SIMULATION-BASED SCHEDULING FOR DYNAMIC DISCRETE MANUFACTURING. Robert Gay. Electrical and Electronics Engineering. Nanyang Avenue SINGAPORE

Transcription

1 Proceedgs of the 2003 Wter mulato Coferece. Chck, P. J. áchez, D. Ferr, ad D. J. Morrce, eds. IMULATION-BAED CHEDULING FOR DYNAMIC DICRETE MANUFACTURING Ch oo Chog gapore Isttute of Maufacturg Techology Nayag Techologcal Uversty 7 Nayag Drve INGAPORE Appa Iyer vakumar Mechacal ad Producto Egeerg Nayag Techologcal Uversty Nayag Aveue INGAPORE Robert Gay Electrcal ad Electrocs Egeerg Nayag Techologcal Uversty Nayag Aveue INGAPORE ABTRACT A smulato-based real-tme schedulg mechasm for dyamc dscrete maufacturg s preseted ths paper. Modfed mea flow tme performace for dfferet schedulg approaches s compared through off-le smulato expermets, uder dyamc maufacturg evromets that are subjects to dsturbaces such as mache breakdows. These expermetal results are used as referece dces for the real-tme schedulg mechasm to select the better schedulg approaches for further evaluato based o the actual maufacturg codtos. Dscreteevet smulato s used o-le to evaluate the selected approaches ad the correspodg schedules to determe the best soluto. The selected schedule s used utl the devato of actual performace from the estmated oe exceeds a gve lmt, or whe a major evet occurs. A ew smulato s the performed wth the remag operatos to select a ew schedule. INTRODUCTION Market globalzato ot oly creates ew busess opportutes for compaes but also troduces ew compettors, ad chages the busess evromet from a vedor s to a customer s market. Ths gves rse to a rage of cosequeces o the producto process. The most promet s the requremet for hgher productvty over the whole maufacturg perod. Most maufacturg systems today are operatg at ear optmal productvty uder ormal codtos, but fal to susta the performace uder process dsturbaces of ay kd. A recet study shows that producto dsturbaces ca reach 80% of the total loss of the overall equpmet effectveess (OEE) of eve 50% mea value utlzato (Ylpää 2002). To stay compettve the global market, t s thus vtal for maufacturg compaes ot oly to cope wth frequet product chages ad fluctuatg demad, but also to reduce dsturbaces or at least the mpact of dsturbaces o the overall maufacturg performace. To deal wth the challege, a effectve schedulg system that ca mata ts performace whle reactg to producto dsruptos a tmely maer s essetal. I ths respect, schedulg s o loger a statc optmzato problem, but a ogog reactve process. Ths challege s ot trval because most schedulg problems are NP-hard, ad local dsturbaces ca affect the global performace of the system a o-lear way (Bogaerts, Brussel, ad Valckeaers 998; Paruak 99). Moreover, practcal schedulg problems are dyamc, ucerta ad ofte upredctable due to the cotuous arrval of ew ad uforesee orders, ad the occurrece of all kds of dsturbaces (e.g. mache breakdows, process ad yeld varatos, etc.). These maufacturg characterstcs lmt the effectveess of covetoal schedulg approaches, whch are statc ad determstc. uch efforts formulate schedulg as combatoral optmzato problem, wth the schedules computed over a specfc tme frame assumg all problem characterstcs are kow advace, wthout cosderato of recoclg ay dscrepaces wth the actual progress o the shop floor (Matsuura, Tsuboe, ad Kaezash 993). Reactve (ad/or proactve) schedulg, whch ca react to dyamc ad stochastc maufacturg evro-

