Inventory Balancing in Disassembly Line: A Multiperiod Problem

Transcription

1 Invenory Balancng n Dsassembly Lne: A Mulperod Problem [ ] Badr O. Johar and Surendra M. Gupa * Laboraory for Responsble Manufacurng 334 SN Deparmen of MIE Norheasern Unversy 360 Hunngon Avenue Boson MA USA Proceedngs of he 2007 POMS-Dallas Meeng May 4 -May *Correspondence: e-mal: gupa@neu.edu; URL: hp:// Phone: (617) ; Fax: (617)

2 ABSTRACT Produc recovery has been he cener of aenon of OEMs n recen years because of he mposed envronmenal regulaons and he economcal benefs behnd. The process of dsassembly (demanufacurng) nvolves many challenges ha complcae he process furher. Addonal nvenory conrol and plannng complcaons arse because of he dspary beween demand and he lne yeld. In prevous research we proposed a model o balance he nvenory a he dfferen worksaons. In hs paper we wll valdae he model n a Mulperod case where he nvenory and demand forecasng of fuure perods s consdered n he model. Conrollng he quany of produc dsassembled wll mnmze he mpac of dsassembled pars nvenory. An example of a PC module s consdered o llusrae he approach. Keywords: Dsassembly lne Invenory conrol End of lfe producs Dsassembly modelng Opmzaon 1. INTRODUCTION Research has focused laely on he reverse supply chan mpac on he produc lfe cycle and he envronmen. Frms ha nvolved n reverse logsc grealy benef from hese acves by reusng maerals and reducng energy use. Many reasons were behnd he grea aenon ha has been devoed o he EOL producs reurns and recovery sysems. Manly n recen year frms have faced ncreasng pressures from consumers and governmenal regulaons o become more envronmenally responsble [1]. Also Consumers become more envronmenally conscous and producers have realzed he economcal benefs behnd he pracce. In shor organzaons are acvely workng o

3 mprove her reverse logscs funcons o manage he flow of producs and servces movng backward hrough he supply chan [2]. The managemen of a reverse supply chan sysem s compleely dfferen from he managemen of a radonal forward logscs sysem. The former s very complex o manage and ha s due o he hgh varably n qualy of reurned ems quany of ems suppled and demanded and mng of reurns [1]. One of he aspecs of he dsassembly feld s producon and nvenory managemen. Our research wll focus on hs aspec assumng ha a vald ransporaon and dsrbuon nework exss. Due o he dspary beween demand and lne yelds many nvenory problem arses durng he dsassembly process. Uncerany abou he qualy of reurned producs or knowledge abou prevous modfcaons ha have been done o he EOL or he workng envronmen ha produc used o operae n could sgnfcanly affec he over all performance of he lne hence he managemen of he producs flow. Thus he esablshmen of dsassembly and remanufacurng facles are necessary o handle he overwhelmng number of producs rereved every year. So for hese facles o be profable we have o develop models and echnques o help opmze her operaons [3]. Frms nvolved n he dsassembly acves requre producon plannng and conrol sysem. Such sysems wll allow decson makers o examne he profably of he sysem before engagng n any recovery process. In hs paper we nend o develop a mahemacal model based on prevous model developed for remanufacurng envronmen by Jayaraman. I s a mulperod formulaon ha wll help us provde more nsgh o planners. The model wll consder he opons of dsposal recyclng of cores

4 and subassembly. Manly he demand s for dsassembled pars raher han remnaufacrured producs. Also our model wll ake n consderaon of space requremens. remanufacured or refurbshed EOL producs. The model assumed a sngle produc ype; however fuure research wll nclude a mul-produc model. 2. PROBLEM DESCRIPTION In dsassembly envronmen he radonal managemen ools and supply chan mehods hardly apply o he suaon. One of he mos challengng ssues s he nvenory managemen of reurned producs and he dsassembled pars and subassembles. Afer producs are acqured from he end cusomers hey are brough back o he dsassembly facly. Producs are hen sor no caegores and some are sen for dsassembly recyclng and ohers are dsposed of. Fgure 1 s a graphcal represenaon of he process. In regular remanufacurng envronmen demand exss for core producs. Sore EOL Producs Brough Back o Facly Dsassembly Operaons Demand Sources Dsposal Fgure 1. Graphcal represenaon of he process These producs are brough back and beng dsassembled remanufacured and reassembled o flow back o he end cusomers as a remanufacured produc. The purpose of remanufacurng s o brng he used produc o as new condon. In hs research

