Francesco Cosanno e al. / Inernaonal Journal of Engneerng and Technology (IJET) SPC-based Invenory Conrol Polcy o Improve Supply Chan ynamcs Francesco Cosanno #, Gulo Gravo #, Ahmed Shaban #3,*, Massmo Tronc #4 # eparmen of Mechancal and Aerospace Engneerng, Unversy of Rome La Sapenza, va Eudossana 8, 0084 Rome, Ialy *eparmen of Indusral Engneerng, Faculy of Engneerng, Fayoum Unversy, Fayoum 6354, Egyp francesco.cosanno@unroma. gulo.dgravo@unroma. 3 ahmed.shaban@unroma. 4 massmo.ronc @unroma. Absrac Invenory conrol polces have been recognzed as a conrbuory facor o he bullwhp effec and nvenory nsably. Prevous sudes have ndcaed ha here s a rade-off beween bullwhp effec and nvenory performance where he bullwhp effec reducon mgh ncrease nvenory nsably. Therefore, here s a need for nvenory conrol polces ha can cope wh supply chan dynamcs. Ths paper proposes an nvenory conrol polcy based on a sascal process conrol approach (SPC) o handle supply chan dynamcs. The polcy reles on applyng ndvdual conrol chars o conrol boh he nvenory poson and he placed orders adequaely. A smulaon sudy has been conduced o evaluae and compare he proposed SPC polcy wh a radonal order-up-o n a mul-echelon supply chan. The comparson showed ha he SPC polcy ouperforms he order-up-o n erms of bullwhp effec and nvenory performances. The SPC succeeded o elmnae he bullwhp effec whls keepng a compeve nvenory performance. Keyword Supply Chan, Invenory Conrol, SPC, Conrol Char, Bullwhp Effec, Invenory Varance, Smulaon I. INTROUCTION In supply chans, he varably n he orderng paerns ofen ncreases as demand nformaon moves upsream n he supply chan, from he realer owards he facory and he supplers. Ths phenomenon of nformaon dsoron has been recognzed as he bullwhp effec []. Fg. depcs an example of he bullwhp effec n whch he orders placed by four supply chan echelons over he same 00 perods are ploed sde-by-sde. The bullwhp effec has been observed n many ndusres such as Campbell Soup s [], HP and Procor & Gamble [], fas movng consumer goods [3], and car manufacurng [4]. Forreser [5] was mosly he frs o sudy hs problem hrough a se of smulaon expermens usng sysem dynamcs approach. Anoher number of researchers developed smulaon games o llusrae he bullwhp effec exsence and s negave mpacs on supply chan performance [6]. Towll, Zhou, and sney [7] ndcaed ha he bullwhp effec could lead o sock-ous, large and expensve capacy ulzaon swngs, lower qualy producs, and consderable producon/ranspor on-coss as delveres are ramped up and down a he whm of he supply chan [8], [9]. Lee, Padmanabhan, and Whang [] denfed fve fundamenal causes of bullwhp effec: demand sgnal processng, non-zero lead-me, order bachng, prce flucuaons and raonng and shorage gamng. Under demand sgnal processng, demand s forecased usng a forecasng mehod, and hen he parameers of he nvenory replenshmen rules are updaed n accordance o demand changes. By dong hs, he sysem may over reac o shor-run flucuaons, whch nduces varance amplfcaon [0]. Burbdge s Law of Indusral ynamcs saes ha If demand s ransmed along a seres of nvenores usng sock conrol orderng, hen he amplude of demand varaon wll ncrease wh each ransfer []. Thus, nvenory managemen decsons can be consdered as a man drver of bullwhp effec and can be classfed under he demand sgnal processng cause [0]. However, nvenory managers mus consder wo prmary facors when makng nvenory replenshmens []. Frs, a replenshmen rule has an mpac on order varably (as measured by he bullwhp effec,.e., he rao of he varance of orders over he varance of demand) shown o he suppler (see Fg. ). Second, he replenshmen rule has an mpac on he varance of he ne sock (as measured by he ne sock amplfcaon,.e., he rao of ne sock varance over he varance of demand). The bullwhp effec manly conrbues o upsream coss, whle he varance of ne sock deermnes he sage s ably o mee a servce level n a cos-effecve manner. Ths rade-off needs desgnng a good replenshmen rule o balance he nvenory and producon coss whls ensurng a cusomer servce level []. Exhausve research has been conduced o sudy he mpac of varous orderng polces on bullwhp effec and oher research has also aemped o develop orderng and replenshmen rules ha can avod he creaon of bullwhp effec [3]-[9]. ISSN : 0975-404 Vol 6 No Feb-Mar 04 48