2 Chog, vakumar, ad Gay mets, becomes a better alteratve for today's maufacturg schedulg problems. Two broad categores of reactve schedulg approaches ca be detfed (Matsuura, Tsuboe, ad Kaezash 993; Vera, Herrma, ad L 2002): predctve-reactve schedulg (.e. sequecg or optmzato-based) ad dyamc schedulg (.e. dspatchg). The predctve-reactve approach seeks to establsh a order for all the ope jobs ad reacts to process dsturbaces by reorderg the jobs, whle the dyamc approach provdes a soluto by the use of dspatchg rules for selecto from the queue of jobs. Predctve-reactve schedulg s a two-stage approach, the frst stage geerates a schedule ad the secod updates the schedule respose to dsruptos. chedule geerato acts as a predctve mechasm for producto actvtes, ad s mportat to serve as the bass for plag support actvtes such as materal procuremet, etc. chedule geerato ca be ether omal or robust (.e. proactve). I the former, foreseeable dsturbaces are ot cosdered whereas the latter cosders them the schedule, e.g. by sertg dle tmes the schedule. Updatg the schedule ca volve ether partal repar of the dsrupted schedule or complete reschedulg. The update ca be ether perodc, evet-drve or hybrd (Vera, Herrma, ad L 2002). A perodc polcy regeerates schedule perodcally. A evet-drve polcy performs reschedulg upo the occurrece of evets. A hybrd polcy, whch combes both perodc ad evetdrve polces, reschedules the system perodcally or whe major evets take place. I a attempt to costruct a effectve reactve schedulg system, varous approaches have bee proposed ad evaluated by the research commuty. I dyamc schedulg research, a extesve lst of dspatchg rules s proposed ad studed, ragg from smple rules to complex combatos of rules (Naroska ad chwegelshoh 2002, Pawalkar ad Iskader 977, Perks ad Kumar 989). I predctvereactve schedulg lterature, several research domas ca be detfed. Frst, reschedulg polcy s studed (Church ad Uzsoy 992, Holloway ad Nelso 974). ecod, optmzato-based reschedulg (.e. ether perodc, evetdrve or hybrd) s compared to real-tme heurstcs or dspatchg rules (Chag, ullva, Bagch, ad Wlso 985; abucuoglu ad Bayz 2000; Wa 995; Yamamoto ad Nof 985). Thrd, both ew schedulg ad reschedulg methods are proposed (Akturk ad Gorgulu 999; Dor, Kerr, ad Thalhammer 995; Ja ad Elmaraghy 997; Matsuura, Tsuboe, ad Kaezash 993; Wu ad L 995). I geeral, a umber of coclusos ca be draw from the reactve schedulg lterature. The performace of optmzato methods ad dspatchg based heurstcs coverges whe there s cosderable ucertaty ad varablty the system (Lawrece ad ewell 997; abucuoglu ad Karabuk 997; abucuoglu ad Bayz 2000). The optmzato-based methods perform better tha real-tme dspatchg rules whe workload across the maches s ot uform.e. there are bottleecks (abucuoglu ad Bayz 2000). The geeral cosesus reactve schedulg s that the performace of a schedulg method s problem-depedet (abucuoglu ad Bayz 2000; Wa 995), ad that a schedulg/reschedulg approach ca mprove performace compared wth fxed sequecg ad dspatchg procedures (Yamamoto ad Nof 985). Towards ths ed, there are some efforts developg schedulg techques that ca adapt to the schedulg problems. Matsuura, Tsuboe, ad Kaezash (993) proposed a schedulg approach that swtches sequecg to dspatchg accordg to the maufacturg codto. I the approach, sequecg s favored whe maufacturg codtos rema smlar to the orgal oe (.e., mmal varablty) ad dspatchg s preferred whe departure from the orgal stuato caot be gored. Km ad Km (994) preseted a schedulg mechasm that selects the best dspatchg rule by evaluatg a set of caddate rules usg smulato. The selected rule s used utl the dfferece betwee the actual system performace ad the estmated performace exceeds a gve lmt. A ew smulato s the performed to select a ew rule. Ths cycle of smulate-select-evaluate s terated repeatedly. Our work exteds research ths area, ad a smulatobased schedulg mechasm, whch dyamcally adapts to the chagg maufacturg codto, s proposed. I the approach, dscrete-evet smulato s used both off-le ad o-le. mulato s used off-le to buld referece dces based o the performace of dfferet schedulg approaches uder varyg shop floor codtos. mulato s the used o-le to evaluate