhas a great impact on the productivity of cutting departmentswas not considered. A lack of proper planning and schedulingcauses much anguish among manufacturers when the supply ofcut pieces do not meet the requirements of production units.Skyes and McGregor [3] proposed the use of object-orientedtechnology to design a computer simulation model for the pin-ning and cutting processes in apparel manufacturing such thatthe fabric-cutting manager of fabric-cutting departments couldestimate the effects of various resource allocation to meet pro-duction goals. Wong et al. [4] proposed a spreading and cut-ting sequencing model to minimize the idle time of a com-puterized fabric-cutting system. Studies of optimizing cut-piecefulfilment, which refers to the quantities of cut-pieces requiredby sewing lines, has been neglected. This is a critical factoron the smoothness of downstream operations in sewing lines,which affects the overall efficiency of the apparel plant and thedelivery date of the whole production order to the customerssubstantially.

    2 Mechanism of job placement in manualfabric-cutting systems

    One of the major objectives of a job sequencing problem is tominimize the makespan/idle time. The job placement mechan-ism of a manual cutting system is first described to explain theway for calculating makespan time. The manual cutting systeminvestigated in this project is assumed as an efficient model.The model is referred to the fabric pieces being taken away,after spreading and cutting operations, from the spreading ta-bles for bundling operations, which can help to make room forthe new fabric lay spreading. In an efficient fabric-cutting de-partment, a group consisting of four operatives is assigned toeach spreading table. The group is divided into two subgroupsin which two operatives are responsible for fabric-spreading.The remaining operatives are responsible for cutting the fab-ric lay which has already been spread. The division of labourallows operatives to focus on their competent operations, thus

    improving the overall operation efficiency. Spreading operativesneed to continue to spread new fabric lays (jobs) once theyhave finished the present jobs. The purpose is to reduce de-lay due to switching from spreading to cutting. However, be-cause of the limited length of spreading tables, idle time canoccur when there is not sufficient free area on the spread-ing table available for the new fabric lay. In a cutting de-partment with multiple spreading tables, m, a first-come-first-serve rule is applied. For a given job sequence, jobs are allo-cated to different spreading tables with the use of the followingrules:1. Allocate the first m jobs, Xi (i = 1, . . ., m), to the m spread-

    ing tables.2. If any of the spreading table has enough room for the job

    Xi+1 (free area > fabric length (Xi+1)), allocate Xi+1 tothe first available spreading table and set i = i +1.

    3. If there is no spreading table available (free areas of allm tables < fabric length (Xi+1)), wait until enough spread-ing area is obtained by clearing up the cutting jobs Xjqueues.

    4. Repeat procedures 2 and 3 until all the jobs in the sequenceare allocated subsequently.In manual cutting systems, cutting operatives cut the fabric

    lays according to the spreading sequence, i.e. i = j , at eachspreading table. However, idle time occurs when the cutting op-eratives have finished the current job while the new job is stillbeing spread and not yet ready to cut. According to the describedjob placement mechanism, the operation sequences at differentspreading tables are defined for a given job sequence. Thus, thesystem makespan time, which is defined as the maximal op-eration duration of the m spreading tables, and the completednumber of garments of different production orders, , at variousinstants can be calculated accordingly.

    3 Optimization model for the manual fabric cuttingprocess using genetic algorithms

    3.1 Coding or representation

    In this paper, genetic algorithms (GAs) are used to optimizethe job processing sequence in a manual fabric-cutting de-partment. To apply GAs in solving an industrial optimizationproblem, it is usually assumed that a potential solution to theproblem may be represented as a set of variables. These vari-ables (genes) are joined together to form a string of values(chromosome). The string can be of binary digits, integersor real numbers. Although the binary representation proposedby Holland [5] is the most widely accepted one, GAs are notrestricted to binary representation. The choice of representa-tion in GAs is related to the nature of the problem. In thisjob sequencing problem, it is convenient to use integer chro-mosome representation to indicate the job sequences. It canbe noted that the setup sequence (spreading) is the same asthe processing sequence (cutting) in manual cutting systems.

