DEVELOPMENT OF SIMULATION-BASED ENVIRONMENT FOR MULTI-ECHELON CYCLIC PLANNING AND OPTIMISATION

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1 From he SelecedWorks of Lana Napalkova Sepember, 2007 DEVELOPMENT OF SIMULATION-BASED ENVIRONMENT FOR MULTI-ECHELON CYCLIC PLANNING AND OPTIMISATION Galna Merkuryeva Lana Napalkova Avalable a: hps://works.bepress.com/lana_napalkova/2/

2 DEVELOPMENT OF SIMULATION-BASED ENVIRONMENT FOR MULTI-ECHELON CYCLIC PLANNING AND OPTIMISATION Galna Merkuryeva and Lana Napalkova Deparmen of Modellng and Smulaon Rga Techncal Unversy 1 Kalku Sree LV-1658, Rga, Lava lana@l.ru.lv (Lana Napalkova) Absrac Ths paper focuses on he developmen of smulaon-based envronmen for mul-echelon cyclc plannng and opmsaon n he produc maury phase. I s based on negraon of analycal and smulaon echnques. Analycal echnques are used o oban nal plannng decsons under condons of sochasc demand and lead me, whereas smulaon echnques exend hese condons o backloggng and capacy consrans. Smulaon s used o analyse and mprove cyclcal decsons receved from he analycal model. The proposed envronmen ncludes four componens, such as daabase, process, opmsaon and procedural one. Daabase componen defnes a supply chan nework and s npu parameers. Procedural componen generaes cyclc schedules usng analycal calculus. Process componen performs auomac generaon of a supply chan smulaon model and smulaes cyclc schedules n mul-echelon envronmen whle conrollng nvenory levels and esmang he performance measures. Opmsaon componen defnes opmal cyclc schedule for each of he supply chan sages n order o mnmze he sum of nvenory holdng, seup and orderng coss whle sasfyng cusomer servce requremens defned by a arge cusomer servce level. The paper provdes examples of dfferen nework ype smulaon models generaed for mul-echelon cyclc plannng and opmsaon. The presen research s funded by he ECLIPS Specfc Targeed Research Projec of he European Commsson "Exended Collaborave Inegraed Lfe Cycle Supply Chan Plannng Sysem". Keywords: Mul-echelon cyclc plannng, supply chan smulaon, auomac programmng. Presenng Auhor s bography Lana Napalkova holds an MSc degree n Compuer Scence from Rga Techncal Unversy (2006). Currenly, she s a PhD suden and a research asssan a he Deparmen of Modellng and Smulaon, Rga Techncal Unversy. ISBN Copyrgh 2007 EUROSIM / SLOSIM

3 1 Inroducon For years, researchers and praconers have prmarly nvesgaed he varous processes whn manufacurng supply chans ndvdually. Ths approach s also called a sngle echelon approach, where a sage or facly n he supply chan s managed as such. For example, n [1] Campbell and Maber deal wh he plannng of producon on a sngle machne. Recenly, however, here has been ncreasng aenon placed on he performance, desgn, and analyss of he supply chan as a whole. Almos every produc s produced n a chan of successve processes (eher n dfferen companes or dfferen deparmens whn he same company). A mul-echelon envronmen consders mulple processes and mulple sock pons. Supply chan managemen s no jus managng every echelon n solaon; s really abou he challenge o manage all he echelons n a holsc way. The mul-echelon approach can gve an answer o he always ncreasng pressure on mprovng performance and a more holsc vew of he supply chan. In comparson o complex polces, whch are preferable from heorecal pon of vew, cyclc plannng n mul-echelon envronmen has more praccal benefs, because provdes easy conrol and reduced admnsrave coss. The man dea of cyclc plannng s o use cyclc schedules a each echelon and synchronze hem wh one anoher [2]. Ths paper s dvded no 8 secons. Secon 2 descrbes he problem. A concepual vew on he supply chan model s provded n Secon 3. Secon 4 represens a smulaon-based envronmen for smulang and opmsng mul-echelon cyclc schedules. Ths envronmen s used o perform expermens n Secons 5 and 6. Secon 7 concludes he paper and suggess furher nvesgaons. 