SIMULATION-BASED RISK MEASUREMENT IN SUPPLY CHAINS

Transcription

1 SMULATN-BASED RSK MEASUREMENT N SUPPLY CHANS Ruslan A. Klmov and Yur A. Merkuryev Department of Modellng and Smulaton Rga Techncal Unversty 1/4 Meza Street, Rga LV 1048, Latva E-mal: rklmov@tl.rtu.lv KEYWRDS Rsk, Supply Chan, Beer Game ABSTRACT Because of modern supply chans complexty, supply chan managers are presently makng decsons whch are assocated wth some rsk. Ths paper dscusses rsk problem n supply chans and presents a supply chan rsk assessment approach. The Beer Game model, whch s a smplfed example of a supply chan, s used to demonstrate applcaton of the suggested rsk assessment approach. Two rsk events are taken nto account: nventory excessve accumulaton and backorderng. Smulaton experments wth the computersed verson of the Beer Game show that the approach presented can be used for assessng supply chan rsk; at the same tme, t s possble to llustrate rsk occurrence usng the Beer Game model. NTRDUCTN t s self-evdent that modern supply chans are becomng very complex. Managers have to organse numerous parallel physcal and nformaton flows wth the purpose to access the man logstc goals such as rght producton quantty, rght producton delvery place, rght producton delvery tme etc. Technology development provdes supply chan specalsts wth more effcent management approaches, whch help them mnmse nventores, defne customer demand more accurately and count other values that consderably reduce logstc costs. As a result of such accurate management, these supply networks become very vulnerable to dsruptons and unexpected stuatons. t s easer to create qute an effectve management approach for the case of determnstc systems, where all the nput data are known to managers, whereas most of the real-world supply chans systems can only be represented wth the help of stochastc models wth strongly expressed nfluence of uncertanty. Unfortunately the uncertanty factor generates rsks. Besdes, many of the key rsk factors n supply network have developed from such pressures as productvty enhancng, waste elmnatng, supply chan duplcaton removng, cost mprovement drvng etc (Strauffer 2003). But actually, takng decsons amed to decrease rsks event probablty, supply chan managers may ncrease total yelds. Stll, manager has to use technques for measurng rsk probablty. Due to modern supply networks complexty, t s dffcult to get precse values of such rsk event probabltes usng analytcal modellng only. Here, smulaton approaches prove to be effectve for obtanng adequate nformaton about rsks n supply chans. Ths paper descrbes the smulaton-based approach to assessng rsks n the concretsed supply chan, whch s the Beer Game network. The Beer Game s a wdely-known smplfed supply chan smulaton model, whch s used for studyng (usually for students) features of nformaton and physcal flows dstrbuton n supply networks (Smch Lev D. et al. 2003). The man dea of the present paper s to descrbe supply chan rsk assessment approach and ts applcaton to the Beer Game model. t should be noted that the work presented s exploratory and the approach descrbed should not be seen as a defnte soluton for calculatng rsk values. BACKGRUND Before representng the Beer Game model and descrbng the approach to calculatng rsk values n t, t s necessary to outlne common rsks n supply chans. Besdes, the followng paragraph provdes some nformaton about exstng researches n the sphere of smulaton-based rsk management. Rsk Management Accordng to common defnton, rsk s the potental harm that may arse from some present process or from some future event. Stll, n some cases (spheres) a defnton of that knd may not fully represent meanng of rsk. Thus, for successful rsk management n the determned sphere, t s necessary to specfy these meanngs: meanng of rsk, types of rsk and rsk measurement approaches (Gnyatov). Let us present the followng supply chan rsk defnton (accordng to Assstant Professor of Supply Chan Management at Mchgan State Unversty, George Zsdsn): the potental occurrence of an ncdent assocated wth nbound supply from ndvdual suppler falures or the supply market, n whch ts outcomes result n the nablty of the purchasng frm to meet customer demand or cause threats to customer lfe and safety (Clouse and Busch 2003).

