THE EFFECTS OF BACKORDER INFORMATION AND REDUCED-SETUP DISPATCHING UNDER REORDER POINT OR KANBAN REPLENISHMENT. S. T. Enns

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1 Proceedngs of he 2006 Wner Smulaon Conference L. F. Perrone, F. P. Weland, J. Lu, B. G. Lawson, D. M. Ncol, and R. M. Fujmoo, eds. THE EFFECTS OF BACKORDER INFORMATION AND REDUCED-SETUP DISPATCHING UNDER REORDER POINT OR KANBAN REPLENISHMENT S. T. Dep. of Mechancal and Manufacurng Engneerng Unversy of Calgary Calgary, AB., T2NN4, CANADA ABSTRACT Ths research consders a sngle-sage, capacy-consraned worksaon wh crculang ransporers used for replenshmen and ndependen cusomer demand for compleed pars. Characerscs of reorder pon versus Kanban replenshmen are examned. One objecve s o deermne he usefulness of backorder nformaon for upsream order placemen. A second objecve s o nvesgae he benefs of dspachng based on seup me reducon. Performance s measured n erms nvenory couns and he proporon of cusomer orders flled from sock. The area under radeoff curves s used o evaluae comparsons sascally. Resuls show backorder nformaon and seup me reducon boh mprove performance and ha neracon effecs are no sgnfcan. Ths ndcaes ha reorder pon sysems can ouperform Kanban sysems wheher or no dspachng based on seup me reducon s used. INTRODUCTION Connuous-revew reorder pon and Kanban replenshmen sysems are relaed n ha boh pull nvenory downsream. The closeness of her relaonshp depends on how hey are mplemened or, n he case of research sudes, he assumpons made n analyss or expermenaon. There are many good references on reorder pon and Kanban sysems, ncludng Spper and Bulfn (997), Slver e. al (998) and Vollmann e. al (2005). Kanban modelng and research s revewed by Groenevel (992). Connuous-revew reorder pon sudes commonly assume backorder nformaon s ncorporaed n he order release decson. They also usually assume orders are nsananeously ransmed o upsream saons and ha, gven sock s avalable, shpmens are mmedaely made. Shppng, or lead me, delays are hen ncurred pror o downsream delvery. The decson varables are commonly consdered o be he reorder pon and he order lo sze. Kanban sudes do no assume he use of backorder nformaon. The decson varables nclude he number of Kanban cards and he Kanban lo sze. If a wo-card Kanban sysem s used, he number of boh ransporaon and producon cards needs o be deermned. Whle wo-card sysems are common, especally for assembly operaons, furher consderaon n hs sudy s gven only o snglecard sysems. Anoher ype of connuous-revew replenshmen ha s even smpler han a Kanban sysem s he wo-bn sysem. In hs sysem he reorder pon s based on he sze of he smaller bn and he order lo s equal o he larger bn sze. No backorder nformaon s used and only one lo sze order can be n he replenshmen loop a a me. The consderaon of ransporaon ssues furher complcaes he desgn and analyss of replenshmen sysems. In reorder pon sysems upsream supply saons are no lkely o make shpmens nsananeously when an order s receved snce here s lkely o be a delay before a ransporer becomes avalable. In Kanban sysems s also possble ha orders are ransmed nsananeously o upsream supply saons usng an elecronc Kanban, where lghs or oher sgnals replace he use of physcal cards. Ths makes order placemen smlar o a reorder pon sysem wh elecronc order placemen. Delays n boh cases wll be dependen on he number of ransporers or frequency of shpmen. More ofen Kanban cards crculae and ac o delver orders o upsream supply saons n he form of cards or conaners. Therefore order placemens are no nsananeous and hs may affec ransporaon varable sengs. Furhermore, f nvenory s no avalable upsream here may sll wll be a shppng delay and he lengh of hs delay wll depend on wheher he ransporer crculaes connuously or was upsream unl he order can be flled. Ths llusraes ha assumpons abou order placemen and shpmen delays are no always clear cu for eher reorder pon or Kanban sysems and mus be clearly saed. Wh capacy-consraned worksaons here are also ssues of prory dspachng for los n queue. There has been a far amoun of dscusson on seup me reducon n Kanban sysems under crcumsances where wo or more /06/$ IEEE 94

