Proceedings of the 2017 Winter Simulation Conference W. K. V. Chan, A. D'Ambrogio, G. Zacharewicz, N. Mustafee, G. Wainer, and E. Page, eds.

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1 Proceedgs of the 2017 Wter Smulato Coferece W. K. V. Cha, A. D'Ambrogo, G. Zacharewcz, N. Mustafee, G. Waer, ad E. Page, eds. A STUDY OF REMANUFACTURING SYSTEM IN PRESENCE OF UNRELIABLE SUPPLY OF NEW PRODUCTS Suma Nraja College of Busess Admstrato Savaah State Uversty 3219 College St. Savaah, GA 31404, USA ABSTRACT We aalyze a two-echelo remaufacturg system whch utlzes a mx of ew compoets as well as remaufactured old compoets to produce a ew product. We fd the optmal mx of ew ad old compoets that mmzes vetory ad overall costs of the system for a fxed servce level. Addtoally, ths system s vestgated assumg urelable supplers for ew compoets. The system performace s aalyzed usg a seres of dyamc equatos that s developed to descrbe the system. A smulato-based optmzato approach s used to aalyze varous scearos as the demad ad capacty uder cosderato s stochastc ature. ARENA ad OptQuest s used for updatg the equatos ad optmzg the system, respectvely. Several cases cosdered for computatoal evaluato order to uderstad the mpacts. 1 INTRODUCTION Closed Loop Supply Cha (CLSC) has garered a great deal of terest over last two decades. Remaufacturg forms a small porto of CLSC, ad t s sometmes also referred to as reverse logstcs. CLSC ad reverse logstcs have bee studed by may corporate compaes as well as academa over the course of the last two decades. CLSC focuses o several busess models such as refurbshg, reusg, remaufacturg, recyclg, upcyclg, dowcyclg, etc., depedg o the ature of the product ad ts specfc use to the market. I the case of remaufacturg, the products after ther ed-of-useful lfe s ether retured by the customers, or collected by certa compaes, whch evetually get to the orgal maufacturer or a orgal equpmet maufacturer (OEM). Ay such product s the checked for ts fuctoalty, whe a partcular compoet (or compoets) from the used product s extracted ad used ether as a spare part or tegrated to a ew product, whch sometmes ca be sold as a ew product or refurbshed product. Remaufacturg has a massve facal prospect. Accordg to a report from the Europea Commsso - Europea Remaufacturg Network, the curret remaufacturg market Europe aloe s close to 30 bllo ad s expected to reach a aual value of 70b to 100b wth the drect ad drect employmet reachg 600,000. I the Uted States, accordg to a USITC (Uted States Iteratoal Trade Commsso) report 2012, the remaufacturg has a market to $43 bllo. I addto, coformg to a recet report from KPMG Ic., 90-95% of all automoble starters ad alterators the U.S. are sold as replacemets ad remaufactured. U.S. Auto Parts Remaufacture Assocato estmates that remaufactured parts form a $36 bllo market. Globally, customers buy ad retur $642.6 bllo of goods aually (KPMG Iteratoal 2017). Ths mauscrpt focuses o the products retured pror to ther useful lfe completo. For example, out of may possble stuatos, a couple of them could be: () the product s retured before ts useful lfe fshes, ad compoets of that product s used makg a ew product, ad () the product useful lfe has completed, but few compoets the product /17/$ IEEE 3459

2 Nraja have useful lfe beyod the product tself, ad these compoets ca be used makg a ew product (Gude ad Va Wassehove 2009). Nke reuses ad recycles 100% of ts materal that s retured through ther program to make sports surfaces. Xerox, CAT Rema (Caterpllar Ic.), ad Joh Deere Corporatos are utlzg remaufacturg programs (Kerr ad Raya 2001). Xerox has always collected ts compoets sce 1960 s, but the remaufacturg ut tured proftable oly 1980 s. The products retured are spected, ad compoets from these products are extracted ad used makg ew products, or sold as spare parts. CAT Rema also works smlar to Xerox, where the equpmet s brought back to lfe after the ed of lease-term or edof-product lfe cycle, sometmes oly certa compoets ca be brought back to orgal codto, these compoets are used ew products. IBM s also has a smlar model of busess through ther server lease program where more tha 35% of compoets that go to makg a IBM s ew product cotas hardware extracted at ed-of-lfe products (Fleschma, Va Nue, ad Gräve 2001). More tha 80% of the moble phoes the Uted States are upgraded after ther two-year perod although the useful lfe