5 we are focused on only he dsassembly facly where demand exss for he dsassembled pars and subassembles ndvdually raher han as a whole un. Produc ends o explode durng he dsassembly process generang smaller subassembles. Worksaons end o experence dfferen accumulaon raes of subassembles or pars as well as dfferen depleon raes because of dfferences n her demands. Such dfferences creae unceranes n nvenores and space requremens a he worksaons. I s herefore necessary o develop a mehod o deermne approprae nvenory levels her upper and lower bounds and ways o handle and manan work-n-process (WIP) a suable levels [5]. Also he proper managemen of he excess nvenory ha s beyond demand s mporan. Decson maker has o deermne wha s necessary and how much safey sock o keep. Carryng cos s a facor n hs decson n addon o space requremens. 3. INVENTORY MANAGEMENT SYSTEM 3.1 Invenory Managemen Sysem Descrpon In hs secon we consder a dsassembly facly whose general framework s shown n fgure 1. End-of-Lfe (EOL) producs are beng brough back o he dsassembly facly from cusomers when producs lfe cycle ends. Producs vary n her qualy and condons. Producs are hen sored based on her qualy and sen o dsassembly operaons recyclng or are dsposed of [6]. There are hree qualy levels for EOL producs: Good qualy average qualy and mperfec qualy. In order o mee he demand of subassembles or pars dsassembled orders for new pars can be acqured hrough ousde supplers f can no be fulflled from dsassembled componens. The

6 objecve of he sysem s o conrol he nvenory levels of core producs and dsassembled pars n he sysem o sasfy demand and mnmze he sum of varable coss. 3.2 Noaon I J K T Se of core producs ha are elgble for dsassembly Se of subassembles and/or pars dsassembled ualy level of he EOL produc Tme perod Known Parameers: dc C k Cos o dspose one un of core ype wh qualy level k n perod. recc C k Cos o recycle one un of core ype wh qualy level k n perod holc C k Cos o hold one un of core ype wh qualy level k n perod. ($)/Un/Tme C Cos o dspose one un of subassembly j n perod dss j C Cos o recycle one un of subassembly j n perod recs j C Cos o hold one un of subassembly j n perod. ($)/Un/Tme hols j C Cos of purchasng a new subassembly j from an ousde suppler n perod. pur j re k uany reurned of core ype wh qualy level k n perod. T k Tm o dsassemble one un of core ype wh qualy level k n perod AT Tme allowed for dsassembly operaons n perod D j Demand of subassembly ype j n perod WC Invenory space avalably of core ype n perod expressed n cubc uns

7 WS j Bn space avalably of subassembly ype j n perod expressed n cubc uns w Amoun of space consumed by one un of core ype w j Amoun of space consumed by one un of subassembly ype j dc CAP Facly capacy of dsassembled cores n perod ds CAP Dsposal capacy n perod rec CAP Recyclng capacy n perod ψ Mass o un converson of core ype ψ j Mass o un converson of subassembly ype j Decson Varables: dc k uany of core ype wh qualy level k dsassembled n perod dsc k uany of core ype wh qualy level k dsposed of n perod recc k uany of core ype wh qualy level k recycled n perod nvc k uany of core ype wh qualy level k reman a end of perod uany of subassembly ype j wh qualy level k dsposed of n perod dss j uany of subassembly ype j wh qualy level k recycled n perod recs j uany of subassembly ype j wh qualy level k reman a end of perod nvs j uany of subassembly ype j purchased n perod pur j Assumpons: 1. Sngle produc model wh sac deermnsc nvenory 2. Demand and reurns are consan and known.

8 3. Zero nvenory a he end of las perod 3.2 Formulaon: Mn dc dc dsc dsc recc recc C k * k + C k * k + k k + C * k k k k dss dss recs recs hols nvs pur + C j * j + C j * j + C j * j + C j * j holc k * j j j j C pur nvc k Subjec o nvc re dc = + k. (1) nvc k k 1 k k nvs nvs dc pur dss recs = D j. (2) j k j k k k w k j j dc T k * k AT. (3) dc dc k CAP. (4) nvc w * WC. (5) k nvs * WS j. (6) j j j dsc dss ds * k + ψ j * j CAP ψ. (7) k j recc recs rec * k + ψ j * j CAP ψ. (8) k j j dc rec dsc + k. (9) re k k k k All varables 0 j k j

9 DISCUSSION The nvenory managemen model n hs paper s an exenson o a prevous model. The work on hs model was based on Jayaraman work n he producon plannng for closed loop supply chan. However our model s dfferen n focusng on dsassembly aspec raher han remanufacurng. Ths model akes n consderaon he recyclng and dsposal opon of EOL producs ha do no qualfy for dsassembly. Also our work focuses on he nvenory of pars and/or subassembles along he dsassembly lne. In realy he space avalable a each worksaon (sorage bn) and n any sorage facly whn a warehouse n general s a lmed resource [6]. Ths model akes n consderaon ha any carred nvenory of core producs ha have no ye been dsassembled from a prevous perod can acually be carred n house. Also only allows a lmed number of subassembles and/or pars o be sored n he sorage bn. EOL producs and subassembles ha are sen o recyclng or dsposal should mee he regulaons where usually a lm of how much o dspose a each perod s mposed and do no exceed capacy of recyclng facly. The model wll be valdaed and furher analyzed n fuure research under he proposed consran. The resuls wll be compared o a model where no such consrans apply. An example of a PC s presened nex o show he accumulaon of nvenory. NUMERICAL EXAMPLE As an example we consder he dsassembly lne of a personal compuer (PC). Ths example provdes a relevan and real applcaon of a dsassembly lne problem and was aken from McGovern and Gupa [7]. The purpose of hs example s o show he mpac of dsassembly of personal compuer (PC) on he oal nvenory generaed a each