Francesco Cosanno e al. / Inernaonal Journal of Engneerng and Technology (IJET) Order quany 90 80 70 60 50 40 30 0 Cusomer Realer Wholesaler srbuor Facory 0 0 0 00 00 300 400 500 Fg.. An example of demand amplfcaon (bullwhp effec). The rade-off beween bullwhp effec and nvenory performance s sll a major concern for boh supply chan managers and academcs. The praconers need a smple orderng polcy ha can handle hs rade-off whou major mplemenaon effor [3]. The orderng polces should also be smar enough o monor s nernal and exernal envronmens and makng he approprae changes whenever s needed. Recenly, a few number of researchers have nroduced he Sascal Process Conrol (SPC) ools n he area of nvenory plannng and conrol. Was e al. [0] was mosly he frs o presen a conrol char approach for monorng he performance of a reorder-pon nvenory sysem hrough monorng sock-ous and applyng conrol chars for demand and nvenory urnover o denfy wheher he causes of sysem malfuncons relaed o sysem fness or ongong operaons. Pfohl, Cullmann, and Sölzle [] developed a real-me nvenory decson suppor sysem by usng he radonal Shewhar conrol chars for nvenory level and demand n whch a seres of decson rules are provded o help he nvenory manager o deermne he me and he quany o order. They argued ha he proposed nvenory decson sysem showed very good resuls where he average nvenory levels could have been reduced by 0% o 65% whch mgh save nvenory coss. Cheng and Chou [] exended he work of Pfohl, e al. and nroduced an nvenory decson sysem n whch he ARMA conrol char was employed o monor he marke demand and he ndvdual conrol char wh wesern elecrc rules was used o monor he nvenory level. Lee and Wu [3] compared wo replenshmen approaches, namely, radonal replenshmen polces and sascal process conrol SPC-based replenshmen polcy. They concluded ha SPC-based polcy had shown beer reducon of nvenory varably han he radonal mehods. Wh excepon o Lee and Wu [3] who adoped a wo-echelon supply chan o compare a SPC polcy wh he radonal polces, he majory of he above SPC work consdered a sngle echelon supply chan n order o evaluae he effecveness of SPC orderng polces. Also, some of hose auhors negleced he effec of leadme n her nvenory models. Furhermore, he performance measures ha have been used n he prevous work o evaluae hose nvenory models dd no consder he supply chan dynamcs such as bullwhp effec rao and nvenory varance. The common measures n her sudes were servce level and average nvenory level. In hs sudy, we wll be more neresed n he dynamc performance of he supply chan under orderng polces. Ths research consders he prevous aemps o ulze SPC conrol chars for nvenory conrol. In parcular, hs work proposes a new nvenory conrol polcy based on SPC conrol chars o be used n dynamc and complex envronmens lke mul-echelon supply chans. The man objecve of he SPC polcy s o overcome he dynamc problems of he radonal nvenory managemen sysems hrough conrollng manly he problem of demand varably amplfcaon whls managng smulaneously he nvenory poson. A smulaon approach s adoped o conduc he sudy and o evaluae he performance of a mul-echelon supply chan under he proposed SPC polcy. Furhermore, a comparson wll be conduced beween he SPC polcy and he radonal order-up-o orderng polcy n erms manly of bullwhp effec, nvenory sably and servce level. The