2 The Problem Descrpon 2.1 Assumpons and noaons Consder an acyclc dreced graph represenng he producon and dsrbuon sysem. I s formed by wo dfferen ypes of nodes, such as sock pons and processes [3]. The sock pons correspond o any place o sore he oupu producs of he process. The processes denoe ransformaon acves wh a se of npu producs and a se of oupu producs, such as assembly, ransporaon and packagng operaons [4]. The performed research s based on he followng assumpons abou he sysem s srucure and he ype of conrol polces. End-cusomers demand s normally dsrbued and occurs a a saonary, connuous rae. The sock pons drecly conneced o end-cusomers mus provde produc oupu n order o sasfy he demand. Shorages are backlogged and only full delveres o cusomers are allowed. The sock pons are conrolled by perodc revew polcy (POR), and reorder nervals (or replenshmen cycles) are defned accordng o he neger-rao polcy. Order-up-o levels are fxed n he plannng perod. Safey socks are used o proec agans sock-ous due o demand and lead mes varaon. Inal socks are consdered o be equal o order-up-o levels. Processng lead mes are assumed o be normally dsrbued. Capacy consrans are nroduced o lm he ransformaon acves specfed by processes. Toal coss are defned by a sum of fxed seup coss, lnear nvenory holdng coss and orderng coss. The followng noaons are nroduced: I: number of sock pons n supply chan nework, J: number of processes n supply chan nework, K: number of end-cusomers, T: number of perods n he plannng horzon, Pred : he se of ndces of sock pons mmedaely precedng he sock pon, Succ : he se of ndces of sock pons mmedaely followng he sock pon, IsConSock : 1 f sock decreases connuously; 0 oherwse, d k, : average demand of end-cusomer k for sock pon, d k, : sandard devaon of demand of end-cusomer k for sock pon, d m, : average demand receved n sock pon for sock pon m, d m, : sandard devaon of demand receved n sock pon for sock pon m, D k,, : demand of end-cusomer k for sock pon a me perod (generaed from normal dsrbuon), Lj: average lead me of process j, Lj: sandard devaon of lead me of process j, DDLCyk,: average demand of end-cusomer k o sock pon durng lead me and replenshmen cycle, DDLCyk,: sandard devaon of demand of endcusomer k o sock pon durng lead me and replenshmen cycle, Cy : replenshmen cycle of sock pon, S : order-up-o level of sock pon, SS : safey sock of sock pon, H, : on hand sock a he end of perod a sock pon, Q, : replenshmen order of sock pon per perod, QS,m, : quany of producs provded by sock pon o sock pon m a me perod, QC,k, : quany of producs provded by sock pon o end-cusomer k a me perod, QP j, : producon quany of process j a me perod, BP j, : 1 f process j s swched on a me perod ; 0 f process j s swched off a me perod, CAP j : maxmal capacy of process j, CSL : cusomer servce level of sock pon, Cs : seup cos a sock pon, Ch : un nvenory holdng cos a sock pon, Co : un orderng cos a sock pon. ISBN Copyrgh 2007 EUROSIM / SLOSIM

4 2.2 The MILP problem formulaon The objecve s o mnmze he sum of nvenory holdng, seup and orderng coss whle sasfyng cusomer servce requremens defned by a arge cusomer servce level. The mxed neger lnear programmng (MILP) formulaon of he problem s as follows: Mnmze subjec o: IsConSock T 1, IsConSock 1, Cs Co j j j,, H msucc Q BP, Ch Ch ksucc H ( H, ( 1) m,,( L j, ) m pred QS, m, QS QC, k, j QPj, BPj, H, 1 H j, ) / 2 (1) (2), CAP (3) k D k,, QC, k, ksucc, (4),, 0 (5) H, Cy * (6) j, BP, 01, (7) j The frs and fourh erms of he objecve funcon (1) represen orderng and seup coss, respecvely; he second erm s used o calculae nvenory holdng coss a he sock pon mmedaely precedng he end-cusomers, and he hrd one calculaes holdng coss a oher sock pons; (2) descrbes nvenory balance consrans; (3) represens producon capacy consrans, (4) ensures ha he end-cusomer demand s equal o he sum of produc quanes provded by sock pons mmedaely precedng he end-cusomer, (5) ensures ha on hand socks wll be nonnegave, (6) saes ha replenshmen cycles mus be chosen from a se of neger numbers, (7) saes ha processng ndcaor mus be equal o 0 or 1. 