Optimal Production Planning in Aromatic Coconuts Supply Chain Based On Mixed-Integer Linear Programming

Transcription

1 World Academy of Scence, Engneerng and Technology Inernaonal Journal of Indusral and Manufacurng Engneerng Opmal Producon Plannng n Aromac Coconus Supply Chan Based On Mxed-Ineger Lnear Programmng Chamongkol Lmpanchob Inernaonal Scence Index, Indusral and Manufacurng Engneerng wase.org/publcaon/ Absrac Ths work addresses he problem of producon plannng ha arses n he producon of aromac coconus from Samudsakhorn provnce n Thaland. The plannng nvolves he forwardng of aromac coconus from he harves areas o he facory, whch s classfed no wo groups; self-owned areas and conraced areas, he decsons of aromac coconus flow n he plan, and addressng a queson of whch warehouse wll be n use. The problem s formulaed as a mxed-neger lnear programmng model whn supply chan managemen framework. The objecve funcon seeks o mnmze he oal cos ncludng he harvesng, labor and nvenory coss. Consrans on he sysem nclude he producon acves n he company and demand requremens. Numercal resuls are presened o demonsrae he feasbly of coconus supply chan model compared wh base case. Keywords Aromac coconu, supply chan managemen, producon plannng, mxed-neger lnear programmng. A I. INTRODUCTION ROMATIC coconus s an agrculural commody of Thaland where have a rend for more exporaon [1]. However, he aromac coconu exporng company n Thaland s ofen facng problem n managng large volume of aromac coconus due o an unbalance beween supply from harves areas and demands of cusomers as a resul from an neffcency of producon plannng. There are a few large companes n Thaland ha operae along he complee aromac coconu ndusry supply chan. Raw maeral for hese companes can be suppled from selfowned and/or conraced areas. A processng plan, afer recevng raw maeral, a decson has o be made wheher he coconu s sen o warehouse for laer processng or drecly sen o he processng lne. The processng lne nvolves several seps; rmmng no apered-cylnder form, qualy classfcaon, chemcal reamen, and packagng n dfferen ways dependng on cusomer preferences. Supply chan modelng and supply chan managemen have receved a lo of aenon among companes n recen years, [2]. I provdes a ool for negraed plannng of several nerrelaed plannng suaons. A drvng force o he developmen of supply chan managemen sysems has been he developmen of company wde daabase for daa collecon Ths research s suppored by he Posharves Technology Innovaon Cener, Commsson on Hgher Educaon, Bangkok, Thaland. Chamongkol Lmpanchob s wh he Indusral Engneerng Deparmen, Faculy of Engneerng a Kamphaeng Saen, Kasesar Unversy, Nakhonpahom, Thaland (e-mal: fengckl@ku.ac.h). and effcen opmzers o solve he resulng, ofen large, opmzaon models. A basc descrpon of supply chan modelng s found n Gunnarsson and Vllalobos [3]. A more dealed descrpon of ndusral cases can be found n Sadler and Klger [4]. Examples nclude a case of foresry producon by Troncoso and Garrdo [5] and a case of wood urnng company by Pasor [6]. Wh respec o developng and applyng plannng model n dfferen nsances of he food ndusry and n parcular n he fru ndusry, mahemacal programmng plannng models have been proposed. For example as n a case of packagng plan n he fru ndusry by Blanco [7] who gve an overvew of operaons managemen modelng n he Argenna fru ndusry and developed a mxed neger lnear programmng o formulaed plannng and schedulng models. The model can be appled o esmae he fru processng capacy of he facly n order o esablsh fuure sales polces. Blgen and Ozkarahan [8] revew models for he producon and dsrbuon problem n whea supply chan. The resulng mxed neger lnear programmng problem was solved o opmaly usng decomposon mehods o reduce he compuaonal effor requred, and anoher case abou supply chan nework of pea-based novel proen foods was suded by Apaah and Hendrx [9]. They suded he harvesng and ransporaon plannng problem under uncerany. The problem was formulaed as a mahemacal programmng model o mprove he performance of supply chan neworks have manly focused on fndng he lowes cos a whch novel proen foods can be manufacured whle decdng on locaon of producon and modes of ransporaon based on mnmzng he sum of producon and ransporaon coss. The purpose of hs work s o formulae an opmzaon model descrbng he producon plannng problem, whch ncludes s sorage and processng acves. The model s a mxed neger lnear programmng model and s nended o operae n a mnmum cos mode. The model can be used boh as an operaonal plannng ool, and a sraegc ool o analyze he effecs on he curren plannng n varous suaons. The oulne of he paper s as follow. In Secon II we descrbe he supply chan problem from harves areas o he plan. Then, n Secon III, we formulae he mahemacal model for he problem. In Secon IV we descrbe he soluon mehod and presen compuaonal resuls usng daa from acual operaon of one aromac coconu company n Thaland, and fnally, a concluson n Secon V. Inernaonal Scholarly and Scenfc Research & Innovaon 8(5) scholar.wase.org/ /