exteds far beyod that, ad ths s also a perfect stuato for remaufacturg/recyclg. Workg compoets of a used cell phoe or ed-of-lfe cell phoe ca be substtuted for ew compoets ew moble phoe maufacturg or other electroc devces. Although several examples of CLSC descrbed earler, the prmary motvato of ths research s Kodak s sgle-use camera, where leses are reused. The mportat research questos that arses from compoet reuse are: () optmal vetory levels for reused ad ew compoets for a gve servce level, () mpact o total cost whe shortage to reused or ew compoets occurs resultg last mute chages to orders, ad () ucertaty ew ad reused compoets supply mpact the total cost. If a frm decdes to use hgher proportos of ew compoets or remaufactured compoets to satsfy ed-product demad, t may ot ecessarly be effcet. Thus, strkg a balace betwee the two s mportat. Supplers of a ew compoet are assumed to be urelable ths research. Supply msmaagemet has severe mpact o a frm s facal performace, ad t s crtcal for a compay to have relable supply. O average, a frm speds 55% of the eared come o procurg materals (Leeders ad Fearso 1998), whch suggests that supply dsruptos have a tremedous mpact o the frm s facal performace. Hedrcks ad Sghal (2003) show that a frm sufferg wth gltches from supplers typcally experece about 12 % reducto shareholders retur, further Hedrcks ad Sghal (2005) show that frms sufferg from dsrupto problems have a egatve mpact o ther stock prce. There are three key decsos a frm has to make for sourcg materal (Burke, Carrllo, ad Vakhara 2007): ) lst of crtera for selectg a suppler, ) selectg supplers from the lst for order placemet, ) order quattes to be placed from each of the selected supplers. I our paper, we assume that the frst two steps have bee already take care by the frm ad we focus o the last step. If a suppler s urelable, havg a depedece o sgle-suppler has a greater rsk of terrupto (Burke, Carrllo, ad Vakhara. 2007). Operatoally, multple-supplers provde greater flexblty, creased chaces of tmely delvery, ad fewer dsruptos. Two supplers are cosdered ths research uder varyg relablty codtos. Ketzeberg, Wee, ad Yag (2006) study a sgle-echelo model ad determe the producto amout of ew product, where both recovered product ad ew product s sold. The model does ot cosder capactated producto evromet or ether t cosders yeld loss recovery as ths research. Ketzeberg (2009) study the value of formato whe demad, product returs, capacty utlzato, ad recovery yeld are stochastc ature. Ketzeberg (2009) determe the quatty of ew product to produce, product retur quatty that gets dsposed of, ad recover quatty. The aforemetoed problem s ot mult-echelo, does ot cosder lead-tme, ad supplers ae ot ucerta. Chug, Wee, ad Yag (2008) cosder a mult-echelo vetory system wth remaufacturg capacty usg smulatooptmzato approach. The authors develop a closed loop supply cha vetory model whch results optmzg the profts for the maufacturer, suppler ad recycle dealer. The model cosdered by Chug, Wee, ad Yag (2008) s smlar to ths research, but does ot volve the supply ucertaty/dsruptos cosdered the preset model. A follow-up research s coducted by Yua ad Gao (2010) where a 3460

3 Nraja closed-loop supply cha (CLSC) system s vestgated usg smulato optmzato approach. Where authors report f oe or more cycles of maufacturg followed by oe or more cycles of remaufacturg ca be performed to mmze the overall cost ad maxmze the profts ad fd that t s very much sestve to retur rates, based o the retur rate polcy s determed. Yua et al. (2015) exted the prevous research by cosderg varous CLSC system proft-maxmzato models usg (1, R) ad (P, 1) polces by elmato theory, ad deduce several maageral sghts. A recet artcle publshed by Govda et al. (2015) provde a comprehesve revew of reverse-logstcs ad CLSC. The artcle ctes gaps the lterature, ad amog the gaps preseted, oe of the gaps CSLC lterature s related to the study of CLSC uder ucerta supply codtos. The bref lterature descrbed earler focuses o several aspects of demad, capacty ad vetory polces, but does ot focus o supply ucertaty ad dsruptos whch s oe of the prmary focus of ths research. Ths study ams to fll the gap wth advace research the area of ucerta supples for ew product cojucto wth remaufactured product. A two-echelo remaufacturg system wth a sgle ed product, dual compoet sourcg, ad fte horzo (multple perods), fxed lead-tme s cosdered