3 The supply chan model The supply chan s represened by aomc elemens, such as sock pons and processes defned n Secon 2. Sock pons are graphcally represened by rangles, and processes by recangles. The par of a process and sock pon conneced wh dreced arc s called a sage. A he hgher absracon level, he supply chan s consruced by basc sub-neworks, such as lnear, convergen and dvergen (see Fgure 1) sock pon - process - sage Fg. 1 Basc sub-neworks of he supply chan Replenshmen and delvery logc [5] bul n subneworks s descrbed below. 3.1 The lnear sub-nework In he lnear sub-nework (1), a sage has one predecessor and one successor (excep he las echelon). Replenshmen order s placed o he mmedaely precedng sage. If he on hand sock s nsuffcen o fulfl hs order, hen he backorder s creaed. Orders and backorders are delvered o he mmedaely succeedng sage. 3.2 The convergen sub-nework In he convergen sub-nework (2), a sage has one successor and many predecessors. Replenshmen procedure s changed so ha order s placed o he number of mmedaely precedng sages. If a leas one of hem has nsuffcen on hand sock, hen he backorder s creaed, and he ransformaon operaon assocaed o he process s delayed. Delvery procedure s smlar o he lnear sub-nework. 3.3 The dvergen sub-nework In he dvergen sub-nework (3), a sage has many successors and one predecessor. Replenshmen procedure corresponds o he lnear sub-nework. Delvery procedure s changed so ha orders are delvered o succeedng sages sequenally accordng o her ID numbers. In oher words, he demand of a sage wh he smalles ID number s fulflled frs. 4 Smulaon-based envronmen 4.1 Archecure Smulaon-based envronmen o defne opmal cyclc schedules for mul-echelon envronmen s nroduced n [2] akng no accoun sochasc naure of he supply chan sysem and nonlnear relaonshps beween s nodes (see Fgure 2). The envronmen for cyclc plannng and opmsaon ncludes hese four componens: Daabase componen, Procedural componen, Process componen, Opmsaon componen. ISBN Copyrgh 2007 EUROSIM / SLOSIM

5 4.2 Daabase componen Daabase componen consss [2] of a nework and daase subcomponens. The nework subcomponen descrbes a srucure of he supply chan. The daase subcomponen ncludes basc daa abou nvenory conrol polces, coss, capaces and end-cusomer demand. Daabase componen s bul n he Excel forma; ncludes he followng sx workshees (Fgure 3): 1) Nework_marx workshee defnes a supply chan srucure by s marx represenaon. Rows and columns correspond o sock pons, bu cells o connecng hem process numbers. 2) Nework_daa workshee s auomacally generaed from Nework_marx and s used o effcenly read marx daa from VBA code. 3) Sockpon_daa workshee defnes graphcal posons of sock pons n he model layou, nal nvenory levels, replenshmen cycles, order-up-o levels and safey socks, whch are obaned from he procedural componen. 4) Process_daa workshee conans graphcal posons of processes n he model layou, as well as average processng lead me and s sandard devaon, and capacy consrans. 