KANBAN DEVS MODELLING, SIMULATION AND VERIFICATION

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1 KANBAN DEVS MODELLING, SIMULATION AND VERIFICATION Alex Cave and Saed Nahavand School of Engneeng and Technology, Deakn Unvesty, Geelong, Vctoa 3216, Austala ABSTRACT Kanban Contol Systems (KCS) have become a wdely accepted fom of nventoy and poducton contol. The ceaton of ealstc Dscete Events Smulaton (DES) models of KCS eque specfcaton of both nfomaton and mateal flow. Thee ae seveal commecally avalable smulaton packages that ae able to model these systems although the use of an applcaton specfc modellng language povdes means fo apd model development. A new Kanban specfc smulaton language as well as a hgh-speed executon engne s vefed n ths pape though the smulaton of a sngle stage sngle pat type poducton lne. A sngle stage sngle pat KCS s modelled wth exhaustve enumeaton of the decson vaables of contane szes and numbe of Kanbans. Seveal pefomance measues wee used; 95% Confdence Inteval (CI) of contane Flow Tme (FT), mean lne thoughput as well as the Coeffcent of Vaance (CV) of FT and Cycle Tme wee used to detemne the obustness of the contol system. Key Wods: Smulaton, Inventoy Theoy & Applcatons 1. INTRODUCTION Kanban meanng cad n Japanese s a type of poducton contol system developed as pat of the Toyota Poducton System (TPS) and was accepted by Westen academc and ndustal pactce n the ealy 1980 s. The ognal KCS was descbed by Monden (1981a,b,c,d) and snce that tme eseache have pesented seveal dffeent alteatons of ths system categozed by Baynat et al (2002). These systems use Kanban to contol both the amount of Wok In Pogess (WIP) as well as the amount of nventoy at the end of poducton stages. The KCS pescbed, as pat of the TPS s a pull system whee the consumpton of pats s used to tgge poducton o mateal accusatons fo pecedng poducton stages of supples espectvely. A pue pull system has seveal advantages that nclude; egulaton of nventoy at all poducton stages, self-management of pat equements fom the bll of mateals and educton of WIP buld-up. These advantages come at the cost of educed flexblty of the poducton mx as nventoy of sub assembles and aw mateals must be mantaned at all stages of the poducton system. The lmtatons of the ognal Kanban ae descbed by Hall (1981), Huang et al (1983) and Fnch et al (1986). One challenge of usng push oentated Mateal Requements Plannng (MRP) systems s that fnte capacty of poducton stages s not often ncopoated nto the models used. The effect s that WIP bulds up as wok odes ae pushed onto poducton stages at a ate that s faste than poducton. The advantage of ths MRP s that only the equed amount of pats and sub assembles need to be mantaned n the poducton system. Seveal of the late vesons of KCS elaxed the equements fo pats to be mantaned between poducton