the schedules geerated by the better schedulg approaches (.e. based o both smulated ad hstorcal performace) for the actual maufacturg codtos to detfy the best to use. The schedule s used utl the devato of actual performace from the estmated performace goes beyod a predefed lmt, or whe a major evet occurs. A ew schedulg approach ad ts schedule wll the be selected usg o-le smulato. The rest of the paper s orgazed as follows. We wll frst dscuss o typcal producto dsturbaces dscrete maufacturg evromets, ther characterstcs, dsturbace metrcs, ad reactve schedulg approaches that ca react to dsturbaces. Ths s followed by a descrpto of the proposed smulato-based schedulg mechasm. Fally, we wll coclude ecto 4. 2 PRODUCTION CHANGE AND DITUR- BANCE IN DICRETE MANUFACTURING A producto chage s a tetoally alterato to the producto codtos whereas a dsturbace s a uatcpated chage to the producto codtos (Bruecker 998). Producto chages are usually plaed much advace of tme ad thus beyod the scope of reactve

3 Chog, vakumar, ad Gay schedulg research. Dsturbaces the maufacturg evromets ca be related to capacty, orders or measuremet of data (see Table ). ome smlartes ca be foud amog these dsturbaces terms of ther mpacts o schedulg. For example, mache falures would have smlar effect as (.e. loger) devato of actual processg tme from the estmated oe. Uavalablty of tools or operators wll evetually result o-operatoal maches, whch requre the tools or operators to ru. Delayed, shortage or defectve of supples may later cause delayed or cacelled orders. Chage due date of orders, ad urget orders may affect schedulg a smlar maer to the effect of chage job prorty. 2. Characterstcs of Producto Dsturbaces tudes show that the followg characterstcs of dsturbaces ca mpact maufacturg performace: Type of dsturbace The type of evets for whch the system s subject to, ad ths has bee descrbed earler. ze of dsturbace The magtude of a dsturbace, for example mache breakdow durato ca be short or log, or devato of actual processg tme from the estmated processg tme ca be small or large. Iterval of dsturbace The durato (.e. mea ad varace) betwee two dsturbaces, whch ca be expressed terms of frequecy (.e. versely proportoal) of dsturbaces. Icdece of dsturbace The tme of occurrece, whch ca occur ether earler or late a schedule. Early otfcato of dsturbace The extet of tme for whch the system s otfed earler tha the actual tme of evet. For example, a urget order ca oly be released to the shop floor hours later. There are other characterstcs of dsturbaces such as gradual troducto of dsturbace (e.g. a ramp-up way), propagato of dsturbace.e. dsrupto that trggers other dsruptos, etc., whch, a way, ca be trasformed to oe or a combato of the prmary characterstcs metoed earler. A dsturbace ca affect producto process, causg devato from steady operatg codtos, ad ca have the greatest effect o the crtcal (.e. bottleeck) resources producto systems. Dsturbaces ca result shortfall (e.g. mache breakdows) or surplus (e.g. shorter processg tmes) of capacty, ad/or crease (e.g. urget orders) or decrease (e.g. cacelled orders) of workload. To eable rapd respose to dsturbaces ad to reduce the mpact of dsturbaces o the producto system, capacty (or tme) ad/or work (or materal) buffer ca be troduced to the systems Dsturbace class Related to capacty Related to orders Related to measuremet of data Table : Typcal Dsturbaces Dscrete Maufacturg Examples of dsturbaces Refereces Mache falures Church ad Uzsoy 992; Ja ad Elmaraghy 997; Km ad Km 994; L, hyu, ad Adga 993; abucuoglu ad Karabuk 997; Yamamoto ad Nof 985 Uavalablty of tools toop ad Wers 996, uresh ad Chaudhar 993 Operator abseteesm Church ad Uzsoy 992 Delayed, shortage or defectve of materals or Abumazar ad vestka 997; L, hyu, ad Adga supples 993 Qualty