5) Coss_daa workshee specfes nvenory holdng, seup and orderng coss. 6) Endcusomer_demand workshee deermnes average end-cusomers demand per perod and s sandard devaon. Fg. 2 Archecure of smulaon-based envronmen "Endcusomer_ demand" w orkshee "Coss_daa" workshee "Nework_marx" w orkshee Daabase componen "Process_daa" w orkshee "Nework_daa" w orkshee "Sockpon_daa" w orkshee Fg. 3 Srucure of daabase componen 4.3 Procedural componen Procedural componen s bul o generae cyclc schedules usng analycal calculus [2]. An analycal model assumes ha end-cusomer demand s normally dsrbued, lead mes are consan, process capaces are nfne and backloggng s no allowed. The followng formulas are used o esmae replenshmen conrol parameers ha refer o he sock pons mmedaely precedng end-cusomers: Cy 2 dk succ k, ksucc Cs dk, Ch (8) ( Cy ) (9) DDLCyk, d k, L j ISBN Copyrgh 2007 EUROSIM / SLOSIM

6 ( Cy ) (10) DDLCy k, d k, L j 2 DDLCyk, ksucc SS NORMSINV ( CSL ) (11) S DDLCy SS k, (12) ksucc In formulas (8) and (11), aggregae demand s nroduced. I allows mulple end-cusomers o be conneced o he same sock pon. If a sock pon s no mmedaely conneced o endcusomer(-s), hen he followng updaes are made o formulas (9) and (10) [6]: ( Cy ) (13) DDLCym, d k, j L j ( Cy ) (14) DDLCy m, d k, j In hs case, replenshmen orders from he curren sage are used as he demand n mmedaely precedng sages. 4.4 Process componen Process componen performs [2] wo dfferen asks: 1) auomac generaon of a supply chan smulaon model, and 2) smulaon runs,.e. smulaon of cyclc schedules n mul-echelon envronmen whle conrollng nvenory levels and esmang he performance measures. L j Auomac generaon of a supply chan smulaon model Auomac generaon of a supply chan smulaon model s suppored by ProModel s AcveX Auomaon capably ha allows one o auomacally generae smulaon models from exernal applcaons by usng VBA programmng language [7]. Fg. 4 AcveX-based VBA program Here, he AcveX-based VBA program developed n MS Excel (see Fgure 4) consss of he subrounes ha provde an ProModel operaonal conrol: allows accessng he model nformaon, e.g. loadng a blank smulaon model; defnng a le of he model, pah o a graphcal lbrary, anmaon speed, smulaon lengh and number of replcaons; creang enes, locaons of sock pons and processes, pah neworks used o esablsh lnks beween sock and process pons; creang arrays, varables, funcons and procedures; defnon of enes arrval schedule, sequence of processes and her operaonal logc The logc of smulaon model The general algorhm of a sngle sage n he model s represened n Fgure 5. I s smlar for all sages n supply chan. The only dfference s ha n sages no drecly conneced o end-cusomers he demand even s subsued by orders from succeedng sages. When several evens occur a a sage a he same perod, hey are processed n he followng sequence: recevng orders and backorders from precedng sages; fulfllng open backorders from succeedng sages; fulfllng of orders from succeedng sages; and hen sendng replenshmen orders o precedng sages. 4.5 Opmsaon componen Opmsaon componen ams [2] o defne an opmal cyclc schedule for each of he supply chan sages durng a maury phase of he produc lfe cycle n order o mnmze he sum of nvenory holdng, seup and orderng coss whle sasfyng cusomer servce requremens defned by a arge cusomer servce level. A meaheursc algorhm s used o search for opmal soluons. Inal soluons are receved from procedural componen. Furher, soluons are obaned from smulaon runs. The meaheursc algorhm mproves curren soluons and sends hem back o he smulaon model unl he opmal soluon s found. A feasble se of replenshmen cycles s consraned by neger-rao polcy. 5 Examples Ths secon llusraes esng of he smulaon models auomacally generaed and some resuls of analyzng assumpons mpac on opmsaon resuls. 5.1 Tes envronmen 3-echelon supply chan s smulaed. Inpu daase sored n daabase componen s shown n Table 1. Inpus Sages Tab. 1 Inpu daase Invenory holdng cos, CU Seup cos, CU Orderng cos, CU Average lead me, perods Cusomer servce level, % Average demand per perod, 2500 uns Sandard devaon of 500 demand per perod, uns ISBN Copyrgh 2007 EUROSIM / SLOSIM