2 stages. The CONstant WIP (CONWIP) pesented by Speaman et al (1990) s an example of such systems and ths concept was futhe extended by the Genec Kanban Contol System (GKCS) detaled by Chang and Yh (1994) whle the Extended Kanban Contol System (EKCS) attbuted to Dalley and Lbeopoulos (1995) commonly may use Kanbans that ae shaed between pat types and do not have to mantan base stock at all stages. Genec Kanban (GK) cculates the poducton stages and lmts the oveall WIP by estctng the total numbe of contanes on the stage at any pont n tme. The EKCS also povdes methods fo the demand fo pats to each all poducton stages at the same tme to ncease the esponsveness of the poducton system. Rapd modellng of these Kanban lke poducton systems eques defnton of the physcal flow of both nfomaton and mateal n the fom of Kanban, contanes and pats. Usng DES the complexty of the manufactung system s not lmted by the modellng technology used. Aytug and Dogan (1998) dentfed the need fo an applcaton specfc model geneaton engne fo Kanban systems whle Swnehat and Blackstone (1991) also povde gudance fo modellng such systems usng DES. A base smulaton engne called A Dscete EVent Specfcaton (ADEVS) wtten by Nutao (2004) was extended fo Kanban manufactung systems. Ths was an expesson of Zegle s (1984) wok on Dscete EVent Specfcaton (DEVS) fomalzaton n C++. A scptng language was developed n exensble Makup Langauge (XML), both XML and DEVS ae heachc and make a natual pa. Natonal Insttute of Standads and Technology (NIST) of the US govenment s wokng on standads to descbe pocesses fo the open exchange of pocess data and models between smulaton platfoms usng XML as descbed by Qao et al (2003). Ths was called a Shop Defnton Fle and ths wok shows the gowng mpotance of XML and DES. Wang and Lu (2002) epoted usng an XML based expesson of DEVS that s tanslated nto souce code and then compled to geneate a combned smulaton engne and model. The appoach epoted n ths wok s dffeent as the scptng language s hgh level descbng pe-defned manufactung model components that ae connected togethe to ceate netwok flow models. These netwoks expessed n XML wee ntepeted to ceate models by connectng components that wee defned wthn object lbaes. Wthn ths famewok all ntenal logcs ae pecompled and the ceaton of new enttes eques alteaton of souce code. The pedefned enttes that may be used wth the model scpt nclude; machnes, buffes, delays, Kanban outes, Kanban dspatch posts, demand geneatos, and aw mateal supply. The netwoks detaled n XML nclude the flow of Kanban, pats and dffeent types of Kanban lke contol systems that may be expessed though the placement of Kanban outng enttes and pedefned dspatch post logcs. The contane sze n Kanban systems affects the lot sze and the fequency of mateal tansfes. Contane szes also has mpact on the vaance of cycle tme and the tme between mateal tansfes whle the combnaton of the numbe of Kanbans and the sze of the contanes, contol the total sze of the Fnshed Goods Inventoy (FGI) and the amount of WIP. Consdeng the cental ole of contane szes on Kanban systems, many eseaches have not nvestgated ths nteacton nstead settng the contane sze to ethe a sngle pat fo KCS o the job sze fo GKCS. Ths may be attbuted to the added poblem dmensons ncued when contane szes ae ncluded. Two example smulaton studes that nvestgate contanes szes ae unde evew. Gupta and Gupta (1989) pefomed smulaton studes usng system dynamcs models. They eseached a mult-stage poducton faclty whee each stage poduced a sngle pat type. The effects of educng WIP though contollng the contane szes wee epoted usng smulaton taces. They stessed that nceasng the sze of the contanes had negatve mpact on system pefomance and the numbe of Kanban and the sze of the contanes needed to be tghtly contolled

3 Fgue 1 - Kanban Contol System Dagam Key to Fg. 1: R The set of pat-types. I The set of stages. System Objects P Pat of type K Kanban of pat type on stage D Poduct Demand System Enttes P Pocess numbe q at stage q MB m Machne buffe numbe m on stage PB KB pat specfc poducton cads at stage Pat buffe of pat specfc poducton cads at stage Kanban buffe of pat specfc poducton cads at stage DB Poduct Demand pat specfc poducton cads at stage Decson Vaables CS Contane sze of poduct pat specfc poducton cads at stage NK Numbe of -type Kanban cads at stage Bekley (1996) pefomed a DES study of a seal mxed model poducton lne to povde gudance to the sze of contanes that should be used n Kanban systems. Ths wok showed that the effects of contane sze on WIP, FGI and ode watng tmes wee not easly undestood. Gven constant aveage demand small contane szes ae bette suted to fequent small odes howeve as the effects of setup tme nceases, contane sze should be lage. Smalle contane szes stablze the poduct mx wth the FGI although ths may educe the thoughput of the system and decease custome sevce. The pocessng tme dstbutons fo each pat type used wee equal as wee the demand ates. Bekley povded no clea ecommendatons fo contane sze selecton even wth the smplstc model hghlghtng the dmensonal complexty of these poblems

4 Fgue 2 ManDEVS Scpt Example 2. EXAMPLE SIMULATION MODEL A smulaton model was ceated to vefy the new Kanban applcaton specfc modellng language developed and named Manufactung Dscete Event Specfcaton (ManDEVS). A smplstc sngle stage sngle pat type smulaton model was developed fo checkng the engne and s shown n Fgue 1 wth notaton defned n Equaton 1. Ths seal lne has 10 machnes as ndcated by the ccles and 10 fst n fst out buffes shown as tangles. The poducton stage uses a GKCS as the Kanbans ae emoved po to any FGI that may be pesent at the end of the stage. The Kanbans ae ecycled geneatng nfnte demand whle the pats buffe at the begnnng of the stage also has nfnte supply of pats. The tem Kanban and Genec Kanban (GK) ae used ntechangeably as thee s only a sngle pat type beng poduced on the poducton stage. The conclusons dawn fom the smulaton expeence ae ntended to be appled to sngle stage mult-pat GKCS whee the GK plays a smla ole to the pat specfc Kanban n ths wok. The flow dagam shows a poducton stage whee the contol system s a two dmensonal functon of the contane sze and the numbe of Kanban. The Kanban dspatch post encompasses the pat, demand and Kanban buffe at the begnnng of the stage and as thee s only a sngle pat type poduced thee s no need fo dspatch ules o schedulng. The flow dagam of Fgue 1 was modelled usng ManDEVS. It does not detal the components that wee used to ceate the model that wee defned n the model scpt fle. Ths scpt s stoed n XML though t s less dffcult to ceate and edt models usng a gaphcal