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    An example of integer chromosome representation is shownbelow.

    Chromosome: 3 7 10 1 2 5 8 4 6 9Job sequence: X3 X7 X10 X1 X2 X5 X8 X4 X6 X9

    It has been defined early in nomenclature that each job has itsattributes such as production order (PO) number, , number ofgarments, , spreading time, s, cutting time, c, etc.

    3.2 Fitness function

    In GAs, a fitness function is defined to measure the fitness ofeach individual chromosome to determine which to reproduceand survive into the next generation. Thus, given a particularchromosome, a fitness function returns a single numerical score,fitness, which is proportional to the ability of the individ-ual that the chromosome represents. The fitness score assignedto each individual in the population depends on how well thatindividual solves a specific problem. In most of the job sequenc-ing problems, minimizing the makespan/idle time would be theobjective. In a fabric-cutting department environment, job se-quencing sometimes not only requires minimizing the makespan,but also requires maximising cut-piece fulfilment rates. Let denote the set of feasible sequences between fabric lays (jobs).For a given sequence , fitness () can be defined as()

    = makespan()+order() (1)

    where makespan() and order() are the makespan fitness andcut-piece fulfilment fitness, respectively. In Eq. 1, makespan fit-ness, decreases as the makespan time, Tmakespan, of job sequence increases.

    makespan() = Ttarget/Tmakespan wT (2)In Eq. 2 Ttarget is the target completion time, and wT is theweighting for makespan factor.

    The cut-piece fulfilment fitness is defined as

    order() =PO

    =1

    CR

    =1C() /D

    () w() (3)

    where C() and D() are the respective completed and re-

    quired number of garments of the th production order ( =1, 2, . . ., PO) at the th checking run ( = 1, 2, . . ., CR), and w()is the corresponding cut-piece fulfilment weighting.

    3.3 Initialization

    The evolution procedure begins by randomly generating an ini-tial population of integer strings (chromosome) in which eachsuch string represents a processing sequence, , of the job. Eachchromosome is processed according to the manual cutting jobplacement mechanism described in Sect. 2, and thus obtains themakespan time and cut-piece fulfilment rates which facilitate thefitness evaluation using Eq. 1.

    3.4 Genetic operators

    In GAs, crossover and mutation are the two major genetic oper-ators to provide genetic variations to the population by bringingin chromosomal changes. Crossover, as the name implies, ex-changes information (gene) among chromosomes. Mutationrandomly alters some genes in chromosomes. However, apply-ing such genetic operators may cause lost features in some genesand result in infeasible solutions. In order to prevent such infeasi-ble solution in the job sequencing problem, uniform order-basedcrossover and inversion mutation are adopted.

    3.4.1 Uniform order-based crossover

    Uniform order-based crossover has the below procedures.1. Randomly select two parents for mating from the population.2. Generate a mask binary string with the same length as its

    parents.3. Fill in some of the positions in the children by copying them

    from parents wherever the mask binary string contains a 1.4. After that, a list of the elements in parents associated with

    a 0 in the mask string is recorded and these elements arepermuted so that they appear in the same order as they appearin the mating parents.

    5. Finally, these permuted elements are filled into the gaps inthe children in the order generated in the previous step.The uniform order-based crossover preserves part of the first

    parent while it incorporates information from the second parent.More specifically, this operator respects the absolute positions ofjobs in one schedule and the relative orders of jobs in the otherstring. Figure 1 illustrates the uniform order-based crossover em-ployed in this job sequencing problem.

    Crossover is not usually applied to all pairs of individuals se-lected for mating. Indeed, the crossover operation is a randomprocess with an application likelihood, which is called the prob-ability of crossover: a typical probability of crossover is between0.6 and 1.0. If crossover is not applied, offspring are producedsimply by duplicating the parents.