ths research. The supply source s aalyzed uder relable ad urelable scearos. Suppler delvers less tha the requred quatty wth a certa probablty, specfcally these ew compoets are used the assembly of a ew product. The compoet ca be ether a ew compoet or remaufactured. The remaufactured part s assumed a perfect substtute for the ew product. The demad for the fal fshed product s stochastc, each echelo the supplycha has stochastc supply, betwee the odes lead tme s fxed, the arrvals of the remaufactured product are stochastc ature ad follow a probablty dstrbuto. The two-echelo system utlzes a base-stock polcy. A fracto of the ed-products s assumed to be retured as remaufactured product. Due to may stochastc parameters, t s dffcult to have a tractable closed form soluto, so we use smulato as a meas to get a ear-optmal soluto. A smulato-based optmzato approach s used to aalyze the performace of the system, specfcally usg OptQuest (optmzato tool provded by ARENA). A desg of expermets cosstg of aforemetoed varables wll be utlzed to coduct computatoal expermets. The computatoal expermets wll acheve the followg: ) ear optmal total cost of the supply cha uder dfferet scearos, ad ) optmal order-up-to level ad safety-stock for the remaufactured ad ew compoets uder a gve servce level. The paper s orgazed as follows, secto 2 we troduce the model, secto 3 we descrbe the proposed umercal aalyss, secto 4 prelmary results are dscussed, ad coclude secto 5. 2 MODEL Fgure 1 demostrates the represetato of the two-echelo remaufacturg system. Node 2 s where remaufacturg takes place, whch s assumed to acqure returs from varous sources. Returs are processed as a fucto of the fal fshed product. A yeld s related wth ode 2, we expect that ot all tems that are retured are effectvely usable, because of two reasos ) compoets are ot always usable, as they are sometmes damaged, ) remaufacturg cost exceeds the cost of utlzg the compoet the fal product. The warehouse s represeted by ode 1, whch holds the ew ad remaufactured compoets, whch are the suppled to ode 0 for assembly. The ew compoets are acqured from two supplers, the ature of the supply s stochastc ad urelable. Node 0 fabrcates the last tem, each fal product corporates oe basc part whch ca ether be the remaufactured from ode 2 or ew compoet acqured from ode 1. A determstc lead tme exsts betwee ode 2-ode 1, ode 1-ode 0, the lead tme ca be assumed as lead tme for orderg or assemblg. The cost at whch the ew compoet ca be procured from the two supplers chages dyamcally each perod. To descrbe the operatos through the rest of the paper the followg otatos are used: 3461

4 Nraja Suppler 2 Suppler 1 Node 1 Node 0 Fal Product Node 2 Remaufactured Product Yeld Returs are a fucto of Fal product Fgure 1: Two-echelo remaufacturg system. j c s : Capacty realzed perod at stage : Demad perod for Product j : Ut cost of tem : Target stock (order up to or base-stock) level for tem : Shortages of orders perod for tem for whch the delvery has ot bee made IL : Ivetory level perod for tem pror to demad beg realzed : Physcal (O-had) vetory level perod for tem pror to demad beg realzed : Shortage dowstream perod at ode Y I DS INU : Ital ew uts perod IRU ENU : Ital recycled uts perod : Excess ew uts perod : Excess recycled uts perod : Fracto of demad comg from the recycled products : Requred servce level (type-i) at ode ERU : Remaufacturg yeld perod (represets a porto of retured products whch are uusable) : Arrval rate perod r : Proposto of ew compoet order to suppler 1 AUD: average uts dsposed due to maufacturg yeld 2.1 Operatos ad Assumptos of System The system cosdered ths research operates uder a perodc base-stock polcy. Ivetory posto s computed as: orders + o-had vetory backorders, as the vetory level falls below the base-stock level, a order s placed to brg the vetory to target stock level. The orders that are ot fulflled are backordered. The expected value of demad s assumed to be lower tha capacty: E E. The capacty costrat s oly preset for ode 0. Oly a fracto ( ) of the demad for compoets s cosdered as returg products. The objectve fucto (1) drectly pealzes holdg more vetory at each locato, as hgher dcates more vetory of tem. Node 1 correspods to the warehouse whch cotas both, ew ad remaufactured compoets. Two super-scrpt otatos for ode 1 are cosdered, whch correspod to 1 ad 1s for ew ad remaufactured compoets respectvely. The volume of remaufactured product dstrbuted from ode 1 to ode 0 correspods to Ital Recycled Uts IRU a specfc perod. IRU ca be further defed as: mmum remaufactured compoets avalable or remaufactured compoets demad a gve perod. ENU s the amout of ew compoets perod whe proporto of demad from remaufactured compoets s ot met. Ital New Uts INU correspods to the amout of ew compoets that s s 3462