5 edto such as XML Notepad. A sample of the ManDEVS as ntepeted by the edto s shown f Fgue 2. The objectve of the extact s to povde some detal of the syntax of ManDEVS. The example code has two components that ae of the type KB_Route and KB_Dspatch. The components nhet the type fom the paent node the fst devce has the use defned name Pat_KB_Route_Cell_1 whle the second Shed_Post_Cell_1. Whle thee s only a sngle component of each type t s possble to defne multple nstances by addng a new banch to the devce type node and supplyng a new use name. The Pat_KB_Route_Cell_1 epesents the fok at the end of the poducton stage as n Fgue 1 whle the KB_Dspatch s the Kanban buffe and jonng devce at the begnnng of the stage. Components have attbutes that contol pedefned logcs. Pat_KB_Route_Cell_1 wll fok only pat specfc Kanban as the attbute KB_Route_Type s set to be Pat Specfc. The flow of nfomaton and pats s contolled by the defnton of pots that contol outng. The component outes two types of objects, pats and Kanban as ndcated by the sub banches unde Pot. Statng wth the Pot and the sub banch Pat_1 has the attbutes Job_Gen_Pat_1 and 11, ths secton defnes that all pats of type Pat_1 and pocess numbe 11 ae outed to Job_Gen_Pat_1. The logc s smla fo all of the pots although the object types and the attbuted that contol the outng of objects change. 3. EXPERIMENTAL RESULTS Expements wee pefomed on an Alphaseve SC system 64-bt pocesso compute unnng Tue 64-bt. The pocessng tmes on the machnes wee balanced so the each machne poduced 100 pats pe day when machnes utlzaton was set to 80%. Ths utlzaton ncluded beakdowns on the machnes whee the tme to falue, the mean tme to epa and the pat pocessng tmes wee sampled fom exponental dstbutons. Ths epoted nstance had no bottleneck machne and the pofle of the beakdown and pocessng tmes wee dentcal on all the machnes. Ths poblem had lage than nomal amounts of system vaance as all pocess dstbutons wee exponental whle the actual pocess defntons wee omtted fo bevty. The test poblems wee smulated fo two yeas of poducton, fve shfts pe week wth 480 mnutes of opeatng tme pe shft. A smulaton wam-up peod of 50,000 mnutes o 140 shfts of poducton was suffcent to ensue accuate smulaton data measuements of flow-tme. The pelmnay expements ndcated the wam-up peod had lttle effect on the cycle tme and was pmaly equed fo flow tme measuements. Run duatons of two yeas wee found to be suffcent fo accuate statstcal nfeence fo these expements. The effect of the numbe of GK and the contane sze was studed wth 676 sepaate smulaton uns pefomed to exhaustvely cove a wde ange of opeatng polcy. Statng wth one Kanban and a contane sze of one, the numbes of Kanban and contanes szes wee ncemented by 4 to 101. Ths esulted n 26x26 sepaate contol polces that wee smulated. The numbe of decson vaables fo the contol system was two enablng the geneaton of thee-dmensonal plots whee the thd dmenson was the system esponse. Thee wee fou key pefomance measues fo the set of contol polces appled to the poducton stage. Ths ncluded a custom 95% Flow Tme (FT) confdence nteval, CV of FT fo the same sample, the mean numbe of pats poduced pe day and lastly the CV fo the Cycle Tme (CT). The cycle tme s a measue of the tme between the poducton contanes on the fnal machnes on the poducton stage and s elated to thoughput o the mean numbe of pats poduced pe day. Flow tme s the amount of tme that t takes fo a contane cycle fom the begnnng of the poducton stage to the dspatch post and back agan. The pefomance measues wee used to geneate the multple esponse sufaces fo the same paamete settng yelded fom the smulaton expements and ae n Fgue