    Fig. 1. Uniform order-based crossovers

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    Fig. 2. Inversion mutations

    3.4.2 Inversion mutation

    In GAs, mutation is another genetic operator that is applied toeach offspring. Compared with crossover, mutation is only seenas an background operator in GAs. However, previous researchshows that though mutation is of a generally low probabilityof use (small value of mutation probability), it is a very im-portant operator because it becomes more productive while thepopulation converges [6]. In this job sequencing study, inversionmutation is used. Under inversion mutation, two points are cho-sen randomly along the length of the chromosome. The geneswithin the two selected positions are inversed in order and therest of the genes are left as they were in the parent. Thus, for ex-ample, Fig. 2 shows an illustration where genes between the fifthgene and the seventh gene are mutated.

    3.5 Parent selection

    In nature, different individuals compete for resources in the en-vironment. Some are better than others. The better ones are morelikely to survive and propagate their genetic materials. This pro-cess of natural selection is mimicked in GAs using selectionschemes in which parental chromosomes with higher fitness havea greater chance to producing offspring than parental strings withlower fitness. One of the most widely used selection schemes iscalled the biased roulette wheel scheme in which each currentstring in the population has a roulette wheel slot sized in propor-tion to its fitness [7]. The biased roulette wheel scheme can bedescribed as follows:1. Sum the fitness of all the population members; call the result

    total fitness.

    Fig. 3. Biased roulette-wheel selection scheme

    2. Generate a random number, , between zero and the totalfitness.

    3. Return if the first population member whose fitness is addedto the one of the preceding population members, is greaterthan or equal to .In roulette wheel selection, the chance of a parent being se-

    lected is directly proportional to its fitness. In the example shownin Fig. 3, from a population of ten chromosomes with a set of fit-ness evaluations totalling 80, six individuals are selected by thebiased roulette wheel scheme, according to six random numbersgenerated from the interval of 0 to 80.

    3.6 Elitism

    Since the biased roulette wheel selection processes are based onthe survival of the fittest and are in random nature, there is noguarantee that some fit individuals will be selected. In order to

    Fig. 4. Flow diagram of genetic algorithms

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    improve the selection mechanism, De Jong [8] therefore intro-duced elitism. Elitism is an addition to many selection methodsthat forces the GAs to retain some of the best individuals in eachgeneration. This elitist strategy copies the best individuals of eachgeneration directly onto the succeeding generation. Such individ-uals might be lost if they are not selected to reproduce, or aredestroyed by crossover or mutation. The elitist strategy can in-crease the speed of the domination of populations using the bestindividuals and provide an improvement of the GAs perform-ance. Elitism is thus considered in this job sequencing problem.

    3.7 Evolution

    After the initialization, evolution is caused to occur in accor-dance with the standard genetic operations of crossover, muta-tion and selection. The evolutionary process is allowed to con-tinue until no further increase is obtained in the finesse of thefittest binary string or the pre-defined maximum number of gen-erations is reached. Thus, the fittest string will result and theoptimal job sequencing can be determined. The operations ofGAs can be represented by a flow diagram as shown in Fig. 4.

    4 Case studies

    Two sets of real production data denoted as cases A and B, areused to demonstrate this multiobjective job sequencing optimiza-tion problem. All the data listed in Table 1 was obtained fromthe fabric-cutting department of a Hong Kong-based garmentmanufacturing company in China. These two-day spreading pro-duction schedules were recorded in the fabric-cutting department