smulaon resul showed ha he SPC performs beer han he radonal order-up-o polcy where SPC succeeded o elmnae he bullwhp effec whs achevng a sasfacory nvenory performance. II. SPC REPLENISHMENT POLICY The proposed SPC replenshmen polcy s an negraed nvenory conrol sysem ha can monor he nvenory poson and place balanced orders o he upsream echelons n he supply chan. The man dea s ha usng a conrol char o esablsh a sascally vald zone, defned by upper and lower conrol lms nsead of sngle pon replenshmen, would allow dampenng he overreacons ha can cause he bullwhp effec and nvenory varance amplfcaon. The SPC replenshmen polcy reles on wo conrol chars o be used for monorng demand and nvenory poson smulaneously. The frs conrol char s devoed o monor he varaon of he cusomer demand over me so ha he approprae changes n he orderng behavor can be made whenever a consderable change n he demand has been deeced. In oher words, f he cusomer demand s sable (.e., n-conrol), hen he order quany wll be he same as ever before. However, f he demand conrol char sgnals he presence of an ou-ofconrol suaon (.e., demand change), hen he order quany should be adjused n order o accoun for he n- ISSN : 0975-404 Vol 6 No Feb-Mar 04 49
Francesco Cosanno e al. / Inernaonal Journal of Engneerng and Technology (IJET) venory sably. Accordngly, he demand conrol char should be complemened wh a number of decson rules n order o decde abou he ou-of-conrol suaon and how much o order under dfferen ou-of-conrol suaons. The base order quany wll hen be added o he requred adjusmen for he nvenory poson n order o consue he fnal order o place. The second conrol char s employed for monorng and adjusng he nvenory poson whenever s needed. Ths conrol char wll be employed o denfy wheher he nvenory poson varable s n-conrol or no. Ths conrol char s complemened wh a number of decson rules o adjus he nvenory poson whenever s needed. For example, f he curren daa pon of nvenory poson s very low, hen a decson rule wll be needed o deec hs suaon and propose an amoun of adjusmen o be added o he base order quany. A. Conrol Chars and ecson Rules The ype of conrol char ha wll be used for boh demand and nvenory poson s called he ndvdual conrol char n whch he sample sze s equal o one. A ypcal conrol char consss of hree basc elemens: cenerlne ha represens he average of he process varable, and upper and lower conrol lms [4]. Based on he normaly assumpon, s expeced ha 99.73% of he demand daa pons wll be whn he lower and upper conrol lms f a process varable (e.g., cusomer demand process) s n-conrol. The conrol lms of he demand and nvenory poson conrol chars can be calculaed as follows n Table I. Table I Conrol Chars Calculaons emand Conrol Char Invenory Poson Conrol Char UCL = CL + 3 ˆ σ UCL = CL + 3 ˆ σ CL = w w + IP IP IP CL = L CL + SS IP d CL = ( L + k ) CL IP d LCL = CL 3 ˆ σ UCL = CL 3 ˆ σ IP IP IP In he above able, he CL represens he cenerlne of he demand/ncomng order conrol char and s calculaed based on he average of he las consecuve w daa pons of he ncomng order daa. The LCL represens he lower conrol lm and equals he dfference beween CL and 3 ˆ σ where ˆ σ s he sandard devaon of he demand varable over he las consecuve w daa pons. The upper conrol lm ( UCL ) equals he sum of CL and 3 ˆ σ. The cenerlne of he nvenory poson conrol char s equal o CL mulpled by he delvery lead-me ( L d ) and added o he safey sock componen. Alernavely, we exend he delvery lead-me wh k o accoun for he safey sock. The decson rules correspondng o he demand conrol char wll be dependen on he saus of he las observaons of he ncomng order as hey are he mos mporan nformaon for managng he orderng process. Ths s smlar o he radonal polces n whch he orderng process s drven by a forecasng echnque ha usually reles on he laes nformaon o