2 World Academy of Scence, Engneerng and Technology Inernaonal Journal of Indusral and Manufacurng Engneerng Inernaonal Scence Index, Indusral and Manufacurng Engneerng wase.org/publcaon/ II. PROBLEM DERIPTION The problem s an acual supply chan problem of aromac coconu from one company n Samudsakhorn provnce of Thaland whch has mulple sources, several processng lnes, several demand nodes, and several me perods. The supply chan problem of he company conans decsons concernng whch he desgn of producon flow, he mng of shppng and he sorage a warehouse. Man decsons are also wheher or no a harves are should be conraced and consder he flow of aromac coconus n each process n order o sasfy demand. In addon we have o consder resrcons on capaces of harvesed areas, producon lnes, shppng and sorage a warehouse. The flow dagram for a sngle processng lne s shown n Fg. 1. 1) Fresh coconu from harves areas boh forwardng from self-owned areas and conraced areas, a decson has o be made wheher he coconus s sored n warehouse for furher processng (X 1 ) or s processed (X 2 ). In general, a sorage non-processed coconu s undesrable due o economc reasons bu could be necessary f an ncome of coconus exceed he processng capacy of he lne. 2) The coconus from harves areas and warehouse (X 3 ) are fed o he processng lne. These coconus have been rmmed ou he shell, n a module for frs process coconu rm called PI. 3) Afer frs rm sage, he coconus (X 4 ) ener o he second rm (PII) sage, where hey are rmmed on he op par no cone-cover shape and par of green peel s cu. The coconus ener o he pre-classfcaon (dependng on sze and wegh) where non-radable coconu s separaed for juce producon (W1). 4) Once he coconus have been classfed by sze, hese coconus (X 5 ) ener he hrd rm module (PIII), where hey are rmmed on he op and boom o apered cylnder form wh cone-cover op (he sem end or spkele end of he fru). 5) The coconus receve a reamen wh waer conanng specal chemcal producs (DIP) ha preven brown skn on coconu. The coconu s hen reaed and dred before furher processng. 6) Each coconu eners o qualy classfcaon secor where s classfed by qualy, accordng o he degree of defecs or damage. Some wase s also produced a hs sage (W2). 7) Afer he qualy classfcaon secor, he coconu (X 6 ) eners o he packagng secon (PAK) where s packed accordng o he characerscs of he conaner specfed by he clen. 8) Fnally, processed coconu s sen drecly o cusomers (X 7 ) or here s a possbly o sore n cold sorage facles (X 8 ) for furher delvery (X 9 ). In he followng a bref descrpon of several mporan ssues are dscussed o presen a more complee pcure of he acves. Fg. 1 An llusraon of he possble flows n he model A. Supply of Coconus The supplyng company obans coconus from several sources. The harvesed areas can be classfed no wo groups; self-owned harves areas and conraced harves areas. A he areas ha are owned by he company, he coconus have o be removed durng he plannng perod. The coconu n conraced harves areas can be made avalable by enerng no a conrac wh a suppler. B. Warehouse Warehouse s used o balance seasonal varaon of supply and demand and also o offer more shppng possbles. I receves coconu for sorage from wo sources durng he whole season: fresh aromac coconus ha exceed he processng capacy of he lne whch mus are sorage n warehouse for laer processng and conaners of coconu produced n he packagng secon whch need are sorage n cold sorage. Moreover, here s a separae capacy warehouse for fresh aromac coconus from harvesed areas and coconu producs ha mus be sored n cold sorage. There are dfferen coss of sorage beween cold and general sorage. C. Wase A fracon of non-radable coconu due o aeshec ssues (damage, mperfecons, sze, ec.) are elmnaed from he processng sysem n he dfferen classfcaon modules and sold for coconu juce producon. D. Labor Polcy The company has a permanen labor saff, whch covers a sngle egh-hour workng shf along he whole season. III. MATHEMATICAL MODEL In hs secon we presen he mahemacal model of aromac coconu supply chan problem. We frs descrbe he ses of varables, and hen follow he consrans and he objecve funcon. Inernaonal Scholarly and Scenfc Research & Innovaon 8(5) scholar.wase.org/ /