5 ERU Nraja suppled from ode 1 to ode 0 perod. (excess remaufactured uts perod ) s the amout of remaufactured product whe proporto of demad from ew compoets s ot met. The cost of the ew compoets suppled by two of the supplers chages dyamcally each perod. The lower cost suppler s selected to receve the majorty of the demad. The two-echelo problem formulato s stated below: m * ENU * ERU * dsp c s ENU c ERU c AUD c s 0 (1) s. t. P IL 0,where 2,1 s,1,0 The objectve fucto s a smple lear equato; the costrats are olear ature. The costs are beg mmzed the objectve fucto, subject to a certa amout of predetermed servce level acheved at every ode. The objectve fucto drectly flueces the holdg cost as greater the basestock level mples hgher overall holdg cost. The costrats are formulated o the bass of a type-i servce level., ad ERU are the average extra ew ad remaufactured uts, the values represet ENU the average over the several perods used smulato. ad s the cost for extra ew uts ad extra remaufactured uts respectvely. The average uts dsposed (AUD) s the average of the umber of uts dsposed every perod durg the remaufacturg process due to some kd of defect the crtcal compoet whch caot be fxed. s the cost of dsposg the retured products, ths s multpled to AUD, whch results the total cost of dsposed products. The outstadg order equatos for ode 2, 1, 1s ad 0 s descrbed equatos (2) to (5), the outstadg orders for 1 ad 1s do ot have capacty costrat, capacty for the warehouse (ode 1) s assumed to have o lmt. The outstadg orders for ode 0 are show below equato (2). 0 1s 1 1s 1 Y 0 0, S S Y 2 Y 2 1 Y 1 Y m (2) 0s 0 0 DS 1 DS 1 ERU ENU, The outstadg orders equato (2) s ether zero, or lmted by the avalable crtcal compoet 0s 0 from ode 1, or could be determed by the ode 0 capacty. Where DS 1 ad DS 1 represet dowstream shortage for remaufactured ad ew compoets. Dowstream shortages at ode 0 occur due to suffcet maufacturg capacty, spte of the ablty of ode 0 to supply the complete requremet to ode 1. We assume ether the excess compoets whch caot be used at ode 0 are set back to ode 1, or does ot get shpped to ode 0 at all Y 1 Y * m Y *, 1 * r * (3) c dsp c ENU c 0 ERU The outstadg orders for ode 2 s show equato (3). The outstadg orders ca be zero, or ca be further costraed by the combato of arrvals ad yeld for the remaufactured compoet 1 * r *. I certa umercal cases we cosder o yeld, whe there s o yeld, ad those stuatos are equal to zero. The equatos for ode 1, depedg o two dfferet codtos s defed as follows: () IRP * ; INP 1 *, () IRP INP. Further uder codto () we have three cases based o where the shortage exsts (.e., due to remaufactured compoets, or ew compoets), ad check f we ca substtute t from aother source where shortage dd ot occur: Case 1: shortage occurred due to remaufactured compoets, ad excess ew compoets avalable, Case 2:- shortage occurred due to ew compoets, ad excess remaufactured compoets avalable, ad Case 3:- shortage occurred due to both remaufactured ad ew compoets. Let us tally cosder codto (), equatos (4) ad (5) represet the outstadg orders for remaufactured compoet as well as ew compoet uder the frst codto. We are ether able to satsfy 3463

6 Nraja the requred compoets for the curret perod (zero outstadg orders) or costraed by the amout of tal product for remaufactured or ew compoet. 1s 1s 0s 1s 0s Y 1 Y * DS m Y * DS, IRP (4) where IRP R m S, * Y 1 Y (1 )* DS m Y (1 )* DS, INP (5) N ; INP m S, 1 *. R S s the amout of supply for R 2 remaufactured compoet from ode 2, we ca mathematcally represet where ERI equato (16) descrbes S 1 * I ERI, s defed as excess recycled vetory, whch s a result of uused recycled uts ode 2, ERI. N S s the amout of ew compoet from the two supplers. amout of ew compoet from the two supplers, the mathematcal equatos for N S N S s the are descrbed the ext sub-secto. For codto (), case 1 the outstadg orders for ew ad remaufactured compoet ca be descrbed as (6) ad (7). There are two sub-cases uder case 1: ) whe the excess ew compoets wll oly be able to satsfy a porto of the defct demad IRP INP a gve perod, equato 6 shows the outstadg order for the remaufactured compoet uder the frst sub-case, ) whe the excess ew compoets wll completely able to satsfy the defct demad, equato (7) shows the outstadg orders for the remaufactured compoet uder the secod sub-case. The outstadg order for the ew compoet uder both the sub-case wll be same as descrbed equato 5. 