make expecaons for he fuure demand. B. Base Order Quany A echelon, f he las consecuve n daa pons of ncomng order/demand are eher above or below a defned safey zone beween CL ˆ Kσ and ˆ CL + Kσ, hen he base order quany ( O ) should be se as follows n equaon (). However, f hs condon s no sasfed, hen he base order quany should be equal o he cenerlne of he demand conrol char as follows n equaon (). In case of he demand or he ncomng order o echelon s zero, hen, he order quany of echelon should be se o zero (.e., O = 0 ). O O = IO () n n + = CL, or O = () w w + C. Invenory Balance ISSN : 0975-404 Vol 6 No Feb-Mar 04 40
Francesco Cosanno e al. / Inernaonal Journal of Engneerng and Technology (IJET) A echelon, f he las observaon on he nvenory poson conrol char, IP, s above he upper lm of a safey zone ( CL + K σ ), hen, a negave nvenory balance should be added o he base order quany. Ths IP IP IP nvenory balance ( Invb ) can be calculaed as follows n equaon (3): Invb = CL + K σ IP (3) IP IP IP Oherwse, f he las observaon on he nvenory poson conrol char, IP, s below he lower lm of a safey zone ( CLIP KIPσ IP ), hen, a posve nvenory balance should be added o he base order quany (see, equaon (4)). Invb = CL K σ IP (4) IP IP IP Fnally, f he las observaon s whn he safey zone (.e., CL K σ IP CL + K σ ), hen, here s no need for nvenory balance,.e., Invb = 0. IP IP IP IP IP IP The fnal order ha should be placed a he end of revew me wll be equal o he sum of he base order quany and he nvenory balance as shown n equaon (5): O = Max{ O + Invb, 0} (5) III. SUPPLY CHAIN MOELING AN SIMULATION A. Supply Chan Model and Assumpons In hs research, we model a sngle produc mul-echelon supply chan ha consss of a cusomer, a realer, a wholesaler, a dsrbuor, and a facory (see Fg. ) o nvesgae he proposed SPC polcy. Ths s a wellknown supply chan model, known as he Beer Game srucure, and has been ulzed n many prevous nvesgaons [6]-[8]. I s assumed ha all echelons have unlmed sockng capacy, boh he suppler and he facory have unlmed capacy, and he lead-mes are deermnsc and fxed across he supply chan wh orderng lead-me = and delvery lead-me =. Each echelon can apply eher he order-up-o or he SPC polcy. However, all echelons n he supply chan wll apply he same orderng polcy (.e., order-up-o or SPC). The order-up-o orderng polcy and s governng rules are explaned below n he nex secon. Cusomer Realer Wholesaler srbuor Facory Informaon flow Produc flow Fg.. A four-echelon supply chan B. Order-Up-To Polcy The order-up-o orderng polcy has been wdely consdered n he leraure of supply chan dynamcs because of s populary n pracce [0]. Ths polcy wll be used o generae he hsorcal daa requred o nae he SPC polcy. I wll also be used o valdae he effecveness of he SPC polcy hrough comparng he performances of he supply chan under each polcy. In hs polcy, a he end of each revew perod ( R ), an order O s placed whenever he nvenory poson IP s lower han a specfc arge level S. The revew perod s consdered o be equal o one (.e., R = ). The order-up-o polcy can be represened mahemacally as follows n equaons (6-9). O = Max{( S IP ), 0}. (6) IP = S IO. (7) ˆ ˆ S = L + SS. (8) =. (9) n IO j+ n j= The arge nvenory poson S s calculaed based on he expeced demand over he oal lead-me (orderng and delvery lead-mes). The movng average forecasng echnque has been consdered o calculae he expeced demand ( ˆ ) and hs forecasng mehod s seleced because of s populary n research and n pracce ISSN : 0975-404 Vol 6 No Feb-Mar 04 4