3 World Academy of Scence, Engneerng and Technology Inernaonal Journal of Indusral and Manufacurng Engneerng Inernaonal Scence Index, Indusral and Manufacurng Engneerng wase.org/publcaon/ Le I be he se of harves areas, C he se of cusomer areas and T he se of me perods. The se of harvesng areas conans subses for self-owned areas (I S ) and harves areas wh a poenal o be conraced (I ). We wll use ndex for harves areas, c for cusomer areas and for me perods. A. Varables Frs we defne varables represenng he supply of coconu n each me perod T. The volumes of forwardng a a harves area can be defned as Sup The volume of coconus ha s harvesed a area n me perod, I S I, X 1 The volume of coconus ha s forwarded from area o warehouse n me perod, I S I, X 2 The volume of coconus ha s drecly forwarded from area o processng lne n me perod, I S I. We also need varables represenng he flows of coconus n producon lnes. We defne X 3 X 4 X 5 X 6 The volume of coconus ha s shpped a warehouse n me perod, The oal volume of coconus ha s forwarded o processng lne n me perod, The oal volume remanng afer screenng a rm process n me perod, The oal volume remanng afer screenng a dppng process n me perod. Varables relaed o ransporng of produc from company o cusomers can be defned as: X 7 X 8 The volume of produc ha s drecly ranspored o cusomer whou sorng a he end of me perod, The volume of produc ha s sored a cold sorage a he end of me perod, X 9 The volume of produc ha s shpped from cold sorage o cusomer a he end of me perod. We also need varables ha are relaed o sorng a warehouse, and we defne as follows ni The volume of coconus ha s sored a warehouse a he end of me perod, nii The volume of produc ha s sored a cold sorage a he end of me perod, Where he volume for = 0 defne he nal condons. All varables defned so far are connuous varables, and hey can be nerpreed as nework flow varables n a mulcommody nework descrbng he possble flows of coconus from harves areas o producon lnes. We also need some se of bnary varable n he model formulaon. For he harves areas we defne Pl = 1, f area s harvesed n perod, I S I, 0, oherwse. B. Inpu Parameers CaA Maxmum harvesng capacy a source, I S I, CapPL The maxmum processng capacy, CaWI Draf capacy of warehouse for coconus sorng, CaWII Draf capacy of cold sorage for coconu produc, Dem c The demand of cusomer c n me perod, RoI The maxmum proporon of wase n preclassfcaon secor, RoII The maxmum proporon of wase n qualy classfcaon secor, SoH The harvesng cos a self-owned area, SoHC The correspondng harvesng cos a conraced area, SoLD The labor cos per volume a rm sage, SoLP The correspondng labor cos a packagng sage, SoIN The nvenory cos per volume a warehouse, SoIC The correspondng nvenory cos a cold sorage. C. Consrans To descrbe he need for harvesng a dfferen areas, we have he followng consrans and T T Pl = 1 I, (1), S Pl 1 I. (2), Consrans (1) specfy ha each self-owned harves area has o be harvesed exacly once (n exacly one me perod) durng he plannng perod, and consrans (2) specfy ha each poenal harves area o be conraced has o be harvesed a mos once durng he plannng perod. If a consran n (2) s sasfed wh src nequaly, no harvesng akes place n any of he me perods n ha harves area, whch s nerpreed as no conrac of he harves area. In such a case, here s no supply from he harves area. The consrans Sup CaA Pl I I, T, (3), S where CaA s he volume of coconu avalable a source o ensure ha he harvesed volume of a coconu n a perod never exceeds he harvesng capaces. To assure ha he coconus are harvesed a all harves area are forwarded o he processng lne and warehouse n he same me perod, we have he consrans. Inernaonal Scholarly and Scenfc Research & Innovaon 8(5) scholar.wase.org/ /