2 los of he same par ype may be n queue along wh oher par ype los. Prory rules have been developed ha faclae processng mulple los of he same par ype sequenally, hus reducng he number of seups. Alhough here has been less dscusson of seup me reducon for reorder pon sysems, he same approach can be used. Comparsons of replenshmen sysems mus be very clear on he assumpons made. As well, hey mus aemp o denfy he characerscs of he sysems whch acually deermne dfferences n performance hey are o be fully undersood. Few sudes have drecly compared Kanban and reorder pon sraeges. Krajewsk e al. (987) conduced comparsons o deermne mporan plannng and conrol facors havng an mpac on manufacurng performance. Resuls of Kanban and reorder pon comparsons showed ha here was no much dfference n performance. Seup me reducon, lo sze reducon, defec reducon and oher facors, whch can be appled usng any replenshmen sraegy, were found o be more sgnfcan han he choce of replenshmen logc. Yang (998) compared resuls usng Kanban and reorder pon sraeges n a sngle-sage, capacy-consraned sysem. He concluded ha resuls usng he Kanban sraegy were superor. However, he Kanban sraegy was modfed o essenally allow lo-szes of one and dspachng whch faclaed seup me reducon. Snce he lo szng and dspachng polces were no conssenly appled, s dffcul o arbue he mproved performance o he Kanban logc n hs sudy. Suwanruj and (2006a) concluded performance usng reorder pons domnaed ha usng Kanbans n a dsrbuon sysem whou capacy consrans. Suwanruj and (2006b) furher concluded ha whle reorder pons are generally beer under me-varyng demand for eher capacy consraned or unconsraned neworks of saons, here are crcumsances wh level demand paerns and capacy consrans where a Kanban sysem may slghly ouperform a reorder pon sysem. The conclusons of boh sudes were based on nsananeous order ransmsson and shpmen assumpons (.e. nfne number of ransporers). Ths sudy s an exenson o anoher sudy examnng he dfferences beween connuous-revew reorder pon and sngle-card Kanban sysems under level and seasonal demand paerns (, 2006). The prevous resuls, usng he proporon of cusomer orders flled from sock as a performance measure, lead o he concluson reorder pon sysems ouperform Kanban sysems. Ths was manly due o nsananeous order ransmsson for he reorder pon sysem, whch resuled n beer response o changes n demand. However backorder nformaon also proved o be value when average backorders were examned, especally under seasonal demand. In hs follow-up sudy he value of backorder nformaon s examned more closely under condons where order ransmsson assumpons are conssen across all replenshmen sysems. A second facor relaes o prory dspachng and he effec of rules based on seup reducon. As well, analyss of possble neracon effecs s nroduced. In he nex secon he logc used n modelng reorder pon sysems s compared wh ha used n Kanban sysems. Followng hs, he smulaon model used n hs research s presened. The expermenal desgn and resuls are descrbed n laer secons. 2 REPLENISHMENT LOGIC AND EXECUTION The connuous-revew reorder pon sraegy assumes ha orders are rggered as soon as nvenory falls below an order pon. Indvdual order pons mus be defned for each par ype, or sock keepng un (sku). If s assumed ha order quanes are mulples of some lo sze Q, he followng equaon can be used o descrbe he order quany, Q, a some gven me. OP ( Inv, + OR, + OT, + OQ, BO, ) Q =, max 0, Q () Q where: OP - Order pon for sku Inv, - Quany of sku fnshed goods n sock OR, - Quany of sku orders released o suppler bu no ye flled OT, - Quany of sku n rans OQ, - Quany of sku n queue or on machne BO, - Quany of sku backordered Under he assumpon ha processed pars become avalable o mee cusomer demand, Inv represens fnshed goods n sock. Wh ROP sraeges s ofen assumed ha orders are placed nsananeously o upsream saons. In hs case OR represens orders ha have no been flled due o lack of nvenory a upsream saons or orders wang upsream for a ransporer. An upsream saon could refer o eher an exernal suppler or an nernal saon performng a precedng operaon. Wh a sngle-card Kanban sraegy he oal number of cards n crculaon for each sock keepng un (sku) mus be specfed. If s assumed he Kanban card s released upsream for recrulaon when a conaner s compleely depleed and K TOT, s he oal number of cards n he replenshmen loop, he order quany, Q, a me s gven by he followng equaon. Q, ( K TOT, ) Q ( Inv, + OR, + OT, + OQ, ) + = max 0, Q Q In hs case he nerpreaon of varables Inv, OT and OQ s he same as for he reorder pon sraegy n Equaon (). However Kanban orders ofen ravel back o he suppler as (2) 95