2 Rsk types can be easly descrbed n the form of classfcaton. Stll, takng nto account the mult-shaped features of rsks, t s self-evdent that classfcaton performance strongly depends on the decson maker s subectve opnon. Thus, dfferent crtera should be used for dfferent classfcaton stuatons. Classfcaton crtera could be busness actvty type, rsk degree, rsk orgn reason etc. For example, Mark Clouse and Jason Busch suggest to group supply rsk nto 5 maor categores based upon companes sourcng and supply management proects and examne the drvers behnd each. Those categores are: strategy rsk, demand rsk, market rsk, mplementaton rsk and performance rsk (Clouse and Busch 2003). The LFA methodology suggests a more detaled supply chan rsk classfcaton that s gven bellow (Logstc Feld Audt TM 2004): foregn rsk; supply chan common elements rsks: o purchasng rsk; o producton rsk; o realsaton rsk; o producton return management rsk. logstc management rsk: o structural rsk; o fnancal rsk; o nformaton technologes rsk; o operaton rsk: transportaton rsk; customs rsk. After dfferent classfcatons are revewed, proper rsk classfcaton for a smplfed supply network, whch s smlar to the Beer Game, can be shown n ths paper. Ths classfcaton contans only three man ponts and takes nto account only those problems, whch can slow down producton movng over the supply chan. They are: purchasng rsk (the suppler doesn t have enough nventory to satsfy current supply chan member s replenshment order, payment transfer delay etc.); delvery rsk (rsk that the suppler wll not provde ordered goods n tme; such rsks nclude transportaton rsk, attendant documentaton falures, recpent warehouse repleton etc.); warehousng rsk (damages durng warehousng, stealng, attendant documentaton falures etc); Two man methods of rsk measurement can be dstngushed: expert opnon based method and statstcal method. For a long tme companes were defnng, prortzng, mtgatng and audtng rsk wth the help of subectve measurement approaches (Agarwal 2005). There are many approaches to modern expert based measurement, whch take nto account experence and ntuton of many people wth the purpose to reduce possble decson mstakes. However, the use of expert method s usually connected wth the tme losses, and t cannot be performed wthout necessary expert help (for example, makng decsons n a new sphere). At the same tme, the result of such measurement stll remans subectve. Thus, statstcal method proves to be more effectve for measurng rsk wthn the framework of smulaton. Takng nto account that rsk event occurrence probablty and precse rsk consequences are unknown varables, probable outcomes are usually assumed to be random varables. Let us dstngush some basc approaches to statstcal measurement of rsk that are based on (Pettere and Voronova 2003): arthmetc mean; average absolute devaton; average square devaton; rsk probablty; coeffcent; rsk scales. n many cases the value of arthmetc mean for losses, whch already happened, can be useful enough for rsk assessng. n other cases average absolute devaton of those losses can expand effcency for rsk measurement. The rsk assessment based on calculatng average absolute devaton s very popular n the sphere of fnance. The Value at Rsk (VaR) measurement s a classcal example of the mentoned approach. n the sphere of logstcs, nventory at Rsk (ar) and Demand at Rsk (DaR) are smlar approaches to such rsk assessment (Sodh 2005). Another approach defnes rsk value as the probablty that rsk event wll occur. When t s necessary to take nto consderaton rsk event probablty and rsk event severty values, the rsk coeffcent can be used to compare dfferent rsk stuatons. The last approach to rsk measurement s based on rsk scales applcaton. Unfortunately, researches n that area do not provde a standartsed approach to rsk scale creaton, whch s the man dsadvantage of ths approach. Smulaton-Based Rsk Measurement Today, smulaton s wdely accepted for predctng, explanng, tranng and dentfyng optmal solutons. Smulaton s used extensvely n sphere of logstc systems to model producton and assembly operatons, develop realstc producton schedules, study nventory polces, analyze relablty, qualty and equpment replacement problems and desgn materal handlng systems. There are many well-known benefts of smulaton. For example, smulaton allows one to evaluate outcomes of any decsons before mplementng them nto real systems; smulaton models are easer to understand than many analytcal approaches; smulaton allows one to create models, whose analytcal realzaton s mpossble or complcated (Evans and lson 1998). t can be assumed, that such abltes make smulaton very useful for rsk analyss. t should be noted that the dea