1s 0s *, 1s 1s 0s Y DS Y 1 Y * DS m N (6) IRP IRP INP S 1 * 1s 1s 0s 1s 0s Y 1 Y * DS m Y * DS, IRP IRP INP (7) For codto (), case 2 the outstadg orders for ew ad remaufactured compoet ca be descrbed as (8) ad (9). We have two sub-cases uder case 2: ) whe the excess remaufactured compoets wll oly be able to satsfy a porto of the defct demad a gve perod. Equato 8 shows the outstadg order for the ew compoet uder the frst sub-case, ) whe the excess remaufactured compoets wll completely be able to satsfy the defct demad, equato (9) shows the outstadg orders for the ew compoet uder the secod sub-case. The outstadg order for the remaufactured compoet uder both the sub-case wll be same as descrbed equato (4). 1 0 (1 )*, Y DS Y 1 Y (1 )* DS m R (8) INP IRP INP S * Y 1 Y (1 )* DS m Y (1 )* DS, INP IRP INP (9) For codto (), case 3 the outstadg orders for ew ad remaufactured compoets rema the same as descrbed (4) ad (5). The vetory level for Node 0, 2, 1s ad 1 are descrbed equatos(10) to (14) respectvely; the subscrpt to the demad (l) represets l perods of lead tme: IL S Y ERU ENU (10) l l... *... * 1 IL S Y * (11) l l IL S Y DS (12) 1 s 1 s 1 s 0 s l 1 2 l 1 IL S Y DS (13) l 1 2 l

7 Nraja The o-had vetory for ode 0, 2, 1, ad 1s are gve as I max 0, IL ; I 0 0 max 0, IL ; 2 2 1s 1s 1 1 I max 0, IL ; I max 0, IL respectvely. The vetory level equato for ode 0 has the outstadg orders for ode 0 that were ot satsfed perod, the demad for perod s -1 to (whch dcate the demad durg the lead tme), subtracted from the base-stock level of ode 0, whereas the excess recycled ad ew uts are added to the vetory l l level. Smlarly the vetory level of ode 2 has the outstadg orders for ode 2 perod ad the demad that s due to the remaufactured product (the actual fal product demad multpled by the fracto of demad due to remaufactured product) subtracted from the base-stock level for ode 2. Equato (12) ad (13) also follow smlar structure, except that both the odes have dowstream shortages added to ther equato whch s explaed below. Dowstream shortages: l s 0 0 DS 0 1 max 0, 1 1 ; DS 1 d 1 * DS 1; DS 1 1 d 1 * DS 1 (14) The dowstream shortage s the shortages that are caused as a result of suffcet capacty at the dowstream ode, the oly ode wth a capacty costrat s ode 0. We assume that the shortage at the dowstream ode 0 due to costraed capacty are ether ever shpped to the dowstream ode or retured back due to suffcet capacty. The uts are set back from ode 0 to the warehouse or ode 1 wll have 0s 0 uts from both the remaufacturg ad ew compoets (represeted as DS 1 & DS 1 respectvely), ad they have to be splt approprately accordg to the proporto of remaufactured ad ew compoets used a gve perod. Ths rato (d) s expressed equato (15). IRU 1 ERU 1 d 1 (15) INU ENU IRU ERU The equato for excess recycled vetory s descrbed (16). The Excess Recycled Ivetory (ERI) whe added to the o-had vetory for ode 2, wll result the upper lmt o the supply for the recycled uts. It s possble that ode 2 ca have more recycled uts avalable tha actually requred to satsfy ts porto of demad. Ths depeds o the rate of retur ad the yeld at ode 2, f the rate of retur s so hgh that eve after the yeld ad demad a gve perod are accouted, f there are uts stll remag, ths could be used to satsfy shortages due to a ew product. If ode 2 has excess uts, t ca be used to satsfy the fal product demad whe there s a suffcet supply for the ew compoets, but at a cost hgher tha the regular recycled products. Y 2, * r * ERI max 0, 1 * r * Y * max 0, ERI ERU (16) * equato 16 represets the actual requremet of recycled product at ode 2 perod of whch wll be used to satsfy the actual requremet at ode 2. The secod part of equato (16) represets the excess uts that were uused the prevous perod, ether because the demad was satsfed wth the tal ew ad recycled product, or there was more tha requred excess recycled uts that were used to satsfy the demad of the crtcal compoet the fal product assembly at ode 0. A postve value of ERI represets that there s a uused porto of the recycled uts whch ca ow be used to satsfy f a 2 represets the total recycled products that wll be avalable perod, Y * shortage occurs the ew product supply future perods. Equato (17) below represets AUD. The average uts dsposed are obtaed by averagg umber of uts dsposed each perod, the umerator of equato (17) shows the umber of uts dsposed each perod. 3465

