Application of Multi-Objective Genetic Algorithm to Quotation of Global Garment Companies

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1 Avalable onlne at Proceda Computer Scence 17 (2013 ) Informaton Technology and Quanttatve Management (ITQM2013) Applcaton of Mult-Obectve Genetc Algorthm to Quotaton of Global Garment Companes Shue-Shun L, Rong-Chang Chen*, Yng-Hua Chen, Me-Hu Wu, Kuan-Hsuan Leng, Hsn-Yu Wang Abstract Department of Dstrbuton Management, Natonal Tachung Unversty of Scence and Technology It s very mportant for companes n enhancng compettve advantages to reach quck response quote demands from customers, especally n the global compettve markets. The process of quotng s dffcult and comple. The quote mechansm provded by ths study could be separate nto two parts. In the frst part, when sellers get order demands and send demands to the operaton offce by Internet, users can reect unsutable factores quckly for some mportant orders bas After the ntervew wth senor managers, there are two maor. For analyzng mult-obectve plannng problems, ths study used Mult-Obectve Genetc Algorthm (MOGA) to be the analytc tool. Based on the results, the mechansm can assst users to fnd some non-nferor solutons n only seconds. In addton, the results are qute comparable to those by Brute-Force Search. Therefore, ths also eplans that the results n ths study process good predctve ablty The Authors. Publshed by by Elsever B.V. B.V. Open access under CC BY-NC-ND lcense. Selecton and/or peer-revew under responsblty of the organzers of of the the 2013 Internatonal Conference Computatonal on Informaton Technology Scence and Quanttatve Management Keywords: Mult-Obectves; Genetc Algorthm; Quote Mechansm; Garment Industry 1. Introducton Global Competton has nfluenced every ndustry. Companes have to face the problem for makng decsons wth effectveness and effcent. In Tawan, the great maorty of companes rely on eportaton and they always confront to quote wthn a short tme. Companes mght lose ther customers and the market share f they cannot quote for quck response [1]. In ths paper, we tred to develop a quotng mechansm for garment companes to make correct prcng decsons wth comple nfluencng factors, and used real manufacturng * Correspondng author. Tel.: ; fa: E-mal address: rcchens@nutc.edu.tw The Authors. Publshed by Elsever B.V. Open access under CC BY-NC-ND lcense. Selecton and peer-revew under responsblty of the organzers of the 2013 Internatonal Conference on Informaton Technology and Quanttatve Management do: /.procs

2 174 Shue-Shun L et al. / Proceda Computer Scence 17 ( 2013 ) data from a famous clothng manufacturer for practcal value. By research results, propretors and senor managers could make quotaton decsons effcently. There are two characterstcs of garment ndustry [2]. The frst one s Short Lfe Cycle. Styles of clothes are always changed and depend on dfferent seasons and customer demands. Not only low prces could be accepted by customers but quckly offerng the new style clothes also play an mportant role n the market. Thus, t s really mportant to shorten the tme for manufacture and transportaton. Second, clothng manufacture s a hgh labor ntensve ndustry. Labor cost s the most serous problem for each ndustry n recently years. Sellng prces of most clothes cannot be made too hgh so how to control manufacturng cost has become a more and more crtcal ssue to clothng manufacturers. Quotaton mechansm depends on producton plan. In the past, senor managers are used to make decsons by own eperences and lmted nformaton. It s hard to make correct quotatons wthn a short tme and lots of nfluencng factors (ncludng materal purchasng, transportaton cost and lead tme, dfferent countres manufacturng facltes and capactes, and et al.). In ths study, we consdered two obectves Make span usually mpacted to each other. For