7 Sar End-cusomer demand generaon Are order arrvals scheduled n hs perod? + Wa ncomng orders - Are here unfulflled backorders + Is on hand sock suffcen o fulfll open backorders? + Fulfll backorders - - Is on hand sock suffcen o fulfll he demand? + Fulfll he demand Reorder decson? - Save new backorders + - Calculae nvenory poson Send replenshmen order Calculae seup & orderng coss Calculae nvenory holdng coss End Fg. 5 General algorhm of a sngle sage n mul-echelon supply chan model Inal values of conrol varables (see Table 2) are esmaed n he procedural componen from analycal formulas (8) (15). The number of perods n he plannng horzon s 34. Tab. 2 Inal values of conrol varables Sages Varables Replenshmen cycle, perods Order-up-o level), uns 5.2 Model The frs smulaon model has been auomacally generaed n he process componen execung he AcveX-based VBA program (see Fgure 6) for he followng assumpons: Demand s normally dsrbued, Lead mes are consan, Backloggng s no allowed, Capaces are nfne. In order o verfy he generaed smulaon model, a specal char-based emplae has been used (Fgure 7). Templae able ncludes he followng columns: (1) demand, (2) on-hand nvenory, (3) oal backorders, (4) sen orders, (5) receved orders, (6) on order quany and (7) nvenory poson. Fg. 6 Auomac generaon of supply chan smulaon model 5.3 Model 2 The second smulaon model has been generaed for hese assumpons: Demand s normally dsrbued, Lead mes are normally dsrbued, Backloggng s no allowed, Capaces are nfne. Normal dsrbuons of lead mes are gven n Table 3. ISBN Copyrgh 2007 EUROSIM / SLOSIM

8 Fg. 7 Example of smulaon model racng Tab. 3 Lead me average values and sandard devaons Sages Varables Average lead me, perods Sandard devaon of lead me, perods 5.4 Model The followng assumpons are aken no accouns n he hrd smulaon model: Demand s normally dsrbued, Lead mes are normally dsrbued, Backloggng s allowed, Capaces are nfne. Backloggng n full s allowed. 5.5 Model 4 The fourh smulaon model s based on assumpons: Demand s normally dsrbued, Lead mes are normally dsrbued, Backloggng s allowed, Capaces are fne. hese poor soluons fade away and good soluons connually evolve n her search for he opmum. The followng opmsaon procedure s appled. A he frs sep, he objecve funcon s defned ha mnmzes oal coss and does no allows sock-ous (see Fgure 8). In order o ensure ha he objecve funcon does no unnenonally favour any parcular sasc, hese values are weghed. For example, n he frs model he maxmum value of oal coss a he nal smulaon run s equal o , bu he maxmum number of sock-ous s equal o 0. In order o balance boh sascs, a wegh of has been appled o he number of sock-ous. Fg. 8 Objecve funcon defnon A he second sep, a search space s defned (Fgure 9). Lower and upper bounds of conrol varables are esmaed n he procedural componen (Table 6), whch correspond o 90 % and o 97 % of CSL level. Replenshmen cycles are vared beween 1 and 12 me perods. Maxmal capaces of processes are shown n Table 4. Sages Varable Maxmal capacy, uns Tab. 4 Capacy consrans Opmsaon usng SmRunner As opmsaon componen, ProModel SmRunner [8] s used ha apples an Evoluonary Algorhm. I manpulaes a populaon of soluons n he way ha Fg. 9 Lower and upper bounds of order-up-o levels A he hrd sep, he requred number of replcaons s esmaed. In our case, a sngle replcaon for all four models s suggesed. ISBN Copyrgh 2007 EUROSIM / SLOSIM