4 World Academy of Scence, Engneerng and Technology Inernaonal Journal of Indusral and Manufacurng Engneerng Inernaonal Scence Index, Indusral and Manufacurng Engneerng wase.org/publcaon/ I ( X + ) X Sup = 2 1, T I (4) These consrans also assure ha he forwarded quany s equal o he avalable quany. Par of he ncomng coconus ( Sup ) feeds he processng lne (X 2 ) and f he producon capacy s exceed he res s derved o sorage (X 1 ). The warehouse has a lmed sorage capacy of fresh coconus. Le CaWI denoe he sorng capacy a warehouse. The capacy consrans can hen be formulaed as X1 CaWI, T I (5) In consrans (5) he capacy s defned as he volume of fresh coconus sored a he end of he perod. To ensure ha he volumes sored a a warehouse never exceeds he saed sorage capacy. The balancng consrans for fresh coconus a warehouse are expressed as: ni + 1 = ni + X1 I X 3, T (6) The maxmum processng capacy of he processng lne has o do wh he volume of coconus ha can be handled a he enrance of he PI module, whch s n urn dependen on he processng capacy. Then, he consrans X I 2 + X 3 CapPL, T (7) make sure ha s capacy s no exceed. The nework srucure ndcaes ha we need some ses of flow balancng consrans. For coconus enerng PI module (X 4 ) f confrmed by fresh coconus enerng he sysem (X 2 ) and non-processed cold sored coconus (X 3 ) f requred, he balancng consrans can be formulaed as X I 2 + X 3 = X 4, T (8) The coconus leavng PII module s he fracon of nonwased peces enerng he module are expressed as X 4 ( 1 RoI )X 5 =, T (9) where RoI s he fracon of wased coconus whch non-sze n pre-classfcaon secor. And afer DIP module, n a smlar way for qualy classfcaon secor he consrans become X 5 ( 1 RoII )X 6 =, T (10) Snce coconus from DIP process have o be packed mmedaely n he same me perod, eher drecly o a cusomer (X 7 ) or o a cold sorage (X 8 ) for laer ransporaon, he flow balancng consran become X 6 X 7 + X 8 =, T (11) We also have o consder a number of capacy resrcons regardng sorng of produc a cold sorage. Le he oal sorng capacy be denoed by CaWII. Then, he consrans X CaWII, (12) 8 T and he balancng consrans for sored producs a cold sorage are expressed as nii = nii + X X 9, T (13) Fnally, we have o express consrans ensurng ha he demand a cusomer s sasfed. The demand a cusomer c n me perod s denoed by Dem c. The demand consrans can now be expressed as and X 7 + X 9 Demc, T c Cus T ( 9 c Cus T (14) X 7 + X ) Dem (15) In consrans (14) and (15) o assure ha he oal demand a he end of perod s sasfed. D. Objecve Funcon The objecve for he supplyng and plannng company s o mnmze he oal cos for sasfyng he conraced demand. The oal cos can be expressed as c z = C har + C lob + C nv where C har = harvesng cos, C lob = labor cos, and C nv = nvenory cos. Le SoH be he harvesng cos of self-owned area, and le SoHC be he correspondng harvesng cos for conraced area. The oal harvesng cos can now be expressed as: har SoH Pl + I S T I T C = SoHC Pl (16) where he frs erm expresses he fxed harvesng cos a selfowned harves areas and he second erm expresses he fxed harvesng cos a conraced harves areas. Le SoLP be he labor cos per volume a rm sage, and le SoLD be he correspondng labor cos a packagng secon. The oal labor cos can hen be expressed as: Inernaonal Scholarly and Scenfc Research & Innovaon 8(5) scholar.wase.org/ /

5 World Academy of Scence, Engneerng and Technology Inernaonal Journal of Indusral and Manufacurng Engneerng Inernaonal Scence Index, Indusral and Manufacurng Engneerng wase.org/publcaon/ ( lab C = ( SoLP )( X + X 5 ) + SoLD )( X 6 T T 4 ) (17) where he frs erm expresses he labor cos of rm secor (PI, PII, and PIII) and he second erm expresses he labor cos of packagng secor. Fnally, we have o express he nvenory cos a warehouse and cold sorage. Le SoIN be he nvenory cos per volume of sorng a warehouse, and le SoIC be he correspondng cos a cold sorage. We can hen express he oal nvenory coss as: C nv I T 1 + T = ( SoIN )X ( SoIC )X (18) where he frs erm express he cos of sorng a warehouse, and where he second erms express he cos of sorng produc a cold sorage. IV. COMPUTATIONAL STUDY AND RESULTS In hs secon, he compuaonal expermens ha were carred ou on real applcaon are presened for he coconu supply chan model. The es problem s gven from one of he larges company whch expors aromac coconu n Samudsakhorn provnce. The company has herefore a large number of harves areas whch can be consdered as self-owned. Informaon regardng o he sze of he es problem s gven n Table I. A. Soluon Mehods The mxed neger lnear programmng formulaon descrbed n he prevous secon was mplemened usng he modelng language AMPL [10], and he problem was solved wh sandard mahemacal programmng sofware wh he branch-and-bound algorhm called ILOG CPLEX 8.0 [11]. The compuaonal ess were performed on a Inel CORE TM 5 wh 3.30 GHz processor and 4.00 GB of RAM. TABLE I THE SIZE OF THE TEST PROBLEM Number of self-owned harves areas 128 Number of conracs harves areas 70 Number of cusomers 3 Number of me perods 20 The modelng Language AMPL has been used o model he problem. As LP-solver we have used CPLEX. To solve he mxed neger lnear programmng problem drecly usng CPLEX, we used he defaul seng. The olerance from he opmal neger soluon was se o 0.05%. B. Compuaonal Resuls The resul of solvng s gven n Table II. The objecve funcon value s gven n cos/conaner, no o reveal he acual values. 