10 worksaon over a seven-day perod. The PC consss of 8 componens (n=8) wh componen removal mes and assocaed demands shown n Table 1. The followng precedence relaonshps hold beween dfferen asks: (2 OR 3) The arrow means mus precede. The number of producs o be dsassembled s based on he hghes demand of a componen. The demand of RAM modules (RAM) s he hghes (750). However every produc dsassembled yelds 2 modules hus he acual needed producs s 375. The nex hghes demand s for he Moherboards (MB) wh 720 uns needed. Thus quany of PC o be dsassembled s 720 uns. The dsassembly lne speed allowed s 40 seconds for each worksaon (CT=40) and s calculaed by assumng an 8 hour shf per day or seconds per day (L= 8 X 60 X 60 =28800 seconds). Thus me allowed for each worksaon (CT) s equal o 28800/720 = 40 S/WS. Table 1. Dsassembly asks of a personal compuer (PC) Task Removal of Componen Componen Removal Tme Hazardous Componen Demand 1 PC op cover 14 No Floppy drve 10 No Hard drve 12 No Back plane 18 No PCI cards 23 No RAM (2) 16 No Power supply 20 Yes Moherboard 36 No 720 For hs example we make he followng assumpons: Componen removal mes are deermnsc consan and neger. Each produc undergoes complee dsassembly.

11 All producs conan all componens wh no addons deleons or modfcaons. Each ask s assgned o one and only one worksaon. The sum of he componen removal mes of all he componens assgned o a worksaon does no exceed CT. The precedence relaonshps among he componens mus no be volaed. Componens have no physcal or funconal defecs. Table 2. DLPB greedy algorhm and ACO soluon Worksaon Allocaed Task(s) An opmal allocaon of asks for hs example a varous worksaons s shown n Table 2. Thus he nvenory generaed s spread over 4 worksaons. Worksaon 1 handles componens 1 and 5. Worksaon 2 handles componens 3 6 and 2. Worksaon 8 handles componen 8 and worksaon 4 handles componens 7 and 4. In addon o he dspary n quanes generaed he szes and he mass of he componens are also dfferen. Table 3 presens he cumulave nvenory balance for each componen recorded for seven days afer dsassemblng 720 PCs every day and meeng he demand for each of he componens as shown n Table 1. From Table 3 one can clearly observe he dermen creaed due o he dspary beween he demand and he yeld from dsassembly. I s obvous ha such rapdly ncreasng nvenores could be devasang o he corporaon.

12 Table 3. Cumulave nvenory balance for each componen recorded for seven days Componen Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7 TC FD HD BP PCI RAM PU MB CONCLUSION In hs paper we dscussed he problem of balancng nvenory n he dsassembly lne. Managng nvenory s an mporan aspec of managng a busness and developng he rgh ools o do so s essenal for frms nvolved n dsassembly o ensure profably. Here we exended our prevous model o balance he amoun of nvenory ha s sored n he worksaon bns along he lne and formulaed he problem as a lnear programmng model. REFERENCES [1] Jayaraman Vadyanahan Producon Plannng for Closed-loop Supply Chans wh Produc Recovery and Reuse: an Analycal Approach Inernaonal Journal of Producon Research Vol. 44 No [2] Oh Yong Hu and Hwang Hark Deermnsc Invenory Model for Recyclng Sysem Journal of Inellgen Manufacurng Vol

13 [3] Guner Kenneh L. Invenory and Value Managemen n Demanufacurng Facles. PhD Dsseraon [4] Gaudee Kevn J. Invenory Plannng for Remanufacurng. PhD Dsseraon [5] Johar Badr O. and Gupa S. M. Invenory Issues Arsng from Balancng a Dsassembly lne Proceedngs of he 17 h Annual Conference of Producon and Operaons Managemen Socey CD-ROM [6] Johar Badr O. and Gupa S. M. Balancng Invenory Generaed from a Dsassembly Lne: Mahemacal Approach Proceedngs of SPIE Conference on Envronmenally Conscous Manufacurng VI Vol [7] McGovern S. M. and Gupa S. M. Local Search Heurscs and Greedy Algorhm for Balancng a Dsassembly Lne Inernaonal Journal of Operaons and uanave Managemen Vol. 11 No