3 to assess rsk usng smulaton, s not new. For example, Monte Carlo smulaton can be used for supply chan rsk analyss whch s assocated wth hazards (Elkns et al. 2004). Another example dscusses the possblty of makng wrong decsons n the sphere of nventory management (Delers and Erhun 2005). Ths paper descrbes an approach to rsk analyss n the smplfed supply chan, whch s represented by the Beer Game. The Beer Game s the tranng program, whch llustrates the dynamcs of supply chans and teaches prncples for effectve nventory replenshment management. The goal of ths game s to mnmse the total nventory holdng and unmet demand (backorder) cost. At the same tme, the modellng wth the Beer Game can llustrate rsk nfluence n supply chan and smulaton-based rsk measurement approaches. SUPPLY CHAN: BEER GAME BASED MDEL As was mentoned prevously, ths paper dscusses rsk assessment n smple supply chan system, whch s used n the Beer Game. Ths secton descrbes the abovementoned model and also gves nformaton about rsk calculaton wthn the framework of ths supply chan model. t s necessary to notce, that classc Beer Game s typcally played on a large board. n our case the computersed verson of the game s used nstead. Actually, the computersed game can fully represent the classc onboard game. At the same tme, the strong advantage of the computersed model s bult-n nventory replenshment polces whch can be used for automated supply chan component management. Beer Game Model The Beer Game smulates the followng scenaros. Frst, consder a smplfed beer supply chan consstng of a sngle retaler, a sngle wholesaler who supples the retaler, a sngle dstrbutor who supples the wholesaler, and a sngle factory wth unlmted raw materals whch makes (brews) the beer and supples the dstrbutor. Each component n the supply chan has unlmted storage capacty, and there s a fxed supply lead tme and order delay tme between each component. Every week, each component n the supply chan tres to meet the demand of the downstream component. Any orders whch cannot be met are recorded as backorders, and met as soon as possble. No orders wll be gnored, and all orders must eventually be met. At each perod, each component n the supply chan s charged a $1.00 shortage cost per backordered tem. Also, at each perod, each component owns the nventory at that faclty. n addton, the wholesaler owns nventory n transt to the retaler, the dstrbutor owns nventory n transt to the wholesaler, and the factory owns both tems beng manufactured and tems n transt to the dstrbutor. Each locaton s charged $0.50 nventory holdng cost per nventory tem that t owns. Also, each supply chan member orders some amount from ts upstream suppler. t takes one week for ths order to arrve at the suppler. nce the order arrves, the suppler attempts to fll t wth avalable nventory, and there s an addtonal two week transportaton delay before the materal beng shpped by the suppler arrves at the customer who placed the order. Each supply chan member has no knowledge of the external demand (except, of course, the retaler), or the orders and nventory of the other members. The schema of the descrbed system and ts smulaton envronment are shown n Fgure 1. Fgures 1: Computersed Beer Game Model The goal of the retaler, wholesaler, dstrbutor, and factory, s to mnmze total cost, ether ndvdually, or for the system (Kamnsky and Smch Lev 2003). Rsk Measurement Ths paper does not descrbe mathematcally how supply chan parameters affect the rsk probablty. Thus, only local rsk (nventory rsk at each warehouse) calculaton s descrbed. Stll, four rsk events can be dstngushed for the above-mentoned model: current warehouse nventory level cannot be replenshed due to out of stock at the prevous supply chan member warehouse; demand ncreasng causes nventory devastaton, so the current demand cannot be satsfed; demand decreasng causes nventory level excessve ncreasng, whch wll accordngly rase nventory costs; chosen nventory replenshment polcy leads to unplanned total costs. From the above t follows that two model output varables can be used for makng rsk assessment: nventory level and unsatsfed orders quantty (backorderng) at each warehouse. As was mentoned before, there are dfferent types of rsk assessment approaches. Ths paper ntroduces the dea that rsk calculaton approaches can be used to compare the effcency of chosen nventory replenshment polces.