    Table 1. Detailed job characteristics

    (A)-Job (Xn ) 1 2 3 4 5 6 7 8 9 10 11Production order () 4 1 3 7 6 8 8 8 8 7 5Qty of garment () 30 116 114 66 15 224 224 224 300 118 300Marker length () 103 136 139 132 89 130 130 130 130 172 158Spreading time (s) 50 90 90 57 30 161 161 161 209 104 233Cutting time (c) 24 47 47 47 24 47 47 47 47 47 47(A)-Job (Xn ) 25 26 27 28 29 30 31 32 33 34 35Production order () 9 6 5 7 2 7 6 3 9 3 9Qty of garment () 2 33 300 94 33 14 140 146 8 2 3Marker length () 68 91 158 132 91 137 170 140 81 73 72Spreading time (s) 17 48 233 77 48 23 121 113 23 16 18Cutting time (c) 24 24 47 47 24 47 47 47 24 47 24(B)-Job (Xn) 1 2 3 4 5 6 7 8 9 10 11Production order () 2 1 1 3 2 2 2 2 2 2 3Qty of garment () 33 140 316 224 3 8 316 4 14 5 21Marker length () 91 170 170 130 72 81 170 85 87 81 73Spreading time (s) 48 121 254 161 18 23 254 19 29 20 34Cutting time (c) 24 47 47 47 24 24 47 24 24 24 24(B)-Job (Xn) 25 26 27 28 29 30 31 32 33 34 35Production order () 5 3 1 2 6 6 1 2 4 3 1Qty of garment () 14 78 58 42 300 300 42 2 228 224 6Marker length () 137 105 170 91 130 130 91 68 148 130 101Spreading time (s) 23 59 57 60 209 209 60 17 172 161 21Cutting time (c) 47 47 47 24 47 47 24 24 47 47 24

    12 13 14 15 16 17 18 19 20 21 22 23 249 2 8 6 2 9 6 2 6 6 2 4 8

    10 200 300 98 14 4 200 42 52 42 140 13 21106 175 130 169 87 85 175 91 171 91 170 93 7320 170 209 87 29 19 170 60 53 60 121 28 3447 47 47 47 24 24 47 24 47 24 47 24 2436 37 38 39 40 41 42 43 44 45 46 47 48

    1 8 4 3 6 6 6 4 2 2 3 4 978 224 53 228 316 14 58 104 98 316 94 6 5

    105 130 171 148 170 87 170 171 169 170 132 101 8159 161 96 172 254 29 57 174 87 254 77 21 2047 47 24 47 47 24 47 24 47 47 47 24 24

    12 13 14 15 16 17 18 19 20 21 22 23 2410 11 10 3 1 10 1 1 3 1 2 3 394 118 94 116 13 146 33 30 300 200 140 224 224

    132 172 132 136 93 140 91 103 158 175 170 130 13077 104 77 90 28 113 48 50 233 170 121 161 16147 47 47 47 24 47 24 24 47 47 47 47 4736 37 38 39 40 41 42 43 44 45 46 47 48

    1 3 1 2 1 2 4 1 1 5 2 4 214 300 104 10 15 98 114 98 53 66 200 2 5287 158 171 106 89 169 139 169 171 132 175 73 17129 233 174 20 30 87 90 87 96 57 170 16 5324 47 24 47 24 47 47 47 24 47 47 47 47

    Fig. 5. Layout of a fabric-cutting department consisting of four spreadingtables with examples of fabric lays being spread

    in which each schedule 48 jobs were setup and processed by amanual cutting system. The cutting department consists of fourspreading tables, each of length 600 ft, as shown in Fig. 5.

    The job sequences for the cases, A and B, adopted by theindustrial practice are shown in Figs. 6 and 7, and those jobsequences generated by the GAs are shown in Figs. 8 and 9,respectively. The results obtained by GAs are maximized forthe fitness function explained in Eq. 1, where the target com-pletion time (makespan) is Ttarget = 960 min and the cut-piecefulfilment rates are evaluated at two checking times, 480 min and960 min, for both cases A and B. Assuming the makespan fitness,makespan(), and the cut-piece fulfilment fitness, order(), are ofequal weightings, thus the weighting parameters are defined as

    wT =PO

    2

    w() (4)

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    Fig. 6. Job sequences adopted by the industrial practice for the case A

    Fig. 7. Job sequences adopted by the industrial practice for the case B

    and w() = 1 for all production orders. The total productionorders are PO = 9 and PO = 6 for the cases A and B, respec-tively. The production targets at check-time 480 and 960 min arelisted in Table 2.