problems ad rework Church ad Uzsoy 992; L, hyu, ad Adga 993 Urget (or rush, or hot) orders Abumazar ad vestka 997; Ja ad Elmaraghy 997; Km ad Km 994; L, hyu, ad Adga 993 Chage job prorty Ja ad Elmaraghy 997 Job (or order) cacellato Abumazar ad vestka 997; Ja ad Elmaraghy 997; L, hyu, ad Adga 993 Due date chage (.e. delay or advace) L, hyu, ad Adga 993 pecfcato chage (.e. serto of deleto of Matsuura, Tsuboe, ad Kaezash 993 operatos exstg jobs) Dffereces betwee estmated ad actual tmes, L, hyu, ad Adga 993; toop ad Wers 996 e.g. processg steps ad repar tmes Dffereces betwee estmated ad actual yeld uresh ad Chaudhar 993 (qualty mss)

4 (Matso ad McFarlae 998). Ths buffer however, ca degrade system performace partcularly f the level of dsturbaces s less tha expected. To assess the degree of dsturbaces a maufacturg system, the followg approxmate dsturbace measure for a specfc schedule perod (.e. based o rollg horzo) s proposed: = = k f E N ( t t ) f ( t t ) f ( t t ) I N Chog, vakumar, ad Gay Type of shop floor The type of shop floor ca be flow shop, job shop, flexble maufacturg system, etc. Type of workload The workload dstrbuto of shop floor. The shop floor ca be uder-loaded or overloaded, ad uformly or o-uformly loaded (.e. bottleeck). To assess the shop floor evromets, the followg approxmate model measure for a schedule perod s proposed: where η = k = + kw φ, φ N m = Number of dsturbaces wth a specfc = schedule perod, from t to t E, where t = tart tme of dsturbace,, φ = hop floor model sze, E t = Ed tme of dsturbace,, m = Number of maches durg the schedule perod, t = Number of orders (or jobs), = tart tme of schedule, N = Number of operatos for order,, t = Ed tme of schedule, E N t = Notfcato tme of dsturbace,, k = Dsturbace factor, whch depeds o the type of dsturbace,, f = ze fucto, whch relates the effect of dsturbace to ts magtude, f I = Icdece fucto ( 0 f I ), whch relates the effect of dsturbace to ts tme of occurrece the schedule. A fucto wth decreasg value wth tme, f N = Notfcato fucto ( 0 f N ), whch relates the effect of dsturbace to ts tme of otfcato. A fucto wth decreasg value wth tme. I our model, we use the followg factor ad fuctos: k =, f ( x) = x, t t f I ( x) =, f t t 2.2 Maufacturg Evromets E N E N t t ( x) =. t t I addto to the characterstcs of dsturbaces, other factors relatg to producto codtos, ca also affect schedulg performace: ze of shop floor The sze of the problem, ad ca be expressed as approxmate umber of job operatos ad resources preset the shop floor. Ths factor wll affect the computatoal load ad thus the schedulg resposveess. k = Model type factor, whch depeds o the type of shop floor, k W = Workload factor, whch depeds o the workload dstrbuto of the shop floor. To eable mpact evaluato of dsturbaces across dfferet maufacturg evromets, e.g. dfferet types of shop floor, etc., dsturbace measure, ca be dvded by the model measure, η (.e. / η ). The values of the factors such as k (e.g. for flow shop ad job shop) could be estmated usg smulato by performg two sets of expermets wth all codtos uchaged except for the model type. I our schedulg mechasm, we set k k = sce the shop floors are the same both = W smulated ad actual, ad dfferet sets of results are kept for dfferet workload factors. 2.3 chedulg ad Reschedulg Approaches The dfferet perspectves of maufacturg evromets lead to dfferet solvg methodologes for schedulg. The varous reactve schedulg approaches, ther advatages, dsadvatages ad shop floor prerequstes for effectve applcato are preseted Table 2. Predctve schedulg ca ether be used stadaloe by complete reschedulg perodc, evet-drve or hybrd mode, or combed wth reactve reschedulg. Reactve schedule update s commoly used together wth ether omal or robust schedule geerato, whch s used to create a tal schedule.