eample, manufacturers could get low labor cost and materal cost n some remote countres, but transportaton tme and dstances from factores to customers would become more than producng nearby. The past research [3-4] usually used mathematcal methods to solve mult-obectves. It s hard to get nonnferor solutons wth lots of orders and comple nfluencng factors n the polynomal tme. For solvng these comple problems, Chen et al. [5-6] had proposed some orgnal approaches to let senor managers make decsons effcently. Rather than past research, the am of ths paper s to develop a quotaton mechansm by usng Decson Support System (DSS) and Mult-Obectve Genetc Algorthm (MOGA) for vsual output and analyss tools. The paper s arranged as follows. Secton 2 would revew the past research ncludng quotaton methods of garment ndustry and mult-obectve genetc algorthm. By lteratures revew, we could defne the problem clearly and get the sutable method to solve problems wth comple factors. Thus, the quotaton mechansm would be descrbed n Secton 3. Mnmum total cost (ncludng materal purchasng cost, labor cost, and transportaton cost) was defned by mathematcal methods and encoded for systematcal analyss. Secton 4 presents the epermental results and we could fnd and dscuss the meanng from results. In Secton 5, peroraton the fndngs would be shown and these fndngs could be presented by real quotaton polces. 2. Lterature Revew In ths secton, we would lke to ntroduce brefly the quotaton process of clothng manufacture. The quotaton mechansm could be developed based on lteratures collocaton. After that, lteratures of Mult- Obectve Genetc Algorthm would be surveyed and known how t works The quotng process The tradtonal quotng process of clothng manufacture always spent much tme on decson makng. When orders receved, senor managers have to select approprate orgnal places, facltes, and other nfluencng factors. As Fg 1 shows, the quotaton process could be dvded nto 5 maor parts [7]. In the frst stage, managers have to conform to customers demands of styles and quantty, and these demands wll be lmted by capactes of each factory. Managers should make sure of that materal could be prepared and customers requests (ncludng orgnal places, delvery days, and et al.) could be satsfed n the stage 2. After that, prcng s the most mportant and comple stage n the whole process. Customers mght change supplers f prces get too hgh; on the other hand, cost mght cause manufacturers loss f prces get to low. There are three detals of the quotaton process as follows.

3 Shue-Shun L et al. / Proceda Computer Scence 17 ( 2013 ) Make basc prces. The basc prce s made from producton cost and reasonable proft. Estmate addtonal epenses and approprate dscount. Some charges lke duty or transportaton cost should be added to the basc prce. For huge volumes of trade or long-term cooperaton, dscounts always are used n prce negotaton. Consder the etra cost. In the global ndustry, dfferent customers demands usually rase up manufacture s cost. For eample, customers mght desgnate raw materals and the materals mght be far to factores. In the last two stages, senor managers wll check the credts of customers and re-conform condtons of facltes. When above stages were fnshed, quotatons would be offered to customers. Estmate order demands and producton capacty Conform stuatons of materals and customers request Prcng Check customers credts Re-conform producton capacty Offer quotatons Fg. 1. Flow chart of the quotaton process 2.2. Mult-obectve genetc algorthm Mult-obectve plannng s a mathematc method to make decsons and allow more than one obectve estng. The purpose of mult-obectve plannng s to assst decson makers n desgnng strateges based on lmted resources and clashed obectves. There are three advantages n the method of mult-obectve plannng [8]. Frst, each obectve has own measurement unt. Dfferent