    The makespan and cut-piece fulfilment rates are comparedin Table 3 for job sequences adopted by industrial practice andthose optimized by GAs. It can be found that with the useof GAs, the makespan was improved slightly from 1209 to1200 min for case A and from 1209 to 1203 min for case B. Inaddition to the makespan improvement, the cut-piece fulfilment

    Table 3. Comparison on makespan time and cut-piece fulfilment rates of job sequences adopted by industrial practice and those generated by GAs

    Cut-piece fulfilment rate makespan(A) PO 1 2 3 4 5 6 7 8 9 Avg.C(1) /D

    (1) Ind. 0% 100% 67% 100% 0% 100% 100% 0% 100% 64% 1209 min

    C(2) /D(2) Ind. 100% 71% 100% 100% 50% 67% 100% 49% 100% 82%

    C(1) /D(1) GA 100% 47% 100% 100% 100% 55% 100% 69% 100% 86% 1200 min

    C(2) /D(1) GA 100% 89% 84% 74% 100% 70% 100% 65% 84% 85%

    Cut-piece fulfilment rate makespan(B) PO 1 2 3 4 5 6 Avg.C(1) /D

    (1) Ind. 100% 100% 0% 67% 100% 0% 61% 1209 min

    C(2) /D(2) Ind. 72% 74% 55% 100% 100% 50% 75%

    C(1) /D(1) GA 97% 100% 35% 100% 100% 100% 89% 1203 min

    C(2) /D(1) GA 59% 92% 73% 100% 100% 100% 87%

    Fig. 8. Job sequences generated by the optimization model using GAs forthe case A

    Fig. 9. Job sequences generated by the optimization model using GAs forthe case B

    Table 2. Production targets of different production orders (PO)

    (A) PO 1 2 3 4 5 6 7 8 9D(1) 97 422 292 103 300 484 146 759 16D(2) 194 843 584 206 600 968 292 1517 32

    (B) PO 1 2 3 4 5 6D(1) 561 463 856 339 99 300D(2) 1122 927 1711 678 198 600

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    rates at check-times were improved significantly. In case A, theaverage cut-piece fulfilment rates have increased from 64 to 86%and from 82 to 85% at the check-time 480 and 960 min, respec-tively. In the case B, the average cut-piece fulfilment rates haveincreased from 61 to 89% and from 75 to 87%.

    5 Conclusions

    This paper proposes a genetic algorithms approach to solve theoptimization problem of the manual fabric-cutting process forapparel manufacturing. Experiments were conducted to validatethe performance of the proposed method. The experimental re-sults have indicated that the production (spreading and cutting)schedules generated by GAs can improve both the cut-piece ful-filment rate and the makespan using the same number of opera-tives. The results also indicated that the shop-floor managementin the industry is capable of generating a production schedulewith a short makespan since slight improvement can only be ob-tained by using GAs approach. However, their schedule with ashort makespan cannot guarantee that the cut-pieces providedby the cutting department can fulfil the requirements of sewinglines. The proposed GAs approach has been proven as an effect-ive method to increase the cut-piece fulfilment rates significantlywhich directly affects the smoothness of downstream apparel as-sembly processes and thus ultimate delivery time of apparel to

    the customers. Extensions of the proposed method to incorporatethe influence of the skill level of operatives, fabric characteris-tics, complexity of apparel style, etc. on the production scheduleusing fuzzy concept are now under investigation.

    Acknowledgement The authors would like to thank The Hong Kong Poly-technic University for the financial support in this research project (ProjectNo. G-YD75).

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    3. Sykes DA, McGregor JD (1991) Object-oriented modelling in the ap-parel industry. Proc Fifth International Conference of Technology ofObject-oriented Languages and System Tools, pp 219229

    4. Wong WK, Chan CK, Ip WH (2000) Optimization of spreading andcutting sequencing model in the garment manufacturing. Comput Ind43:110

    5. Holland JH (1975) Adaptation in natural and artificial systems. MITPress, Cambridge, MA

    6. Bck T, Fogel DB, Michalewicz Z (1997) Handbook of evolutionaryComputation. Institute of Physics Publishing and Oxford UniversityPress, Oxford

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