Francesco Cosanno e al. / Inernaonal Journal of Engneerng and Technology (IJET) as well [0], [4]. In hs model, we have consdered he safey sock by exendng he lead-me by k [6], [8], [5] so ha he arge nvenory poson S can hus be reformulaed as shown below n equaon (0). Ths s smlar o wha we have done wh he cenerlne of he nvenory poson conrol char. ( ) ˆ S = L+ k (0) C. Performance Measures The performance of he supply chan under he proposed SPC and OUT polcy wll be evaluaed hrough characerzng he orderng and nvenory behavor under each polcy hroughou he whole supply chan. The orderng behavor wll be evaluaed by esmang he followng performance measures: average order level, oal varance amplfcaon or bullwhp effec ( TVA ), and sage varance amplfcaon ( SVA ). The TVA and SVA are used o quanfy he demand amplfcaon hroughou he supply chan. The TVA, as shown n equaon (), s esmaed n erms of he rao of orders varance dvded by he correspondng orders average a echelon o he cusomer demand varance dvded by he average demand [0], [4], [8]. σ / µ O TVA = () σ / µ O The SVA s esmaed by comparng he order varance a echelon o he order varance a echelon ; each s dvded by he correspondng mean as shown n equaon () [6]. σ / µ SVA = σ µ () O O O / O The nvenory behavor wll be evaluaed hrough esmang he followng performance measures: average ne nvenory, nvenory varance rao, and average servce level. The nvenory varance rao represens he rao of he acual ne nvenor varance ( σ ) o he cusomer demand varance as shown n equaon (3) [7]. NI InvR σ = (3) σ NI The average servce level quanfes he percenage of ems delvered mmedaely by echelon o he ncomng order from echelon. Servce level or fll rae s compued every revew me R over he effecve delvery me (.e., IO > 0 ) as shown n equaon (4), where SR sands for he shpmen from echelon o echelon a, B sands for he nal backlog a echelon a, a me, and T eff sands for he effecve delvery me. IO s he ncomng order o echelon SR B 00 0 f SR B > Sl IO = 0 f SR B 0 (4) Teff = Sl ASl = (5) T eff IV. SIMULATION RESULTS AN ANALYSIS A smulaon model has been developed for he supply chan descrbed above usng SIMUL8 smulaon package. To evaluae he proposed polcy, he smulaon model was run for 0 replcaons of 400 perods each. Each smulaon run consss of four sages, he frs sage s a warm-up perod for he order-up-o polcy, and he second sage s he effecve smulaon run ha he performance of he order-up-o wll be colleced over. Then, anoher warm-perod for he SPC polcy s consdered, followed by an effecve smulaon run for he SPC o collec he supply chan performance for he analyss. Boh warm-up perods are se o be of he same lengh (.e., 00 perods), and boh effecve smulaon runs are se o be of he same lengh (.e., 000 perods). The warm-up perod has been deermned based on a se of prelmnary expermens, and he numbers of replcaons are based on a calculaor ool n SIMUL8. Ths ool connues o run replcaons unl a confdence nerval wh a specfed level (95%) and precson (5%) s obaned for a se of a predeermned performance measures. ISSN : 0975-404 Vol 6 No Feb-Mar 04 4
Francesco Cosanno e al. / Inernaonal Journal of Engneerng and Technology (IJET) The cusomer demand paern was assumed o follow he normal dsrbuon wh a mean of 30 and a sandard devaon of 3. The parameers of he order-up-o are se o k =, and m = 00, and he SPC polcy parameers are se o w = 00, K IP = 0.5, K =.5, and n = 4. Furhermore, for smplcy, we se ˆ σ ˆ IP = σ n all he followng smulaon expermens. A. Orderng Behavor The orderng behavor of he supply chan n erms of average order level, oal varance amplfcaon, and sage varance amplfcaon a each echelon, before and afer applyng he SPC polcy, wh 95% confdence level, s summarzed n Table II. TABLE II Orderng Behavor of All Echelons n he Supply Chan Under Order-Up-To and SPC Polces Performance Measure Average order level Toal varance amplfcaon Sage varance amplfcaon Order-up-o (Before) SPC polcy (Afer) -95% Average 95% -95% Average 95% emand 9.9 30.0 30. 9.9 9.9 30.0 Realer 9.9 30.0 30. 9.9 9.9 30.0 Wholesaler 9.9 30.0 30. 9.9 9.9 30.0 srbuor 9.9 30.0 30. 9.9 30.0 30.0 Facory 9.9 30.0 30. 