3 a Kanban card, or conaner, wh he ransporer. In hs case he OR quany could nclude he quany represened by cards wang downsream for pckup and cards n ranspor o he suppler. If he suppler does no have suffcen nvenory, he orders ha have no been flled due o lack of upsream nvenory or orders wang upsream for a ransporer would also be ncluded, as n he case wh he reorder pon sraegy. In comparng he logc used n reorder pon and Kanban sraeges, a key dfference s n he consderaon of backorders. Snce Kanban sysems do no consder backorders, hey lend hemselves o smpler mplemenaons. There s no requremen o keep rack of anyhng beyond he saus a ceran Kanban card locaons. However, one could argue ha he addonal backorder nformaon used by reorder pon sysems should be benefcal, especally under unceran or me-varyng demand. In a sngle-card sraegy he followng equaon provdes a breakdown of where Kanban cards may be locaed and where me delays may occur for sku. Reference o Fgure can provde clarfcaon. K TOT, K S, I, Q, P, W, E, O, where: K TOT, K S, K I, K Q, K P, K W, K E, K O, = (3) - Cards n oal sysem - Cards a upsream (suppler) saon - Cards on nbound ransporer conaners - Cards on conaners n queue - Cards on conaner beng processed - Cards on fnshed goods conaners - Cards wang for ransporer pckup - Cards oubound o suppler If s assumed ha he suppler always has nvenory avalable and ha Kanban cards crculae wh ransporers ha are consanly cyclng, hen K S wll be zero. However, s also possble o sgnal orders o he upsream saon nsananeously raher han usng Kanban cards o communcae he order. In hs modfed Kanban sraegy ransporers may sll crculae conaners from he downsream saon bu he quany pcked up a he upsream saon depends on he orders receved n he me nerval snce he las ransporer depared. Snce orders would ypcally need o wa for a ransporer o make a downsream pckup, K S would no be zero even f he upsream saon always has sock. However under hese nsananeous orderng assumpons, K E and K O are always zero. 3 A SINGLE-STAGE REPLENISHMENT SCENARIO A smple producon scenaro was modeled usng Arena 5.0 dscree-even smulaon sofware (Kelon, e al, 2004). Ths scenaro s shown n Fgure. Two par ypes, or sock keepng uns (skus), are suppled from dfferen upsream saons. These upsream saons are assumed o always have suffcen sock o fll orders. Lo sze quanes of each sku are shpped from he upsream saon and arrve a a capacy-consraned worksaon. If he worksaon machne s busy when a lo arrves, mus jon a queue. When a lo s loaded on he machne, he pars n he lo are processed on a par-by-par bass. Boh par ypes are assumed o have dencal lo szes, seup mes and par processng mes. The lo szes are 5, he seup mes are 0.05 and he par processng mes are me uns. There s no uncerany assocaed wh he seup or processng mes. K S Trans Tme K I Reurn Tme K O Queue Tme K Q Servce Tme K P Machne Processng Saon Fgure : Confguraon of Sngle-Sage Sysem Once he lo s complee, s mmedaely avalable o mee cusomer demand as fnshed goods nvenory. Cusomer arrvals for each ype of sku are ndependen and can be descrbed as a Posson dsrbuon. Each cusomer requres only one un. However he demand paern s seasonal so he demand rae changes over me. The seasonaly for boh skus s descrbed by a snusodal paern wh a mean demand rae of 50, amplude of 0 and cycle lengh of 250 me uns. The demand paern for he wo skus are offse by 25 me uns. As a resul he aggregae workload requremens a he processng saon are farly consan over me even hough he demand for each of he skus s seasonal. The acual demand rae s deermned once every me un based on he expeced demand from he snusodal demand paern mulpled by an uncerany facor. Ths uncerany facor s sampled from a Normal dsrbuon wh a mean of.0 and a sandard devaon of 0.0. There are 8 ransporers n each of he wo replenshmen loops. These ranspors crculae connuously and are spaced so he nerarrval mes a he machne are consan. The me o move from he upsream suppler o he processng saon s 0.8 me uns. The me o move from he processng saon o he upsream suppler s also 0.8 me uns. The ransporers are no assumed o have any oher delays so he crculaon me s.6 me uns. I K E K W 96