6 Fgue 3 Optmal Opeatng Polcy An example of an optmal opeatng polcy fo a sngle pat s ndcated by the maked opeatng ponts n Fgue 3. The esults show that WIP can be unevenly dstbuted between the contane sze and the numbe of Kanbans fo mpoved system pefomance. Fo maxmum thoughput the contane sze need not be lage than 0.25 tmes the aveage numbe of pats poduced pe day fo the ten machne poducton stage. The most obust opeatng polcy shown by the esponses had a WIP allocaton of 2.73 tmes the numbe of pats to be poduced pe day and ths was unevenly dstbuted between the sze of the contane and the numbe of Kanbans. The polcy had 21 Kanbans, a contane sze of 13 and esulted n maxmum thoughput, mnmum FT and CV of FT fo the poducton envonment. Small contane szes esulted n lage CV of flow tme and fequent mateal tansfe ndcatng that the contanes should be at least 10. The numbe of Kanbans needs to be moe than fve to mantan thoughput. Inceasng the numbe of Kanbans s the most WIP effectve way of movng towads the hghe thoughput level wth a mnmum effect on the lead-tme. Ths polcy s a tade-off between CI of FT, CV of FT, CV of CT, thoughput and WIP. It s seen as the most obust by poducng the mnmum vaance levels and flow tmes wth maxmum thoughput. The gaphs also ndcate the numbe of GK may be nceased wth few negatve sde effects and s pefeable to nceasng the contane szes

7 The smulaton modelled was developed to nvestgate both the undelyng fomaton of multple esponse sufaces to multple pefomance measues as well as to vefy the smulaton engne developed. The vefcaton pocess was conducted n two stages. Fstly as thee was no vsualzaton capablty smulaton tace fles wee wtten by each of the devces n the models. These wee used to check that the objects wee flowng though the model n the coect sequence. The pocess duatons wee extacted fom the tace fles and wee ftted to the known dstbutons fom whch they wee sampled. Ths vefed both the ntenal logcs and the andom vaant geneatos used by the smulaton engne. Secondly the esults geneated by the smulaton engne wee valdated usng woks of othes. Compang the effects of the numbe of Kanban on thoughput, both Hopp and Speaman (1991) and Jodan (1988) epoted a knee functon wth nceasng WIP level fo a sngle contane sze. The esults wee smla to Fgue 3.b whee a secton of the gaph was taken wth a contane sze of one. Smla to epots by Speaman et al (1990) the mean and vaance of flow tme o job lead tme educed when WIP was educed. These esults ndcate that the smulaton engne s geneatng consstent esults and that t s eady to be appled to moe challengng mult-pat nstances usng a vaety of Kanban contol systems. 4. CONCLUSIONS The smulaton expements povded undestandng of the undelyng poblem fom that can be appled to moe complcated multpat expements. Thee s a tade-off between the WIP, thoughput and flow tme nceasng WIP that esults n nceased flow tme and thoughput. Thee s a contol system polcy whee maxmum thoughput can be acheved wthout advesely effectng the contane flow tme. Ths obust opeatng egon was whee the CV of flow tme and CT wee at mnmum. The esults found hee ae contay to the sngle pat flow ecommended by Monden (1981a) as sngle pat flow caused hgh levels of vaance of flow tme and cycle tme. The concluson was smalle contanes should used wth lage numbes of Kanban fo a set level of WIP n whch the system should be opeatng. Ths ecommendaton needs to be used wth cauton as when the contane szes become too small thee s moe vaance n the flow tme and the cycle tme. The esults showed that the contane sze of one had some undesable popetes othe than mposng exta admnstatve effot equed to manage lage numbes of Kanban. Ths povdes motvaton fo futhe nvestgaton on contane szes fo multpat poducton systems. The amount of WIP equed s a functon of the numbe of machnes on the poducton stage. It s useful to detemne decson paamete bounds to povde gudance as well as a statng pont fo contol system desgn. It was detemned empcally that soluton lmted to domans wth an uppe contane sze and numbe of GK lmted to a level of 25% of the aveage numbe of pats poduced pe day fo the poblem nstant. Ths s seen as suffcent fo maxmum thoughput. The contane szes should be no lage than 25% of the numbe of pats poduced pe day and the numbe of GK on the stage should be no lage than 5% of the day demand of pats pe multpled by the numbe of machnes on the stage. Ths opeatng egon contaned the optmal polcy fo the smulated system. Futue wok s equed to detemne f these bounds ae applcable to multpat poducton poblems especally whee the systems have lage setup duatons. The amount of WIP equed s a functon of the numbe of machnes on the poducton stage. It s useful to detemne decson paamete bounds to povde gudance as well as a statng pont fo contol system desgn. It was detemned empcally that soluton lmted to domans wth an uppe contane sze and numbe of GK lmted to a level of 25% of the aveage numbe of pats poduced pe day. Ths s seen as suffcent fo maxmum thoughput. The 25% lmt s vewed as beng poblem dependant as educng the numbe of