4 Rsk assessment s carred out n three ways. The frst one represents rsk assessment due to rsk probablty. The next one descrbes rsk assessment due to rsk coeffcent calculaton for each of output varables whch are nventory level and backorderng. At the fnal step, both rsk coeffcents summaton s descrbed, whch gves a more effectve opportunty for supply chan management decson makng. Probablty as a Measure of Rsk Usually, for adequate rsk assessment, rsk event probablty calculaton s necessary. Stll, the probablty tself can be a good enough measure for rsk estmaton. The probablty can be measured n subectve and obectve ways. For the descrbed Beer Game model, obectve measurement s used that s based on smulaton output statstcs. n such a way, a probablty can be measured, whch descrbes nventory and backorderng levels values for the next tme. Thus, the probablty that nventory level (backorderng level) wll be equal to, s two values relaton (1): the number of smulated weeks, n whch such nventory level (backorderng level) has been regstered; and the number of smulated weeks. nventory and backorderng probabltes can be calculated as follows: p () p ) x L ( (1) : probablty that nventory level wll be equal to number. x : number of smulated weeks, n whch nventory level was equal to number. L: number of smulated weeks. x p ( ) (2) L p () : probablty that backorderng level wll be equal to number. x : number of smulated weeks, n whch backorderng level was equal to number. Stll, a calculaton of that knd does not provde effectve rsk assessment. A more useful form s calculated probabltes accumulaton, whch gves us rsk measurement approach smlar to Value at Rsk. Thus t s possble to calculate the probabltes that nventory level (or backorderng level) wll not exceed the chosen value: P () P ( ) p ( ) (3) 1 : probablty that nventory level wll not exceed value. P ( ) p ( ) (4) 1 P () : probablty that backorderng level wll not exceed value. So, supply chan manager has to choose the restrcton value. Ths paper descrbes calculatons, whch produce the probablty that: nventory level wll not exceed value 10; the number of back orders wll not exceed value 0. Rsk Coeffcent as a Measure of Rsk When rsk s calculated as a rsk event probablty, the rsk costs are not taken nto account. Ths s not a problem when rsk costs are dentcal. n the Beer Game case, each event, spare nventores and backorderng, has dfferent costs, whch depends on the sze of spare nventores and number of unsatsfed orders, accordngly. Thus, the smplest way to calculate such rsk coeffcent s to multply probablty value and costs factor: r N 1 p ( ) * c (5) r : rsk coeffcent for the chosen nventory level exceedng. c : cost functon for the chosen nventory level. N: maxmal nventory level regstered durng smulaton. r K 1 p ( ) * c (6) r : rsk coeffcent for the chosen backorderng level exceedng. c : cost functon for the chosen backorderng level. K: maxmal backorderng level regstered durng smulaton. Complex Rsk Coeffcent Havng an approach to nventory rsk and backorderng rsk assessment, one can make decsons ntended for ther separate management. Nevertheless, as was mentoned prevously, there are many cases when one rsk event probablty decreasng causes other rsks event probabltes. For example, t s possble to create nventory replenshment polcy, whch fully excludes backorderng event, but at the same tme, such a decson wll strongly ncrease average nventory level at the warehouse. So, t s useful to make all rsk crtera summaton, whch follows from multple crtera decson theory: R N 1 K p ( ) * c p ( ) * c (7) 1 R: complex rsk coeffcent. Thus, accordng to the above-mentoned formula, the rsk management ams for coeffcent R mnmsaton. t s also necessary to pont out the dsadvantage of that