5 Chog, vakumar, ad Gay Table 2: Dfferet Approaches to Reactve chedulg Approach Examples Advatages Dsadvatages hop floor codtos for Predctve omal Predctve robust Reactve Dyamc Tabu search, shftg bottleeck procedure (Ja ad Meera 999) Deferred commtmet (Byeo, Wu, ad torer 998), dle tme serto (Mehta ad Uzsoy 998) Rght shft reschedulg, RR (Leo, Wu, ad torer 994), affected operato reschedulg, AOR (Abumazar ad vestka 997) Dspatchg rules such as FIFO, PT, etc. (Church ad Uzsoy 992) Near optmal schedule qualty, ca be globally optmzed for each ru Good schedule qualty, ca corporate robustess to absorb dsruptos Normally low computatoal effort, react to dsruptos wth stablty cosderato Low computatoal effort, effect of dsruptos mmal Computatoally tesve, schedule robustess s ormally ot cosdered Computatoally tesve, schedule qualty may be degraded due to troduced tme ad/or materal buffer chedule qualty s degraded Poor schedule qualty, hghly problem depedet effectve applcato hould be very stable wth absolutely mmal dsruptos hould be stable wth mor ad frequet dsruptos Ca have multple dsruptos Ca be hghly dyamc ad stochastc 3 IMULATION-BAED REACTIVE CHEDULING MECHANIM The schedulg mechasm cossts of two dstct stages: off-le smulato evaluato ad o-le reactve schedulg. The roles of these stages are outled the followg subsectos. 3. Off-Le mulato Evaluato Off-le smulato s used to establsh tal referece dces for the performace of dfferet schedulg approaches. Multple replcatos of stochastc smulato wth creasg degree of dsturbaces uder dfferet maufacturg evromets are performed to obta estmated performace for the schedulg approaches (Fgure ). The dfferet schedulg approaches are evaluated separately usg the same set of smulato replcatos, ad the approaches are trggered o each occurrece of dsturbaces the smulato. The obtaed performace statstcs (mea ad varace) for each value of dsturbace measure, clude: Modfed flow tme F m = = F P = = ( C R ) where = Number of completo jobs, F = Flow tme ( = C ) of job, R P C = Completo tme of job, R = Tme of etry of job, P = Total theoretcal processg tme of job. chedulg respose tme The smulato results eable relatoshps (.e. le plots) to be establshed betwee modfed flow tme ad dsturbace measure uder dfferet shop floor codtos (.e. uder-, over-, uformly, o-uformly loaded). These relatoshps, as well as respose tme, ca the be used o-le schedulg to detfy the schedulg approaches that may perform well (.e. terms of the modfed flow tme) the actual maufacturg evromets, based o the requred respose tme ad values of dsturbace measure. 3.2 O-Le Reactve chedulg At ths stage, schedulg mechasm wll ru cotuously ad react to the actual producto dsturbaces whle performace statstcs (.e. modfed flow tme ad respose tme), based o the actual dsturbace measure, are beg updated for each schedulg approach (.e. whe t s selected). The o-le schedulg mechasm cossts of four major compoets: Real-tme motorg ad cotrol, schedulg mechasm, smulato evaluato, ad schedulg cotroller. A overvew of the system cocept s llustrated Fgure 2. The fuctos of each compoet are: 3.2. Real-Tme Motorg ad Cotrol (RTMC) Ths compoet receves evets from the shop floor, ad per odcally motors performace of the shop floor. It also