9 A he las sep, he opmsaon search s conduced. Opmsaon profle s se o Moderae. In hs case he average populaon sze of possble ones s analysed. Convergence percenage, whch conrols how close are he bes and he average s se o Fg. 10 Opmsaon expermens Resuls of opmsaon expermens for Model 1 are shown n Fgure 10. The search has been compleed afer 602 expermens. As a resul, he followng values of objecve funcon sascs have been found: maxmum oal coss are and number of sock-ous s 0. 6 The resuls The opmal soluon ses relaed o four smulaon models are summarsed n Table 5. In Model 1 an analycal soluon ensures ha orders are fulflled durng he plannng horzon. SmRunner mproves he nal soluon so ha oal coss are decreased by 9.13 %. In Model 2, an analycal soluon resuls n los sales due o he varably of lead mes, whle smulaon-based opmal soluon cu coss up by 9.80 %, and sock-ous don occur durng he plannng horzon. In Model 3, an nal soluon leads o los sales n he las echelon whle shorages n delveres are backlogged. In opmal soluon, oal coss are decreased by %. Fnally, n Model 4 replenshmen orders are lmed by capacy consrans. I leads o addonal los sales whle mplemenng an analycal soluon. SmRunner mproves he nal soluon so ha oal coss are reduced by 6.85 % and orders are fulflled durng he plannng horzon. Model Model 1 Model 2 Model 3 Model 4 Tab. 5 Comparson beween mpacs of dfferen assumpons on he opmsaon resuls The SmRunner soluon Replenshmen cycles Order-up-o levels {7, 6, 1} {19557, 19302, 8610} {1, 7, 2} {19839, 19571, 8974} {5, 7, 2} {19195, 19366, 8887} {5, 4, 2} {19195, 19293, 8658} Toal coss Toal coss Number of Number of (before (afer sock-ous sock-ous opmsaon) opmsaon) (before opmsaon) (afer opmsaon) Conclusons The paper represens he developed smulaon-based envronmen for mul-echelon cyclc plannng and opmsaon. The mpac of dfferen assumpons, such as normally dsrbued lead mes, backloggng and fne capaces, on he opmsaon resuls has been nvesgaed. How o opmally synchronse replenshmen cycles? The neger-rao polcy, appled n hs research, doesn synchronze cycles. Oher polces, such as power-of-wo, nesed and nvered nesed, wll be suded n he fuure. The research wll be focused on developmen of heursc synchronsaon algorhms. 8 Acknowledgemen The presened research s funded by he ECLIPS Specfc Targeed Research Projec of he European Commsson "Exended Collaborave Inegraed Lfe Cycle Supply Chan Plannng Sysem". I has been also parly suppored by he European Socal Fund whn he Naonal Programme "Suppor for he carryng ou docoral sudy programmes and posdocoral researches" projec "Suppor for he developmen of docoral sudes a Rga Techncal Unversy". The auhors would lke o hank Roel De Haes from Möbus Ld. for a concepual model of he daabase componen. ISBN Copyrgh 2007 EUROSIM / SLOSIM

10 9 References [1] G. M. Campbell and V. A. Maber. Cyclcal Schedules for Capacaed Lo Szng wh Dynamc Demands. In: Managemen Scence, vol. 37, no. 4, pp , [2] Y. Merkuryev, G. Merkuryeva, B. Desme, and E. Jacque-Lagrèze. Inegrang Analycal and Smulaon Technques n Mul-Echelon Cyclc Plannng. In: Proceedngs of he Frs Asa Inernaonal Conference on Modellng and Smulaon (AMS 2007), Phuke, Thaland, [3] S. Sms. Taccal desgn of producondsrbuon neworks: safey socks, shpmen consoldaon and producon plannng. Technsche Unverse Endhoven [4] A. Peyraud, C. Verlhac, V. de Vulpllères, and S. Tmmermans. Repor on he opmzaon model for cyclcal nework plannng. Möbus Ld., Eurodecson [5] D. Smch-Lev, Y. Zao. Safey Sock Posonng n Supply Chans wh Sochasc Lead Tmes. In: Manufacurng and Servce Operaons Managemen, vol. 7, no. 4, pp , [6] D. Smch-Lev, P. Kamnsky, and E. Smch- Lev. Desgnng & Managng he Supply Chan: Conceps, sraeges and case sudes. McGraw- Hll Companes, Inc., New York, USA [7] ProModel. ProModel AcveX User Gude. ProModel Corporaon, Orem, Uah, USA, [8] ProModel. SmRunner User Gude. ProModel Corporaon, Orem, Uah, USA, ISBN Copyrgh 2007 EUROSIM / SLOSIM