8 Nraja AUD perods * r * (17) 2.2 New Compoet Supply A porto of the demad for the fal product has to be satsfed va ew compoet procuremet from the supplers for ew product. Two ew compoet supplers s assumed, ad the total amout of supply for the ew product depeds o the two factors, the proporto of demad for ew product the curret perod, ad the outstadg orders for the ew product (f ay). We assume that for each suppler the frm does ot 1 have exact formato o the cost per ut c utl the begg of the perod, but has the formato about approxmate rage of cost for the ew product before the start of the perod. Depedg o the cost of the ew product a gve perod the frm decdes whch suppler wll receve a larger order amog the two. We assume that qualty of the ew compoet suppled by both the supplers s same, ad the cost s the oly factor that would decde whch suppler receves a larger order, a suppler wth lower cost receves a hgher proporto of the ew compoets order. Moreover, we also assume that the supplers are completely urelable, ad we model the urelablty the suppler usg two models ) all-or-othg supply, ad ) supply yeld. I a all-or-othg supply the frm receves the etre supply or receves othg a gve perod, whereas a supply yeld, the suppler mght be uable to satsfy the etre order ad certa amout of yeld assocated wth the order. The supply of ew compoets from suppler 1 ad 2 uder all-or-othg supply s gve as show equato (18) ad (19). Supply from suppler 1 Max Order 1, Normal Order 1, CV * Order 1 * (18) 1 Supply from suppler 2 Max Order 2, Normal Order 2, CV * Order 2 * (19) 2 I equato (18) ad (19) order 1 ad order 2 correspod to the amout of order that s placed wth suppler 1 ad suppler 2 respectvely. The all-or-othg supply modeled by the use of radom varable, 0,1 whch ca take up a radom value equal to zero or oe. We also assume that approxmately % of the tme whe the suppler supples everythg, the suppler has more ew compoets tha the requred order, although the excess uts are used oly whe a eed arses (shortage due to recycled compoets), ad at a addtoal cost per ut. I order to model ths assumpto, a ormal dstrbuto wth a mea equal to the suppler order, ad a stadard devato defed by the CV (coeffcet of varato) s used. The term Max equatos (18) ad (19) esures that oly the values greater tha mea (order 1 or order 2) are used, sce ths s a all-or-othg we caot have quatty less tha the order. Equato (20) descrbes order 1 ad 2, where s fracto (value betwee 0 ad 1) depedet o the supplers cost for the ew compoet, f suppler 1 quotes a lower prce, the a hgher value of s used. 1 1 Order 1 1 * Y * ; Order 2 1 * Y * 1 (20) The supply of ew compoets from suppler 1 ad 2 uder supply yeld s gve as show equato, uform a, b where the value of a ad b s a value betwee 0 ad 1. (21) ad (22). The value of 1 2 1, * Orde 1 1 2, * 2 * 2 Supply from suppler 1 Normal Order CV r * (21) Supply from suppler 2 Normal Order CV Order (22) 3 SIMULATION AND COMPUTATIONAL SET-UP ARENA, a dscrete-evet smulato tool s used to update the dyamc equatos o a perodc bass. The objectve fucto ad the costrats are defed OptQuest (optmzato ege part of ARENA), alog wth all the decso varables defed OptQuest. Lower ad upper boud values of all the decso 3466

9 Nraja varables are defed OptQuest. A umercal aalyss wth three-perod fxed lead tme s assumed betwee the echelos. The values for capacty ad demad are based o a ormal dstrbuto (Carallo, Akella, ad Morto 1994; Bollapragada, Rao, ad Zhag 2004; Nraja ad Carallo 2011; Nraja ad Carallo 2014). Node 2 ad 0 s defed 90% servce level. A desg of expermets wth varyg coeffcet of varablty of demad, capacty, costs of remaufactured compoets, cost of ew compoets, dyamc prcg, ad beta wll be cosdered to fd the optmal vetory level uder each scearo. Ths secto brefly dscusses set-up for umercal results, smulato, varous cases used aalyss, ad valdato based o the results. As metoed earler, we use ARENA as a tool to update the equatos every perod. Each perod the followg