measurement unts can be ested n the same plannng. Second, personal eperences and subectve vewponts are allowed to be put n the equaton. Thrd, senor managers can thnk about trade-off among dfferent obectves. There obectves have an alternatve relatonshp, even these obectves are conflct. Genetc algorthm was presented n 1975 by Dr. Holland [9]. It smulates evoluton and fnds optmal solutons by gene reproducton, crossover, and mutaton. Scholars could set ndvdual obectves for dfferent problems and measure results by ftness functons. The dfference between tradtonal genetc algorthm and mult-obectve genetc algorthm s settng of ftness functon. Mult-obectve genetc algorthm was present by Schaffer n 1985 [10]. If there were k obectves, orgnal populatons would be dvded nto k subpopulatons. Each obectve had own ftness functon and weghts so that every ftness functon could evolve wth nterference from other goals. Most of mult-genetc algorthm researches usually used weght

4 176 Shue-Shun L et al. / Proceda Computer Scence 17 ( 2013 ) method to calculate comple problems and fnd feasble solutons [11-12]. However, some scholars thought that better genes should get more chances to be propagated. Based on results of these researches, the deas had been conform by many eperments [13-18]. Ths method was called Eltst Strategy. Thus, we used multobectve genetc algorthm combned wth elte polcy and weght method to be analytc tools n ths study. 3. Quotaton Mechansm and Epermental Methodology The quotaton mechansm s presented as follows. By ntervew wth clothng manufacturers and ntegraton lteratures, there are some rules and sequence mght be dscovered. When sellers get orders, they have to send demands to the operaton center. The center would consder requests from each order and measure factores condtons and stuatons. Calculaton by mult-obectve genetc algorthm wll be eecuted mmedately when all of condtons had be estmated. After that, senor managers make fnal prces for quotatons by prcng strategy and producton cost. Fg. 2. The process of quotaton mechansm Therefore, t s mportant to fnd the mnmum producton cost and offer products as fast as possble. In ths case, we got two obectves. One s mnmum producton cost; the other s the mnmum make span. Frst, we had consdered the parameters for calculaton. The parameter was defned as follows. denotes the th order, = 1 to n, n means the total number of orders. denotes the th factory, = 1 to m, m means the total numbers of factores.

5 Shue-Shun L et al. / Proceda Computer Scence 17 ( 2013 ) D denotes the volumes of th order (the unt s peces). U denotes the delvery days of th order (the unt s day). pc denotes the penalty cost for delay delvery of th order (the unt s NTD per day). c denotes the raw materal cost of th order n th factory (the unt s NTD per pcs). l denotes the labor cost of th order n th factory (the unt s NTD per day). tc denotes the transportaton cost of th order n th factory (the unt s NTD per pcs). p denotes the capactes n th factory (the unt s pcs per day). denotes the volumes of th order n th factory. y denotes th order was allocated n th factory, t s a bnary varable. T denotes the delay days of th order. The obectve of mnmum producton cost was formulated as equaton 1, and the mnmum make span was formulated as equaton 2. Mn z 1 m n 1 1 y c l p tc n 1 pc T (1) m n 1 1 y c l p tc n 1 pc T Mn z 2 m n 1 1 p (2) These equatons were subect to n p all 1 (3) m n m n D all, (4) m y 1 all (5) y 0 or 1 all, (7) 4. Results and Dscussons As front secton, there are trade-offs between the mnmum producton cost and the mnmum make span. In ths secton, we would ntroduce nput data and parameters for systemc calculates. We used Brute-Force Algorthm to test and verfy the results from the decson support system. The quotaton system s developed by Mcrosoft Vsual C ++, and CPU s Intel Pentum M 1.5GHz.