6 Chog, vakumar, ad Gay Modfed flow tme Modfed flow tme a) Dsturbace measure, b) Dsturbace measure, Fgure : Typcal Performace Plots for Two Dfferet chedulg Approaches Uder Uform Loadg (a) Rght hft chedulg (b) Frst I Frst Out mulato Evaluato chedulg Cotroller mulato model Outputs chedule evaluato ad selecto chedulg mechasm Predctve schedulg Reactve schedulg Dyamc schedulg Real-tme Motorg ad cotrol Dsturbace Performace aalyss aalyss system status ad evets dspatchg Raw materal hop floor Fgure 2: Reactve chedulg Mechasm Fshed products seds all schedulg cotroller formato to the shop floor ad dspatches jobs to mache accordgly. Two sub-compoets ca be detfed RTMC: Dsturbace aalyss (DA) ad performace aalyss (PA). The former checks all comg evets, vokes reschedulg o major dsturbaces (crtera defed by users), ad keeps track of dsturbace statstcs such as the terval, magtude, etc. of each dsturbace type at factory ad/or mache level depedg o the type of dsturbaces. These statstcs are used to dcate the amout of capacty ad/or work buffer that eeds to be corporated to schedule for some of the schedulg approaches (e.g. dle tme serto). Further, the data ca also be used to show the relablty of each mache, ad jobs ca thus be scheduled to avod the urelable maches. PA sub-compoet motors the dfferece betwee actual ad estmated performace values. Oce the dfferece exceeds a predetermed lmt at a pot of motorg, a ew reschedulg s performed wth the remag operatos uder the curret shop floor codtos chedulg Mechasm (M) Ths compoet has a set of schedulg approaches that ca be used for reschedulg. Each approach has statstcal data o smulated ad/or hstorcal performace for dfferet level of dsturbace, ad a user assged preferece dces. New schedulg approaches ca be added f past performace (.e. usually through smulato) s obtaed. The better schedulg approaches, based o the actual shop

7 Chog, vakumar, ad Gay floor codtos, preferece dces ad respose tmes, wll be trggered to geerate ew schedules. I the cases dyamc schedulg approaches (see Table 2), dscrete evet smulato s used to geerate schedule. The legth of schedulg wdow of all schedulg approaches s fxed at three tmes the average total processg tme. The umber of schedulg approaches trggered wll deped maly o the requred respose tme ad computg resources. Compled statstcs from DA ca be used to further ehace the robustess of the schedules mulato Evaluato (E) Ths compoet cludes a smulato model costructed based o the physcal shop floor status from the factory database. Whe the schedulg cotroller passes cotrol to E, a seres of smulato rus are talzed wth the geerated schedules (.e. geerated by the selected schedulg approaches) uder the same stochastc codtos (.e. wth dsturbaces corporated based o the statstcs from DA). The legth of smulato s set to be equal to the legth of schedulg wdow. The results of the smulato wll be passed back to the cotroller. The outputs (.e. modfed flow tme after corporatg dsturbaces) from the smulato are used by schedulg cotroller to selects the best schedule. The selected schedule becomes a put to RTMC, whch dspatches jobs accordg to the schedule to the shop floor chedulg Cotroller (C) M, E ad formato flow the system s cotrolled by C. C selects the better schedulg approaches for further smulato evaluato based o the actual maufacturg codtos, ad subsequetly selects the best approach to be used o the shop floor. Ths selecto process s performed at the begg of a rollg schedulg horzo, whe the system performace s ot as expected, or whe there s a major dsturbace. The selecto s also performed whe the system state s back to ormal (e.g. at the tme of mache operatg after repared). Whe a mor dsturbace occurs, the cotroller wll delay the subsequet operatos (.e. smlar to RR approach). C also keeps track of the estmated performace value (.e. modfed flow tme) of the selected schedulg approach. Ths value s a output from E, ad s used to compare wth the motored performace value of the actual shop floor. 