5 approach. t doesn t take nto account an ncome from supply chan operatons. EXPERMENTS The smulaton llustrates applcaton of the descrbed approaches to rsk assessment n the smplfed supply chan. Ths paper dscusses three experments wth the Beer Game model. For those experments, dentcal clent demand dstrbuton generators were used (nput data). The man goals of the experments were to represent rsk assessment approach and nvestgate how dfferent nventory replenshment polces could be compared based on rsk measurement crtera. For each experment, only one replcaton was used, whose smulaton tme was 300 weeks. Besdes, rsk calculaton does not nclude the frst 100 week perod data (warm-up perod). For the frst experment, basc nventory replenshment polcy (default nventory replenshment polcy of the above-mentoned computersed Beer Game) s used for all supply chan members. Ths polcy s called Updated s. Accordng to that polcy, each order has to fll nventory level up to value s, whch s contnuously updated to the followng value: the movng average of demand receved by current supply chan member over the past 10 weeks tmes the lead tme for an order placed by that member, plus M tmes an estmate of the standard devaton durng the lead tme. Table 1 represents rsk assessment based on rsk event probablty calculaton. Table 1: Rsk Probabltes n Experment 1 Retaler Wholesaler Dstrbutor Factory P (15) probablty that nventory level wll not exceed value of 15 97,5% 84% 55% 25,5% P (0) probablty that backorderng level wll not exceed value of 0 89,5% 88% 88% 95,5% ne can see that the probablty for warehouse to be over-crammed grows up due to the fnal supply chan member; thus t evdently shows the presence of the Bull-whp effect. The next table shows rsk assessment based on rsk coeffcent calculaton. Table 2: Rsk Coeffcents n Experment 1 r r R Retaler 2,945 0,430 3,375 Wholesaler 4,493 0,685 5,178 Dstrbutor 8,058 0,765 8,823 Factory 13,220 1,250 14,470 n the second experment, the nput parameters contan smlar values except for nventory replenshment polcy at Dstrbutor warehouse, whch uses Mn-Max nventory replenshment polcy. Table 3 and Table 4 represent rsk assessment results accordng to the second smulaton experment. t seems that rsk crteron was mproved due to the second experment. Stll, new nventory polcy at Dstrbutor warehouse badly affects the last member of the supply chan. Table 3: Rsk Probabltes n Experment 2 Retaler Wholesaler Dstrbutor Factory P (15) probablty that nventory level wll not exceed value of 15 98,5% 88,0% 72,5% 11,5% P (0) probablty that backorderng level wll not exceed value of 0 92,5% 90,5% 90,0% 99,5% Table 4: Rsk Coeffcents n Experment 2 r r R Retaler 2,820 0,190 3,008 Wholesaler 3,888 0,375 4,263 Dstrbutor 5,240 0,380 5,620 Factory 13,093 0,020 13,113 The last experment s nput data contan Dstrbutor Mn-Max polcy parameters alteraton, whch decreases nventory level exceedng and backorderng rsks. Table 5: Rsk Probabltes n Experment 3 Retaler Wholesaler Dstrbutor Factory P (15) probablty that nventory level wll not exceed value of 15 97,5% 87,5% 65,5% 42% P (0) probablty that backorderng level wll not exceed value of 0 90,5% 89,5% 92,5% 96% Table 6: Rsk Coeffcents n Experment 3 r r R Retaler 2,803 0,315 3,118 Wholesaler 4,065 0,450 4,515 Dstrbutor 6,238 0,500 6,738 Factory 9,525 0,295 9,820 The table data gve an opportunty to ascertan rsk dependence on the changes n the supply chan. Makng the collected rsk measurement values research, one can compare dfferent polces due to collected rsk ndcators research. t s also possble to observe how

6 polcy changes at one member of supply chan affect the rsk factor at other members. t seems that both the rsk probablty and the rsk coeffcent calculatons are usable enough for rsk assessment. Stll, t s much easer to make supply chan management decsons usng percentage values. n the other hand, such an assessment does not take nto account rsk costs functon. CNCLUSNS Ths paper ntroduces a rsk measurement approach, whch can be appled to supply chan management. The obvous advantage of such rsk assessment s calculaton-based measurement that means subectvty dependence reducng. Thus, t s easer to ntegrate ths approach nto models to enable automated rsk calculaton. t should be noted, however, that the descrbed rsk event probablty and rsk coeffcents calculaton results have to be analysed by experts. Another dsadvantage of ths rsk assessment approach s the necessty for the statstcal