9.9 30.0 30.0 Realer.09.09.0 0.77 0.78 0.79 Wholesaler.0..3 0.67 0.69 0.70 srbuor.34.36.39 0.6 0.64 0.67 Facory.50.53.57 0.60 0.63 0.65 Realer.09.09.0 0.77 0.78 0.79 Wholesaler... 0.87 0.88 0.89 srbuor...3 0.9 0.94 0.95 Facory...3 0.96 0.98 0.99 Alhough we have seleced a se of parameers for he order-up-o polcy ha was suffcen o reduce he bullwhp effec o a grea exen, he resuls show ha he order-up-o polcy s sll generang he bullwhp effec and s ncreasng as we move upsream from he realer o he facory. In conras, he SPC polcy was successful o elmnae he bullwhp effec where he oal varance amplfcaon a all echelons (.e., hroughou he supply chan) s less han one. I can also be observed ha he bullwhp effec under he SPC s decreasng as orders moves upsream n he supply chan. Ths can also be explaned by he sage varance amplfcaon ha has a value lower han one a all echelons whch means ha each echelon s acng as a fler for he ncomng order from he preceden echelon. However, he order-up-o s workng as an amplfer as he sage varance amplfcaon has a value hgher han one a all echelons. The major reducon n he bullwhp effec has been acheved a he facory whch places orders wh a varably less han 0.63 of he cusomer demand varably. Boh orderng polces sablze a he same average orderng level wh a very lle dfference beween hem. I can be concluded ha applyng he SPC polcy mgh allow he upsream echelons o save capacy and oher operaonal coss as hey receve balanced orders wh very low varably. B. Invenory Behavor The nvenory behavor s a bg ssue for he local decson makers n he supply chan as hey wan o have a hgh servce level whou keepng a large safey sock. The resuls n Table III show ha boh orderng polces are successful o sablze a he same average nvenory level whle achevng he same average servce level hroughou he supply chan. However, he SPC has acheved a beer performance n erms of he nvenory varance rao han he order-up-o especally a he upsream echelons; wholesaler, dsrbuor, and facory. The realer has acheved a hgher nvenory varance rao under he SPC han when order-up-o s appled. Ths can be arbued o he hgh level of smoohng of orders placed by he realer whls recevng demand of hgher varance o some exen. Ths suaon could be alered by reducng he wdh of he safey zone on he demand ISSN : 0975-404 Vol 6 No Feb-Mar 04 43
Francesco Cosanno e al. / Inernaonal Journal of Engneerng and Technology (IJET) conrol char,.e., decreasng he value of K, o make he SPC polcy more sensve o demand/ncomng order changes. However, hs acon s no mporan because hs hgher nvenory varance rao does no have a sgnfcan mpac on he average servce level a he realer where he realer was able o sasfy 00% of he cusomer demand mmedaely. TABLE III Invenory Behavor a All Echelons n he Supply Chan Under Order-Up-To and SPC Polces Performance Measure Order-up-o (Before) SPC polcy (Afer) -95% Average 95% -95% Average 95% Average nvenory level emand 9.9 30.0 30. 9.9 9.9 30.0 Realer 9.9 30.0 30. 9.9 30.0 30. Wholesaler 9.9 30.0 30. 9.9 30.0 30. srbuor 9.9 30.0 30. 9.9 30.0 30. Facory 9.9 30.0 30. 9.9 30.0 30. Invenory varance rao Realer.95 3.05 3.5 3.04 3.7 3.30 Wholesaler 3.3 3.34 3.45.97 3. 3.7 srbuor 3.57 3.69 3.8.95 3. 3.9 Facory 3.96 4.0 4.5.96 3.5 3.33 Average servce level Realer 00.0 00.0 00.0 00.0 00.0 00.0 Wholesaler 00.0 00.0 00.0 00.0 00.0 00.0 srbuor 00.0 00.0 00.0 00.0 00.0 00.0 Facory 00.0 00.0 00.0 00.0 00.0 00.0 An order-up-o polcy s opmal n he sense ha mnmzes he nvenory cos (.e., expeced holdng and shorage coss). However, some auhors have been worred abou he rade-off beween bullwhp effec and nvenory varance [8] where a replenshmen rule mgh smooh he orders varably bu hs would be on he expense of nvenory varaon and servce level. Here, we nroduced a new, smple, orderng polcy ha can accoun for boh orders and