4 s assumed he ransporers can carry no los, a sngle lo or mulple los of pars. The replenshmen orders are assumed o be ransmed nsananeously o he upsream saon when eher he reorder pon s reached or a Kanban conaner of fnshed goods s empy. The nex ransporer o crculae pas he upsream saon hen pcks up he number of los ordered and shps hem o he processng worksaon. In oher words, K E and K O n Equaon (3) are equal o 0. The only real dfference beween he reorder pon and Kanban sysems, as mplemened n hs research, s ha he reorder pon sysem uses backorder nformaon whle he Kanban sysem does no. 4 SIMULATION EXPERIMENTAL DESIGN The expermenal desgn conssed of wo facors, each wh wo levels. The frs facor, BO, ndcaed no use ( level) or use (+ level) of backorder nformaon. I wll be noed ha he level descrbes he Kanban sysem and he + level descrbes he reorder pon sysem. The second facor, PDR, ndcaed he ype of prory dspachng rule used for los n queue a he capacyconsraned worksaon. The frs dspach rule was a smple frs-come-frs-serve (FCFS) rule ( level). A seup me s ncurred every me a new lo s processed, even f he lo s of he same par ype. The second prory dspach rule consdered boh requremens and seup me reducon (+ level). The seup reducon rule (PDR=+) was mplemened as follows. If only one ype of par was avalable for processng, a lo of hs par ype was loaded. A seup me was ncurred only f he prevous lo was of a dfferen ype. If boh par ypes were n queue, he mnmum fnshed goods nvenory requred o avod sockou was calculaed for each par ype, assumng a lo of he oher par was beng produced frs. Ths benchmark nvenory level was based on average demand raes. In oher words, he average demand over he me nerval requred o produce boh par ypes, wh seups, was used o deermne a mnmum fnshed goods nvenory benchmark. If boh par ypes had nvenory above he benchmark, he same par ype as was prevously processed was loaded agan so ha a seup could be avoded. If boh par ypes were below he benchmark so sockou of a leas one par ype was lkely, he same par ype as was prevously processed was loaded agan o mnmze seups. If one par ype was above he benchmark and he oher below, he par ype below he benchmark was loaded nex, wheher or no a seup would be ncurred. Performance was measured n erms of he oal nvenory couns n he sysem and he proporon of cusomer demand flled from sock. If a cusomer arrved durng a sockou, he desred em was backordered and hen delvered mmedaely upon replenshmen of fnshed goods nvenory. There s a radeoff beween mnmzng nvenory levels and achevng good delvery performance. Snce he objecve s o deermne he relave domnance of one replenshmen sraegy over anoher across dfferen servce levels, s necessary o generae radeoff curves for boh ypes of measures. Ths was done across all combnaons of expermenal facor sengs by runnng each combnaon of facor sengs a varous nvenory levels. Invenory levels were adjused by changng he order pon n ncremens of 5 and by changng he number of Kanban cards n ncremens of. Typcally 0 sengs were used for each full-facoral combnaon of sengs o generae a radeoff curve. In oher words, 40 combnaons of facor sengs and radeoff curve sengs were requred o generae one full se of radeoff curves. Three replcaons were run a each of he 40 combnaons of sengs. Common random numbers were used as a varance reducon echnque. A warmup perod of 250 me uns was used o reach seady-sae condons and daa was hen colleced over he nex 2500 me uns. If a me un s consdered o be one day and here are 250 workng days per year, hs s he equvalen of 5 years of daa collecon per replcaon. 5 EXPERIMENTAL RESULTS The expermenal resuls are summarzed n fgures 2 and 3. Fgure 2 shows he average nvenory as a funcon of delvery performance when no backorder nformaon s used (BO=). Fgure 3 shows smlar resuls wh backorder nformaon (BO=+). These curves are based on averagng he resuls across he hree replcaons a each combnaon of expermenal sengs. Comparng fgures 2 and 3 ndcaes ha backorder nformaon mproves performance slghly. Lower curves ndcae ha less nvenory s requred o oban any gven level of delvery performance. I s also obvous from boh fgures 2 and 3 ha he dspach rule reducng seups (PDR=+) s preferable o he FCFS dspach rule (PDR=), whch ncurs a seup for each lo. The machne ulzaon, defned o nclude boh he machne seup and par processng mes, for PDR= was 90%. Wh PDR=+ he ulzaon ranged from abou 73% when he proporon delvered from sock was 0.50, o 67% when he proporon delvered from sock was.00. A hgher delvery servce levels more nvenory was requred and he longer average queue lenghs ahead of he machne resuled n more opporunes o elmnae lo seups. Fewer seups resuled n lower ulzaon. 97