4 CONCLUION A smulato-based reactve schedulg mechasm s preseted ths paper. Ths schedulg mechasm employs dscrete evet smulato both off-le ad o-le to evaluate a set of reactve schedulg approaches. The basc dea of the mechasm s to egage dscrete evet smulato to combe dfferet schedulg approaches based o the past performace. The mechasm ca therefore adapt tself by reactg to producto dsturbaces ad selects the best avalable reactve schedulg approach based o the actual shop floor status. I the log ru, ths process wll result a combato of dfferet schedulg approaches based o ther performace each short tme perod. Itutvely, by alteratg schedulg approaches such a maer, the approaches wll ted to compesate for the udesrable effects that each approach produces, ad thus yeld a schedule that s more reactve to the system dyamcs. I ths paper, dscrete evet smulato has bee show to be a dspesable tool for detaled schedulg uder a hghly dyamc ad upredctable maufacturg system. REFERENCE Abumazar, R. J., ad J. A. vestka Reschedulg job shops uder radom dsruptos. Iteratoal Joural of Producto Research 35 (7): Akturk, M.., ad E. Gorgulu Match-up schedulg uder a mache breakdow. Europea Joural of Operatoal Research 2 (): Bogaerts, L., H. V. Brussel, ad P. Valckeaers chedule executo usg perturbato aalyss. I Proceedgs of IEEE Iteratoal Coferece o Robotcs ad Automato, Leuve, Belgum, 6-2 May 998. Bruecker, MACADA: Maufacturg cotrol systems capable of maagg producto chage ad dsturbaces. I Newsletter of AgetLk (The Europea Network of Excellece for Aget-Based Computg), ed. Woodrdge. (): 6 9. Byeo, E..,. D. Wu, ad R. H. torer Decomposto heurstcs for robust job shop schedulg. IEEE Trasactos o Robotcs ad Automato 4 (2): Chag, Y. L., R.. ullva, U. Bagch, ad J. R. Wlso Expermetal vestgato of real-tme schedulg flexble maufacturg systems. Auals of Operato Research 3 (): Church, L. K., ad R. Uzsoy Aalyss of perodc ad evet-drve reschedulg polces dyamc shops. Iteratoal Joural of Computer Itegrated Maufacturg 5 (3): Dor, J., R. Kerr, ad G. Thalhammer Reactve schedulg: Improvg the robustess of schedules ad restrctg the effects of shop floor dsturbaces by fuzzy reasog. Iteratoal Joural o Huma- Computer tudes 42 (6): Holloway, C. A., ad R. T. Nelso Job shop schedulg wth due dates ad varable processg tmes. Maagemet cece 20 (9).

8 Chog, vakumar, ad Gay Ja, A. K., ad H. A. Elmaraghy Producto schedulg/reschedulg flexble maufacturg. Iteratoal Joural of Producto Research 35 (): Ja, A.., ad. Meera Determstc job-shop schedulg: Past, preset ad future. Europea Joural of Operatoal Research 3 (2): Km, M. H., ad Y. Km mulato based real tme schedulg a flexble maufacturg systems. Joural of Maufacturg ystems 3 (2): Lawrece,. R., ad E. C. ewell Heurstc, optmal, statc, ad dyamc schedules whe processg tmes are ucerta. Joural of Operatos Maagemet 5 (): Leo, V. J., D. Wu, ad R. H. torer Robustess measures ad robust schedulg for job shops. IIE Trasactos 26 (5): L, R-K., Y. -T. hyu, ad. Adga A heurstc reschedulg algorthm for computer-based producto schedulg systems. Iteratoal Joural of Producto Research 3 (): Matso, J., ad D. McFarlae Tools for assessg the resposveess of exstg producto operatos. I Proceedgs of IEE Workshop, Resposveess Maufacturg, Lodo, February, 998. Matsuura, H., H. Tsuboe, ad M. Kaezash equecg, dspatchg, ad swtchg a dyamc maufacturg evromet. Iteratoal Joural of Producto Research 3 (7): Mehta,. V., ad R. M. Uzsoy Predctable schedulg of a job shop subject to breakdows. IEEE Trasactos o Robotcs ad Automato 4 (): Naroska, E., ad U. chwegelshoh O a o-le schedulg problem for parallel jobs. Iformato Processg Letters 8 (6): Paruak, H. V. D. 99. Characterzg the maufacturg schedulg problem. Joural of Maufacturg ystems 0 (3): Pawalkar,.., ad W. Iskader A survey of schedulg rules. Operatos Research 25 (): Perks, J. R., ad P. R. Kumar table, dstrbuted, real-tme schedulg of flexble maufacturg/ assembly/dsassembly systems. IEEE Trasactos o Automatc Cotrol 34 (2): abucuoglu, I., ad. Karabuk Aalyss of schedulg-reschedulg problems a stochastc maufacturg evromet. Techcal Report IEOR-9704, Departmet of Idustral