nvenory varably. Ths could be a good choce by supply chan managers o conrol her orderng and nvenory sysems. V. SENSITIVITY ANALYSIS Wh usng he above smulaon sengs, we have furher nvesgaed he sensvy of he supply chan performances o he safey sock level ( k ) under boh orderng polces. The sensvy analyss resuls are summarzed n Table IV. I can be observed ha he TVA and InvR values are ncreasng as he safey sock level ncreases whaever he appled orderng polcy. However, he ncreasng rae s much hgher when he order-up-o s appled. Ths confrms he fndngs n he leraure for he order-up-o polcy [4]. Also, he SPC polcy was sable even when he safey sock level was low as we can see ha he SPC ouperforms he order-up-o n erms of average servce level when here s no safey sock (.e., k = 0 ). I can be concluded ha he SPC wll be able o elmnae he bullwhp effec a hgh levels of safey sock whls keepng a compeve nvenory performance a all echelons. However, s sll needed o do furher analyss on he mpac of he varaon of he dfferen parameers of he SPC polcy on he supply chan dynamcs. I s also worh nvesgang he performance of he proposed SPC polcy wh oher radonal orderng polces ha allow order smoohng as n [] and [8]. Ths s planned for fuure work. ISSN : 0975-404 Vol 6 No Feb-Mar 04 44
Francesco Cosanno e al. / Inernaonal Journal of Engneerng and Technology (IJET) TABLE IV The Impac of Safey Sock Varaon on Boh Orderng Polces Performance Measure Order-up-o SPC polcy k = 0 k = k = k = 3 k = 0 k = k = k = 3 TVA SVA InvR ASl Realer.07.09..5 0.76 0.78 0.80 0.8 Wholesaler.7..8.34 0.66 0.69 0.7 0.76 srbuor.8.36.47.58 0.60 0.64 0.69 0.74 Facory.4.53.69.88 0.57 0.63 0.69 0.76 Realer.07.09..5 0.76 0.78 0.80 0.8 Wholesaler.09..4.7 0.86 0.88 0.90 0.9 srbuor.0..5.7 0.9 0.94 0.96 0.98 Facory...5.9 0.95 0.98.00.0 Realer 6.6 3.05 3. 3. 6.6 3.7 3.5 3.36 Wholesaler 5.46 3.34 3.5 3.68 5.55 3. 3.9 3.47 srbuor 4.58 3.69 3.99 4.3 4.35 3. 3.36 3.66 Facory 3.74 4.0 4.55 5.5.87 3.5 3.49 3.9 Realer 80.4 00.0 00.0 00.0 8.4 00.0 00.0 00.0 Wholesaler 83.7 00.0 00.0 00.0 84.9 00.0 00.0 00.0 srbuor 87.7 00.0 00.0 00.0 89.0 00.0 00.0 00.0 Facory 9.8 00.0 00.0 00.0 94.0 00.0 00.0 00.0 VI. CONCLUSIONS Invenory conrol polces have been recognzed as a conrbuory facor o supply chan dynamcs problems such as bullwhp effec and nvenory varance amplfcaon. A lo of research has been conduced consderng he mpac of dfferen orderng polces on supply chan performances n order o provde he decson makers some nsghs on how o selec he approprae polcy. Recenly, some auhors have appled he SPC conrol char n he area of nvenory conrol, however, hey have no evaluaed such polces n mul-echelon supply chans. In hs research, we have consdered a smlar approach and developed an nvenory conrol polcy ha reles on ndvdual conrol chars o monor and conrol boh demand and nvenory poson so ha balanced orders mgh be placed whle achevng he arge servce level whou keepng much safey sock. We adoped a smulaon approach o evaluae he proposed SPC polcy and o compare wh he radonal order-up-o polcy n a mul-echelon supply chan. The smulaon resuls showed ha he SPC ouperforms he order-up-o polcy n erms of bullwhp effec, nvenory varance rao and average servce level. The SPC was generally able o elmnae he bullwhp effec whou hurng he nvenory performance a any of he supply chan echelons. The asonshng performance of he SPC n erms of bullwhp and nvenory varance would movae supply chan mangers o selec for he operaon of her nvenory sysems. However, furher analyss should be done o nvesgae he sensvy of he SPC o oher demand paerns wh auocorrelaon and seasonaly componens. Also, furher analyss should be done o compare he proposed SPC polcy o oher orderng polces ha allow order smoohng. ISSN : 0975-404 Vol 6 No Feb-Mar 04 45
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