5 Avg. Invenory Coun PDR= 60 PDR= Prop. Del. On Tme The ANOVA resuls show ha boh he prory dspach rule (PDR) facor and backorder nformaon (BO) facor were sascally sgnfcan, alhough backorder nformaon provded relavely lle mprovemen. The neracon effec beween he PDR and BO facors was no sgnfcan a he 95% confdence level. Fgure 4 shows a man effecs plo for he resuls whle fgure 5 shows an neracon plo. These graphs confrm ha he dspachng rule based on seup reducon and he use of backorder nformaon boh resul n mproved performance. 62 Man Effecs Plo (fed means) for Area PDR BO 200 Fgure 2: Tradeoff curves wh BO= Mean of Area Avg. Invenory Coun PDR= PDR= Fgure 4: Man Effecs Plo Prop. Del. On Tme Fgure 3: Tradeoff Curves wh BO= Ineracon Plo (fed means) for Area PDR The resuls were also analyzed o deermne sascal sgnfcance and denfy possble neracon effecs. The area under each of he 2 curves generaed (2 BO levels 2 PDR levels 3 replcaons) was calculaed usng a lower servce bound of 0.50 and an upper servce bound of.00. A lower area ndcaes beer performance. These areas were hen reaed as he response n an analyss of varance (ANOVA) model. The resuls are shown n Table. The coeffcen of deermnaon (R 2 ) was 99.45% and resdual analyss ndcaed ha ANOVA modelng assumpons were no beng volaed. Table : ANOVA Resuls Source DF Seq SS Adj SS Adj MS F P PDR BO PDRBO Error Toal Mean CONCLUSIONS BO Fgure 5: Ineracon Plo Ths sudy has denfed some of he ssues concernng he comparson of pull ype replenshmen sysems. The use of backorder nformaon and dspachng based on seup reducon were specfcally examned. Boh were found o be benefcal hrough use of boh radeoff curve and ANOVA comparson echnques. The advanage of usng ANOVA based on measurng he area under radeoff curves was demonsraed. Ths echnque allows dfferences n performance o be sascally verfed when here are radeoffs beween wo performance measures and s desrable o deermne domnance across a range of delvery servce levels. As well, neracon effecs beween varous facors can be deermned. 98

6 ACKNOWLEDGMENTS Ths research was suppored n par by a gran from he Naonal Scence and Engneerng Research Councl (NSERC) of Canada. REFERENCES, S.T A comparson of kanban and reorder pon replenshmen a capacy-consraned worksaon. In Proceedngs of Summer Compuer Smulaon Conference, forhcomng. Groenevel, Harry The Jus-In-Tme Sysem. n Handbooks n Operaons Research and Managemen Scence, Vol. 4, Logscs of Producon and Invenory, Eded by S.C. Graves, A.H.G Rnnooy Kan and P.H. Zpkn, Elsever Scence Publshers, Amserdam, The Neherlands. Kelon, W.D., R.P. Sadowsk, and D.T. Surrock Smulaon wh Arena, 3 rd Ed., New York, NY: McGraw-Hll. Krajewsk, L.J., B.E. Kng, L.P. Rzman, and D.S. Wong Kanban, MRP, and shapng he manufacurng envronmen. Managemen Scence, Vol. 33, No., Slver, E.A., D.F. Pyke, and R. Peerson Invenory Managemen and Producon Plannng and Schedulng, 3 rd Ed., New York, NY: John Wley & Sons. Spper, D., and R.L. Bulfn Producon: Plannng, Conrol and Inegraon, New York, NY: McGraw- Hll. Suwanruj, P., and S.T The role of nformaon, logc and conrol n comparng approaches o supply chan managemen. n Proceedngs of he s Inernaonal Conference on Inegraed Logscs, ed. K.T. Yeo and S. Pokharel, Suwanruj, P., and S.T a. Comparson of supply chan replenshmen sraeges n a non-capacaed dsrbuon sysem. Inernaonal Journal of Rsk Assessmen and Managemen, forhcomng. Suwanruj, P., and S.T b. Evaluang he effecs of capacy consrans and demand paerns on supply chan replenshmen sraeges. Inernaonal Journal of Producon Research, forhcomng. Vollmann, T.E., W.L. Berry, D.C. Whybark, and F.R. Jacobs Manufacurng Plannng and Conrol for Supply Chan Managemen, 5 h Ed., New York, NY: McGraw-Hll. Yang, K.K A comparson of reorder pon and kanban polces for a sngle machne producon sysem. Producon Plannng and Conrol, Vol. 9, No. 4, AUTHOR BIOGRAPHIES SILVANUS T. ENNS s an Assocae Professor a he Unversy of Calgary. He receved a PhD from he Unversy of Mnnesoa. Hs research neress le n he developmen of algorhms o suppor enhanced MRP performance as well as varous aspecs of job shop, bach producon and supply chan modelng and analyss. Hs emal address s <enns@ucalgary.ca>. 99