sequece of actvtes occur: ) the outstadg orders are updated (.e., shortages), ) o-had vetory s updated (.e., the actual physcal vetory), ) demad s realzed, ad v) capacty s realzed. The smulato software s used to smply update the equatos every perod the aforemetoed sequece. The lower ad upper boud values of base-stock levels (decso varables) are defed OptQuest. Each smulato ru starts wth a radomly selected base-stock value selected by OptQuest based o the upper ad lower lmt values selected. The smulato s ru for a mmum of 500 perods (selected based o observato) or utl o further mprovemet (based o the tolerace value setup ARENA) the objectve value s foud, whchever arrves later. The best base-stock values for the odes are determed f o mprovemet the objectve fucto s foud (total cost) after meetg all the servce level costrats. Fgure 2 provdes the detals o how smulato s coducted. The followg base values/assumptos are used for umercal computato: () a three-perod orderg/maufacturg/supply lead tme s assumed, () the values of demad yeld ad capacty are ormally dstrbuted, () Node 0 ad 2 uses a servce level of 90%, ad (v) remaufactured compoet cost < ERU cost < ew compoet cost < ENU cost. For the umercal aalyss we cosder the followg desg of expermets: 4 staces x 3 varyg values of yeld probablty x 3 varyg values of fracto of demad comg from recycles products x 2 cost values of ERU x 2 cost values of ENU x 2 cost values of remaufactured compoets x 2 cost values of ew compoet, a total of 576 uque smulato rus are cosdered for the tal aalyss. Table 1 lsts all the cosdered staces, capacty deoted as average mples a utlzato betwee 65% ad 75%, whereas a tght capacty would mply utlzato betwee 85% ad 95%. The average demad value s 21 uts. If the demad ad capacty CV s 0.2 t s defed as low varablty, 0.4 CV s cosdered as hgh varablty. The capacty utlzato determes the average capacty, based o the fxed demad value. We cosder that both the supplers are all-or-othg, whch meas they would ether supply everythg or othg. 4 VALIDATION-VERIFICATION AND RESULTS As a part of ogog research, we were able to ru several smulato rus but have ot completed the 576 uque scearos. For all the results dscussed, a cost of 1 per ut s assumed, we also assume cost of dsposal as 0.25, cost of remaufacturg s 1, cost of ERU ad ENU same at 1.5. The results that we preset here suffcetly valdate ad verfy the model. We use basc vetory theory prcples to valdate ad verfy the model. For stace whe all varables are fxed ad the CV for demad chages we should be able to see the overall cost go up, ad safety-stock go up as well, smlarly as the capacty utlzato crease the overall cost should go up as a result of optmal stock level o each ode go up as well. The prelmary results are provded Table 2. Table 2 provdes results o the bass of the followg parameters: Table 2 ca also be cosdered as the base stuato. For the radom value of demad ad capacty the followg s cosdered uder four staces dscussed table 1: () average yeld of 10% wth a CV value as 0.2, () average yeld of 25% wth a CV as 0.4, () average yeld of 10% wth a CV value as 0.4, (v) average yeld of 25% wth CV as 0.2. Based o the results table 2 we ca observe that as the CV creases the yeld uder each stace we see a crease average safety stock as well as total cost crease. Addtoally, we also see as the yeld creases uder a gve stace, we fd a crease safety stock as well as total cost. Also across 3467

10 Nraja staces uder a gve colum we see a crease safety stock ad overall cost, whch clearly dcates that hgh varace results hgher safety-stock ad creased overall total cost. Fgure 2: Smulato ARENA wth the OptQuest Framework. Table 1: Istaces for two-echelo system. Istace # Name of stace CV for CV for Capacty Demad 1 Average Capacty (AC) Tght Capacty Hgh Demad Varace wth Average Capacty (HDVAC) Hgh Demad Varace wth Tght Capacty (HDVTC) Addtoal aalyss was coducted wth stuato 1-zero yeld, stuato 2-80% of the ew compoet demad s satsfed from suppler 1 ad rest from suppler 2 (we assume urelable suppler 2 resultg lower proporto of demad ), stuato 3-60% of the ew compoet demad s satsfed from suppler 1 ad rest from suppler 2 we assume urelable suppler 2 resultg lower proporto of demad), stuato 4-Both the supplers are urelable as a result we have a all-or-othg stuato for demad wth a 50% chace of demad beg satsfed fully or uable to satsfy ay. Table 3 has these