8 machnes o pocesses may also educe the amount of WIP equed wthn the system dvdng ths pecentage by the numbe of machnes yeldng 5% pe machne. In summey the contane szes should be no lage than 25% and the numbe of GK no moe than 2.5% of the numbe of pats poduced pe day. Ths opeatng egon contaned the optmal polcy fo the smulated system. Futue wok s equed to detemne f these bounds ae applcable to multpat poducton poblems especally whee the systems have lage setup duatons. REFERENCES Aytug, H. and Dogan, C.A. (1998), A Famewok and a Smulaton Geneato fo Kanban- Contolled Manufactung Systems, Computes and Industal Engneeng, 34.2, Baynat, B., Buzacott, J.A. and Dalley, Y. (2002), Multpoduct Kanban-Lke Contol Systems, Intenatonal Jounal of Poducton Reseach, 40.16, Bekley, B.J. (1996), A Smulaton Study of Contane Sze n Two-Cad Kanban systems, Intenatonal Jounal of Poducton Reseach, 34.12, Chang, T.M. and Yh, Y. (1994), Genec Kanban Systems fo Dynamc Envonments, Intenatonal Jounal of Poducton Reseach, 32.4, Dalley, Y. and Lbeopoulos, G. (1995), Extended Kanban Contol System: A New Kanban Type Pull Contol Mechansm fo Mult-stage Manufactung Systems, 32, Fnch, B.J. and Cox, J.F. (1986), An Examnaton of Just-In-Tme Management fo the Small Manufactue: wth an Illstaton, Intenatonal Jounal of Poducton Reseach, 24, Gupta, Y.P. and Gupta, M.C. (1989), A System Dynamcs Model fo a Mult-Stage Mult- Lne Dual-Cad JIT-Kanban System, Intenatonal Jounal of Poducton Reseach, 27.2, Hall, W.R. (1981), Dvng the Poductvty Machne: Poducton Plannng and Contol n Japan, Poducton and Inventoy Contol Socety, Falls Chuch Vgna: Amecan Hopp, W.J. and Speaman, M.L. (1991), Thoughput of a Constant Wok n Pocess Manufactung Lne Subject Falues, Intenatonal Jounal of Poducton Reseach, 29.3, Huang, P.Y., Rees, L.P. and Taylo, B.W. (1983), A Smulaton Analyss of the Japanese Just-In-Tme Technque (wth Kanbans) fo a Multlne, Multstage Poducton System, Decson Scences, 14, Jodan, S. (1988), Analyss and Appoxmaton of a JIT Poducton Lne, Decson Scences, 19, Monden, Y. (1981a), Adaptable Kanban Systems Help Toyota Mantan The Just-In-Tme Poducton, Industal Engneeng, 13.5, Monden, Y. (1981b), How Toyota Shotened Supply Lot Poducton Tme, Watng Tme and the Conveyance Tme, Industal Engneeng, 13.9, Monden, Y. (1981c), What Makes the Toyota Poducton System Really Tck?, Industal Engneeng, 31.1, Monden, Y. (1981d), Smoothed Poducton Lets Toyota Adapt to Demand Changes and Reduce Inventoy, Industal Engneeng, 13.8, Nutao, J. (2004), A Dscete EVent System smulato ADEVS, Azona Cente fo Integatve Modelng and Smulaton, Accessed on 9/08/04 Qao, G., Rddck, F. and McLean, C. (2003), Data Dven Desgn and Smulaton System Based on XML, Poc Wnte Smulaton Confeence, New Oleans, USA, Decembe Speaman, M.L., Wooduff, D.L. and Hopp, W.J. (1990), CONWIP: A Pull Altenatve to Kanban, Intenatonal Jounal of Poducton Reseach, 28.5,

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