Egeerg, Blket Uversty, Akara. abucuoglu, I., ad M. Bayz Aalyss of reactve schedulg problems a job shop evromet. Europea Joural of Operatos Research 26 (3): , November toop, P. P. M., ad V. C.. Wers The complexty of schedulg practce. Iteratoal Joural of Operatos ad Producto Maagemet 6 (0): uresh, V. ad D. Chaudhar Dyamc schedulg a survey of research. Iteratoal Joural of Producto Ecoomcs 32 (): Vera, G. E., J. W. Herrma, ad E. L Reschedulg maufacturg systems: A framework of strateges, polces, ad methods. Iteratoal Joural of chedulg, March 4, Wa, Y. W Whch s better, off-le or real-tme schedulg. Iteratoal Joural of Producto Research 33 (7): Wu, H. -H., ad R. -K. L A ew reschedulg method for computer based schedulg systems. Iteratoal Joural of Producto Research 33 (8): Yamamoto, M., ad. Y. Nof chedulg/reschedulg the maufacturg operato system evromet. Iteratoal Joural of Producto Research 23 (4): Ylpää, T Correcto, preveto ad elmato of producto dsturbaces. PROPER project descrpto March 2002, Departmet of Product ad Producto Developmet (PPD), Chalmers Uversty of Techology, Gotheburg. AUTHOR BIOGRAPHIE CHIN OON CHONG obtaed hs degree Electrcal ad Electrocs Egeerg from the Cty Uversty of Lodo, UK. He joed IMTech, a research sttute gapore, te years ago ad s curretly the Producto ad Logstcs Plag Group. He obtaed hs Master of Egeerg Computer Itegrated Maufacturg from Nayag Techologcal Uversty, gapore. Durg these te years, he has bee volved smulato, schedulg ad optmzato related projects logstc ad maufacturg IT domas. The dustral projects clude cargo cotaer operato ad yard capacty plag smulato for a cotaer port, dary-prtg process smulato for a prtg compay, maufacturg cycle-tme modelg, schedulg ad optmzato for varous MNCs. Hs curret research terest cludes tellget ad tegrated smulato, plag, schedulg, optmzato the area of maufacturg, logstc, ad supply cha. He ca be reached va emal at <cschog@gtc.gov.sg>. APPA IYER IVAKUMAR (eor member IIE) s a Assocate Professor the chool of Mechacal ad Producto Egeerg at Nayag Techologcal Uversty (NTU), gapore ad a Fellow of gapore Massachusetts Isttute of Techology (MIT) Allace (MA). Pror to ths he was at Gtc Isttute of Maufacturg Techology, gapore. Hs research terests are the area of smulato based optmzato of maufacturg performace, supply cha, ad dyamc schedule optmzato. Pror to jog IMTech 993, he held varous ma-

9 agemet postos cludg techcal maager ad project maager for e years at Lucas ystems ad Egeerg ad Lucas Automotve, UK. He receved a Bachelors of Egeerg from Uversty of Bradford, UK ad a PhD Maufacturg ystems Egeerg from Uversty of Bradford, UK. He has bee the techcal char ad coedted the proceedgs of the 3rd ad 4th Iteratoal Coferece o Computer Itegrated Maufacturg (IC- CIM 95 ad ICCIM 97), gapore. Hs emal ad web addresses are <msva@tu.edu.sg> ad < edu.sg/home/mva/>. ROBERT GAY obtaed hs B. Eg, M. Eg ad PhD degrees at the Uversty of heffeld, Eglad, 965, 967 ad 970 respectvely. He was awarded the Grouped cholarshp Egeerg ad Metallurgy by the Uversty of heffeld from 967 to 970. ce obtag hs PhD, he has bee volved Educato ad R&D workg sttutos such as gapore Uversty ( ), Rutherford ad Appleto Laboratory (Eglad, ), NTU ( ad 999-preset) ad IMTech ( ). He has also bee actvely volved promotg ovato gapore through work varous commttees: cece Quz (MOE), cece Cetre Board, Natoal CAD/CAM (NCB), Ta Kah Kee Youg Ivetors Award (TKK Foudato & NTB), Natoal IT Pla (NCB), Techopreeurshp cubato ceter (ITE), Commerceet gapore, gapore Computer ocety. Curretly Professor Gay s the chool of EEE at NTU ad also Drector ad CEO of the AP Cetre. He has more tha a hudred publcatos jourals, coferece proceedgs ad books. Hs emal ad web addresses are <eklgay@tu.edu.sg> ad < eee/cs/cv/robertgay.html>. Chog, vakumar, ad Gay