data. Therefore, t s worthwhle to use such rsk assessment n combnaton wth smulaton, n order to provde necessary data. The purpose of the paper was to demonstrate rsk assessment possblty usng the Beer Game model. The descrbed approaches were appled to the computersed verson of the Beer Game. Accordng to smulaton results t s possble to draw conclusons about the adequacy of the descrbed rsk measurement approach. n partcular, the calculated rsk values can be used to compare dfferent nventory replenshment polces. Stll, the presented paper s only a start for future research, whch wll be mostly focused on rsk studyng envronment creaton. The chosen computersed verson of the Beer Game causes some dffcultes durng experments mplementaton. Most lkely, t wll be necessary to mplement a new program that would represent the Beer Game supply chan management model wth the ntegrated rsk assessment approach. Future research also has to nclude rsk coeffcent ratonng and mult crtera optmsaton mechansms to provde a more effectve measure for makng management decsons. Another task of future research s to modfy the Beer Game model to make t more ntended for studyng rsk n supply chans. REFERENCES Agarwal, S Managng Rsk n Supply Chan. Supply&Demand Chan Executve. August. Clouse, M. and Busch, J How to dentfy and Manage Supply Rsk. Supply Chan Planet. ctober. Delers, L., Elkns, D. and Pate-Cornell, E Analyzng Losses from Hazards Exposure: a Conservatve Probablstc Estmate Usng Supply Chan Rsk Smulaton. n Proceedngs of the 2004 Wnter Smulaton Conference (Washngton Hlton and Towers Washngton, Dec. 5-8). U.S.A., Delers, A. and Erhun, F Rsk Management n Supply Networks Usng Monte-Carlo Smulaton. n Proceedngs of the 2005 Wnter Smulaton Conference (rlando, FL. Dec. 4-7). U.S.A., Evans, J. and lson, D ntroducton to Smulaton and Rsk Analyss. Prentce-Hall, Englewood Clffs, Gnyatov, R. Rsk and Management (CS Model). Audt Ware (n Russan) Smch-Lev D., Kamnsky, P. and Smch Lev, E Desgnng and Managng the Supply Chan: Concepts, Strateges, and Case Studes. McGrow-Hll/rwn Pettere, G. and Voronova, Busness Rsk Management. Bankng nsttuton of Hgher Educaton (n Latvan) Sodh M Managng Demand Rsk n Tactcal Supply Chan Plannng for a Global Consumer Electroncs Company. Producton and peraton Management. Sprng. Strauffer, D Supply Chan Rsk: Deal wth t. HBS Workng Knowledge. Aprl. Logstc Feld Audt TM Supply Chan Rsk Management Usng LFA Technologes. LFA Supply Chan Rsk Management: Base Concepton. (n Russan) AUTHR BGRAPHES RUSLAN KLMV earned hs master s degree at Rga Techncal Unversty n Snce that tme he has been workng for Rga Techncal Unversty. He s a member of Department Smulaton Socety. Hs professonal nterests are n the feld of smulaton, supply chan and rsk modellng. Prof. YUR MERKURYEV s Full Professor and Head of the Department of Modellng and Smulaton n the nsttute of nformaton Technology at Rga Techncal Unversty (Latva), as well as Vstng Professor at the Unversty of Lublana (Slovena), Faculty of Economcs. Hs professonal nterests nclude the methodology of dscrete-event smulaton, desgn of smulaton experments, optmsaton of smulaton models, practcal mplementaton of dscrete-event smulaton, supply chan modellng and management, and educaton n the areas of modellng and smulaton, and logstcs management as well. He s Programme Drector for the Master-level currculum ndustral Logstcs Management at Rga Techncal Unversty. Prof. Merkuryev regularly partcpates n organsng nternatonal conferences n the area of modellng and smulaton. He has served as General Char of the nternatonal conference "European Conference on Modellng and Smulaton", ECMS'2005 (Rga, Latva, June 1-4, 2005) and Programme Char of the nternatonal workshop Harbour, Martme, & Multmodal Logstcs Modellng and Smulaton, HMS2005 ( Marselle, France, ctober 20-22, 2005). Prof. Merkuryev s a Correspondng member of the Latvan Academy of Scences, Board member of the European Councl of the Socety for Modellng and Smulaton nternatonal (SCS), Presdent of Latvan Smulaton Socety, and Board member of the Latvan Transport Development and Educaton Assocaton.