8 TABLE II COMPUTATIONAL OF THE MODEL BASED ON THE INPUT DATA STRUCTURES Objecve funcon (THB) Toal number of varables Number of bnary varables Number of neger varables Number of lnear varables 420 Number of consrans 504 Solver memory used (MB) Soluon me n CPU (second) 251 Gap olerance 0.05 Table II shows he compuaonal resuls ha he soluon me s accepable and whn praccal me lms. The qualy of soluon s very hgh as we ge very small gaps o he opmal neger soluon. The opmal oal cos of operaon for hs case s THB Ths oal cos was reduced by 10.12%.when compare o he oal cos confguraon of he base case. The resul obaned demonsraes clearly he savngs of opmzaon ha dcae par of he aromac coconu producon nework srucure. Such resuls are a valuable ool for he manager o esmae he processng capacy n order o esablsh sales commmens for he nex busness year. V. CONCLUSION The man purpose of hs paper s o presen a model and soluon approach ha can be used as a decson suppor ool for producon plannng of he supply chan of aromac coconu. The mahemacal model developed gves a dealed descrpon of he supply chan problem consdered. I has been appled n a mnmum cos mode n order o esmae he producon capacy of he facly. Resuls were presened correspondng o a processng plan operang one processng lne. The resul of problem was solved by a commercal IP solver,.e., CPLEX. The qualy of he soluons found s very hgh, he objecve funcon values s whn 0.05% of he opmal value. The model s esed on a real ndusral case and has been possble o evaluae a number of sraegc analyses. The presen model can produce beer and more flexble soluons compared o manual plannng. In concluson, we beleve ha he suggesed model and soluon approach can be used as an mporan ool n he decson makng by he plannng saff a any enrepreneur n he consdered ndusry. Several mprovemens o address more realsc versons of he sysem are possble and wll also movae fuure work. For example, he consderaon of several parallel processes lnes, ransporaon ssues, ec. A furher exenson of he presen work s o nclude he explc consderaon of he sochasc naure of he sysem no he sudy. ACKNOWLEDGMENT Ths research s suppored by he Posharves Technology Innovaon Cener, Commsson on Hgher Educaon, Bangkok, Thaland. Inernaonal Scholarly and Scenfc Research & Innovaon 8(5) scholar.wase.org/ /

6 World Academy of Scence, Engneerng and Technology Inernaonal Journal of Indusral and Manufacurng Engneerng Inernaonal Scence Index, Indusral and Manufacurng Engneerng wase.org/publcaon/ REFERENCES [1] Mnsry of Agrculure and Cooperaves, Aromac coconu, Bangkok, [2] O. Ahumada, and J.R. Vllalobos, Applcaon of plannng models n he agr-food supply chan: A revew, European Journal of Operaonal Research, vol. 195, pp. 1-20, [3] H. Gunnarsson, M. Ronnqvs, and J.T. Lundgren, Supply chan modelng of fores fuel, European Journal of Operaonal Research, vol. 158, pp , [4] H. Sadler, and C. Klger, Supply chan managemen and Advanced plannng, Sprnger-Verlag: Berln, [5] J.J. Troncoso, and R.A. Garrdo, Foresry producon and logscs plannng: an analyss usng mxed-neger programmng, Fores polcy and economcs, vol. 7, pp , [6] R. Pasor, J. Almras, and M. Maeo, Plannng producon usng mahemacal programmng: The case of a woodurnng company, Compuers & Operaons research, vol. 36, pp , [7] A.M. Blanco, G. Masn, N. Peracc, and J.A. Bandon, Operaonal managemen of a packagng plan n he fru ndusry, Journal of food engneerng, vol. 70, pp , [8] B. Blgen, and I. Ozkarahan, A mxed-neger lnear programmng model for bulk gran blendng and shppng, Inernaonal journal of producon economcs, vol. 107, pp , [9] R.K. Apaah, and E.X.T. Hendrx, Desgn of supply chan nework for a pea-based novel proen foods, Journal of food engneerng, vol. 70, pp , [10] R. Fourer, D.M. Gay, and B.W. Kernghan, AMPL A Modelng Language for Mahemacal Programmng (2 nd ed.), Uned Saes: TnomsonLeanng, [11] hp:// Inernaonal Scholarly and Scenfc Research & Innovaon 8(5) scholar.wase.org/ /