6 178 Shue-Shun L et al. / Proceda Computer Scence 17 ( 2013 ) Input data These data was collected by real nvestgatng wth clothng manufacturers. In ths case, the manufacturer has 5 prme factores and 4 products that each product could be dvded nto 2 types. Factores have been allocated n the Unted State, Chna, Vetnam, and Tawan. Take Table 1 for eample; there are 10 orders and each order has ndvdual characterstcs. Because of 8 materals of clothes, factores also have own costs for every needs as Table 2 shows (there are two factores n Tawan). Each factory has ndvdual capacty (Tawan A s 7,000 pcs/day; Tawan B s 7,000 pcs/day; Chna s 10,000 pcs/day); Unted State s 10,000; and Vetnam s 16,667 pcs/day). Table 1. An eample of orders nformaton Order Number Product Number Quantty (pcs) Delay Cost (NTD/day) Delvery Days Delvery to Asa Europe Australa Asa Asa Central Amerca Amerca Asa Amerca Asa Table 2. Cost of factores Factory Materal Cost (NTD/PCS) Labor Transportaton Cost (NTD/PCS) Cost (NTD/ PCS) Europe Asa Amerca Australa Tawan A Tawan B Chna U.S Vetnam Central Amerca 4.2. Parameters of MOGA and epermental results Numbers of generaton and populaton, mutaton rate and crossover rate are four maor parts for usng genetc algorthm. Dfferent data dstrbuton mght use dstnct parameters. For eample, t s easy to get local optmal soluton f mutaton rate has been set too low. On the contrary, the system cannot get convergence wth wrong mutaton rates. Therefore, t s necessary to decde parameters for calculaton of mult-obectve genetc algorthm. By epermentng n many tmes, usng parameters as Table 3 could get feasble solutons effcently. We tred three knds of crossover rates because there s no absolute f crossover rate gets hgher or lower. Hence, usng these three knds of crossover rates could make our research become more complete.

7 Shue-Shun L et al. / Proceda Computer Scence 17 ( 2013 ) Table 3. Parameters of MOGA Parameter Generaton 500 Populaton 200 Number Mutaton rate 0.01 Crossover rate 1.0, 0.8, 0.5 In ths study, we used above parameters to solve the problem for 10 tmes, and we could see the results as follows. Brute-force algorthm spent more tmes to get solutons, and MOGA actually can feasble solutons near the optmal soluton. As Table 4 shows, crossover rate was decded by compared by brute-force algorthm. Table 4. Calculatng results n dfferent crossover rates Crossover Rate Brute-Force Algorthm Mult-Obectve Genetc Algorthm Cost Calculatng Tme (sec.) Average Cost Optmal Cost Average Accuracy Calculatng Tmes (sec.) ,965, ,975,772 34,965, % 6.79 ~ ,965, ,975,772 34,965, % 5.95 ~ ,965, ,965,772 34,965, % 3.51 ~ 4.53 Mnmum make span s 19 ~ 25 days calculated by brute-force algorthm, and t s the same as results from mult-obectve genetc algorthm. Although brute-force algorthm could fnd the optmal soluton, but t also spends too much tme to fnd solutons out. We used 9 ~ 13 peces of orders to analyss the tme that bruteforce algorthm needs. The calculatng tme had ncreased acutely from seconds to 502,955 seconds. Thus, brute-force algorthm cannot be used n the real problems because there are always more than 20 peces of orders. In the end, we used 10, 20, 30, 40, and 50 peces of orders to smulate. The result s presented n Table 5. From results, mult-obectve genetc algorthm could be confrmed n handlng large numbers of orders stably n the fnte tme. Table 5. Calculatng results from dfferent numbers of orders by MOGA Numbers of Orders Calculatng Tme (sec.) Average Producton Cost Mnmum Producton Coeffcent of Varaton ,278,011 35,276, % ,047,550 63,195, % ,8431,186 11,7659, % ,178, ,427, % ,145, ,857, % 5. Concluson In tradtonal quote process, senor managers usually use Cost-Plus Prcng or Competton-Drven Prcng to offer quotatons. Dffculty of makng decsons wth comple nfluencng factors has mpacted ndustry s profts. Thus, the am of ths paper s to develop a quotaton mechansm by usng real data from a famous garment ndustry n Tawan. The results of ths study show that decson support system combned wth mult-obectve genetc algorthm could get nonnferor solutons effcently. There two goals, mnmum total producton cost and the mnmum make span, are estmated to be alternatves for senor managers. The conclusons are arranged as follows:

8 180 Shue-Shun L et al. / Proceda Computer Scence 17 ( 2013 ) The concepts could be used n real clothng manufacture and others ndustry. Besdes the eperences and subectvness, decson makers mght consder more nfluencng factors and make prces obectvely. The analyss tools n ths paper are verfed by Brute-Force Algorthm, and results show that quotaton method we proposed has hgh accuracy near the optmal soluton. There are too many nfluencng factors that cannot be used n quote processes. In ths study, we used some maor factors ncludng raw materal cost, transportaton cost, and penalty cost for delay delvery to calculate producton cost and make spans. Results of ths study played a poneer role for the quotaton mechansm. More nfluencng factors or other algorthms also could be consdered n future research, and the mechansm would be more valuable to assst senor managers to make quotatons. Acknowledgements The authors wsh to epress ther apprecaton to Chh-Chang Ln for hs help durng the course of wrtng ths paper. Ths work was supported by the Natonal Scence Councl under grant number E References [1] Veeraman, D., Josh, P Methodologes for Rapd and Effectve Response to Requests for Quotaton (RFQs). IIE Transactons 29, p [2] Carr, H., Latham, B The Technology of Clothng Manufacture. Blackwell Scentfc Publcaton LTd.; [3] Steuer, R.E Multple Obectve Lnear Programmng wth Interval Crteron Weghts. Management Scence 23, p [4] Nagar, A., Heragu, S.S., Haddock, J A Branch-and-Bound Approach for a Two-Machne Flowshop Schedulng Problem. The Journal of the Operatonal Research Socety 466, p [5] Chen, R.C., Ln, C.C., L, S.S An Automatc Decson Support System Based on Genetc Algorthm for Global Apparel Manufacturng. Internatonal Journal of Soft Computng 1, p [6] L, S.S., Chen, R.C., Ln, C.C A Genetc Algorthm-Based Decson Support System for Allocatng Internatonal Apparel Demand. WSEAS Transacton on Informaton Scence and Applcatons 3, p [7] Taylor, D.A Addson-Wesley. [8] Gao, Z., Tang, L A Mult-Obectve Model for Purchasng of Bulk Raw Materals of a Large-Scale Integrated Steel Plant. Internatonal Journal of Producton Economcs 83, p [9] Holland, J Adaptaton n Natural and Artfcal Systems. Unversty of Mchgan Press, Ann Arbor, Mchgan. [10] Schaffer, J.D Multple Obectve Optmzaton wth Vector Evaluated Genetc Algorthms. The 1st Internatonal Conference on Genetc Algorthms, p [11] Murata, T., Ishbuch, H MOGA: Mult-Obectve Genetc Algorthms. Evolutonary Computaton, 1995., IEEE Internatonal Conference on 1, p [12] Tamak, H., Nshno, E., Abe, S A Genetc Algorthm Approach to Mult-Obectve Schedulng Problems wth Earlness and Tardness Penaltes. Proceedngs of the 1999 Congress on Evolutonary Computaton 1, p [13] Goldberg, D.E Genetc Algorthms n Search, Optmzaton, and Machne Learnng. Mass: Addson, Wesley. [14] Horn, J., Nafplots, N Multobectve Optmzaton Usng the Nched Pareto Genetc Algorthm. Report 93005, Unversty of Illnos at Urbana-Champan, Urbana, Illnos, USA. [15] Fonseca, C.M., Flemng, P.J Genetc Algorthms for Multobectve Optmzaton: Formulaton, Dscusson and Generalzaton. Proceedngs of the 5th Internatonal Conference on Genetc Algorthms, p [16] Murata, T., Ishbuch, H., Tanaka, H Genetc Algorthms for Flowshop Schedulng Problems. Computers and Industral Engneerng 304, p [17] Cochran, J.K., Horng, S.M., Fowler, J.W A Mult-Populaton Genetc Algorthm to Solve Mult-Obectve Schedulng Problems for Parallel Machnes. Computers and Operatons Research 30, p [18] Yamach, H., Tsumura, Y., Kambayash, Y., Yamamoto, H Mult-obectve Genetc Algorthm for Solvng N-verson Program Desgn Problem. Relablty Engneerng and System Safety 91, p