results. The zero yeld stuato has demad splt evely betwee the two supplers ad cosdered to be relable. Stuato 2-4 have at least oe suppler urelable wth zero yelds for the remaufactured product. Table 3 offers a terestg sght to the problem as the results were ot as expected. We ca observe from the table 3 that uder stace 1 ad 2, whch s low varablty, we fd stuato 4 (urelable supplers) has a average total cost lower tha stuato 2 ad 3. Ths ca be attrbuted to the low varablty ad lower capacty utlzato whch dd ot have much mpact o the urelable supplers. Addtoally, the average probablty of 50% of the tme whe the orders are ot fulflled seems to also be aother reaso. 3468

11 Nraja Whereas stace 3 ad 4, we do ot see ay couter-tutve results, ad the results show that the smulato has vald results. Table 2: Prelmary results for two-echelo system. 0.1 Yeld 0.25 Yeld 0.1 Yeld 0.25 Yeld 0.2 CV 0.2 CV 0.4 CV 0.4 CV INSTANCE 1 Average Safety Stock (SS) Average Total Cost (TC) INSTANCE 2 Average SS Average TC INSTANCE 3 Average SS Average TC INSTANCE 4 Average SS Average TC Table 3: Specal stuatos. Stuato 2 Stuato 3 Stuato 4 Stuato 1 - Zero Yeld INSTANCE 1 Average Safety Stock Average Total Cost INSTANCE 2 Average SS Average TC INSTANCE 3 Average SS Average TC INSTANCE 4 Average SS Average TC ONGOING RESEARCH AND CONCLUSION I ths paper, we developed dyamc equatos for a two stage remaufacturg system the presece of urelable supplers for ew compoets. Ital valdato ad verfcato based o umercal aalyss have bee coducted. Curretly, umercal aalyss s beg coducted for 500 plus uque smulato scearos wth maageral fereces that wll be deduced from the results. 3469

12 Nraja REFERENCES Bollapragada, R., U. S. Rao, ad J. Zhag Maagg Ivetory ad Supply Performace Assembly Systems wth Radom Supply Capacty ad Demad. Maagemet Scece 50: Burke, G. J., J. E. Carrllo, ad A. J. Vakhara, Sgle Versus Multple Suppler Sourcg Strateges. Europea Joural of Operatoal Research 182: Carallo, F. W., R. Akella, ad T. E.Morto A Perodc Revew, Producto Plag Model wth Ucerta Capacty ad Ucerta Demad Optmalty of Exteded Myopc Polces. Maagemet Scece 40: Chug, S. L., H. M. Wee, ad P. C. Yag Optmal Polcy for a Closed-Loop Supply Cha Ivetory System wth Remaufacturg. Mathematcal ad Computer Modellg 48: Fleschma, M., J. Va Nue, ad B. Gräve Itegratg Closed-loop Supply Chas ad Spare- Parts Maagemet at IBM. Iterfaces 33: Govda, K., H. Solema, ad D. Kaa Reverse Logstcs ad Closed-Loop Supply Cha: A Comprehesve Revew to Explore the Future. Europea Joural of Operatoal Research 240: Gude, V. D. R., ad L. N. Va Wassehove The Evoluto of Closed-Loop Supply Cha Research. Operatos Research 57: Hedrcks, K. B., ad V. R. Sghal "The Effect of Supply Cha Gltches o Shareholder Wealth." Joural of Operatos Maagemet 21: Hedrcks, K. B., ad V. R. Sghal "Assocato Betwee Supply Cha Gltches ad Operatg Performace." Maagemet Scece 51: Ketzeberg, M. E., E. Laa, ad R. H. Teuter Value of Iformato Closed Loop Supply Chas. Producto ad Operatos Maagemet 15: Kerr, W., ad C. Rya Eco-effcecy Gas from Remaufacturg a Case Study of Photocoper Remaufacturg at Fuj Xerox Australa. Joural of Cleaer Producto KPMG Iteratoal. (2017, March). Future-Proof your Reverse Logstcs. Retreved Jue 29, 2017, from Kumar, S., ad P. Malegeat Strategc Allace a Closed-loop Supply Cha, a Case of Maufacturer ad Eco-No-Proft Orgazato. Techovato Nraja, S., ad F. W. Carallo. (2011). Supply Performace Mult Echelo Ivetory Systems wth Itermedate Product Demad: A Perspectve o Allocato. Decso Sceces 42: Nraja, S., ad F. W. Carallo Impact of Ivetory Allocato Polces o Dowstream Supply Varablty a Two-Echelo System. Iteratoal Joural of Busess Performace ad Supply Cha Modellg 5: Yua, K. F., ad Y. Gao Ivetory Decso-Makg Models for a Closed-Loop Supply Cha System. Iteratoal Joural of Producto Research, 48: Yua, K. F., Ma, S. H., He, B., ad Gao, Y Ivetory Decso-Makg Models for a Closed-Loop Supply Cha System wth Dfferet Decso-Makg Structures. Iteratoal Joural of Producto Research, 53: AUTHOR BIOGRAPHY SUMAN NIRANJAN s a Assocate Professor of Operatos Maagemet at Savaah State Uversty, College of Busess Admstrato. He s also the drector of trasportato studes ad coordator of G- LIB program. Hs research terests clude supply cha optmzato, servce operatos maagemet, vetory cotrol, strategc maagemet, multvarate statstcal aalyss, smulato optmzato. Hs emal address s rajas@savaahstate.edu. 3470