econstor zbw

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1 econsto De Open-Access-Publkatonsseve de ZBW Lebnz-Infomatonszentum Wtschaft The Open Access Publcaton Seve of the ZBW Lebnz Infomaton Cente fo Economcs Babazadeh, Reza; Razm, Jafa; Ghods, Reza Atcle Supply chan netwok desgn poblem fo a new maket oppotunty n an agle manufactung system Jounal of Industal Engneeng Intenatonal Povded n Coopeaton wth: Islamc Azad Unvesty (IAU), Tehan Suggested Ctaton: Babazadeh, Reza; Razm, Jafa; Ghods, Reza (2012) : Supply chan netwok desgn poblem fo a new maket oppotunty n an agle manufactung system, Jounal of Industal Engneeng Intenatonal, ISSN X, SpngeOpen, Hedelbeg, Vol. 8, pp. 1-8, Ths Veson s avalable at: Nutzungsbedngungen: De ZBW äumt Ihnen als Nutzen/Nutze das unentgeltlche, äumlch unbeschänkte und zetlch auf de Daue des Schutzechts beschänkte enfache Recht en, das ausgewählte Wek m Rahmen de unte nachzulesenden vollständgen Nutzungsbedngungen zu vevelfältgen, mt denen de Nutzen/de Nutze sch duch de este Nutzung envestanden eklät. Tems of use: The ZBW gants you, the use, the non-exclusve ght to use the selected wok fee of chage, tetoally unestcted and wthn the tme lmt of the tem of the popety ghts accodng to the tems specfed at By the fst use of the selected wok the use agees and declaes to comply wth these tems of use. zbw Lebnz-Infomatonszentum Wtschaft Lebnz Infomaton Cente fo Economcs

2 Babazadeh et al. Jounal of Industal Engneeng Intenatonal 2012, 8:19 ORIGINAL RESEARCH Supply chan netwok desgn poblem fo a new maket oppotunty n an agle manufactung system Reza Babazadeh, Jafa Razm * and Reza Ghods Open Access Abstact The chaactestcs of today's compettve envonment, such as the speed wth whch poducts ae desgned, manufactued, and dstbuted, and the need fo hghe esponsveness and lowe opeatonal cost, ae focng companes to seach fo nnovatve ways to do busness. The concept of agle manufactung has been poposed n esponse to these challenges fo companes. Ths pape copes wth the stategc and tactcal level decsons n agle supply chan netwok desgn. An effcent mxed-ntege lnea pogammng model that s able to consde the key chaactestcs of agle supply chan such as dect shpments, outsoucng, dffeent tanspotaton modes, dscount, allance (pocess and nfomaton ntegaton) between opened facltes, and maxmum watng tme of customes fo delvees s developed. In addton, n the poposed model, the capacty of facltes s detemned as decson vaables, whch ae often assumed to be fxed. Computatonal esults llustate that the poposed model can be appled as a powe tool n agle supply chan netwok desgn as well as n the ntegaton of stategc decsons wth tactcal decsons. Keywods: Supply chan management, Agle supply chan netwok desgn, Outsoucng, Responsveness Backgound In ecent yeas, the desgn and mplementaton of agle supply chan stateges have nceasngly attacted nteest and some companes such as Zaa and Gna Tcot have acheved many advantages by employng agle stategy. Agle supply chan ncludes companes such as supples, poducton centes, and dstbuton centes, whch ae legally sepaate but, n tems of opeatons, ae lnked togethe by fowad-flow mateals and feedback nfomaton. Agle supply chan s focused on mpovng esponsveness, speed, and flexblty that s able to espond and eact quckly and effectvely to changng makets (Ln et al. 2006). In othe wods, aglty s a tem appled to an oganzaton that has ceated the pocesses, tools, and tanng to enable t to espond quckly to custome needs and unfoeseen maket changes whle stll contollng and qualty (Chstophe et al. 2004). Tadtonal supply chans have long lead tmes * Coespondence: jazm@ut.ac. Depatment of Industal Engneeng, College of Engneeng, Unvesty of Tehan, Tehan, Ian and ae foecast-dven, whch makes these supply chans nventoy-based, whle the agle supply chan wth quck esponse has shote lead tme and s demand-dven and nfomaton-based, n contast wth tadtonal supply chans. Addtonally, whle the maket wnnng facto n agle supply chan s esponsveness and mpoved sevce level, n tadtonal supply chan, cost has been the maket wnnng facto (Mason-Jones et al. 2000). Agle supply chan pactces can be dentfed by fou factos (Hason et al. 1999): 1. Maket senstve. It s concened wth end customes n ode to be able to specfy custome needs and esponds to them as soon as possble. 2. Vtual ntegaton. It depends on nfomaton shang along the supply chan. 3. Netwok-based. It povdes flexblty by employng the stengths of specalsm n each patne wthn the supply chan; theefoe, t s ctcal to leveage the stengths and competences of patnes to ealze quck esponsveness to maket needs Babazadeh et al.; lcensee Spnge. Ths s an Open Access atcle dstbuted unde the tems of the Ceatve Commons Attbuton Lcense ( whch pemts unestcted use, dstbuton, and epoducton n any medum, povded the ognal wok s popely cted.

3 Babazadeh et al. Jounal of Industal Engneeng Intenatonal 2012, 8:19 Page 2 of 8 4. Pocess ntegaton. It s elated to a hgh level of ntegaton between patnes wthn the supply chan and enables collaboatve wokng methods such as jont poduct desgn. Theefoe, the patnes wthn the supply chan netwok wll be able to mpove a vaety of poducts and deal wth uncetanty. Supply chan netwok desgn (SCND) decsons, as the most mpotant stategc level decsons n supply chan management, ae concened wth complex nteelatonshps between vaous tes, such as supples, plants, dstbuton centes, and custome zones as well as detemnng the numbe, locaton, and capacty of facltes to meet custome needs effectvely. Supply chan management ntegates nteelatonshps between vaous enttes though ceatng allance, such as nfomaton system ntegaton and pocess ntegaton, between enttes to mpove esponse to customes n vaous aspects such as, hghe poduct vaety and qualty, lowe, and faste esponses. One of the vtal challenges fo oganzatons n today's compettve makets s the need to espond to custome needs, whch ae vey volatle and can occu n volume and n a vaety of custome needs (Am 2011). Aglty wth ts vaous contexts s the most popula stategy that enables oganzatons to confont unstable and hghly volatle custome demands. Snce the SCND s the most mpotant stategc level decson that affects the oveall pefomance of supply chan, t s necessay to consde aglty concepts such as esponse to customes n maxmum allowable tme, dect shpment, allance (nfomaton and pocess ntegaton) between enttes n dffeent echelons, dscount to acheve compettve supply chan, outsoucng, usng dffeent tanspotaton modes to acheve flexblty, and safety stock to mpove esponsveness. It s evdent that consdeng aglty concepts n SCND plays an ncedble ole n aglty of the oveall supply chan. As yet, many eseaches have ted to show the most mpotant factos n agle supply chan management theoetcally, and ths context has been omtted n the mathematcal modelng aea especally n the supply chan netwok desgn aea. In ths pape, to ovecome lteatue gaps n agle supply chan netwok desgn, we pesent a mxed-ntege lnea pogammng (MILP) model that s able to consde aglty concepts such as esponse to customes n maxmum allowable tme, dect shpments besdes the tadtonal shpments, allance between opened facltes n dffeent tes, safety stock, dffeent tanspotaton modes, dscount, and outsoucng besdes the tadtonal featues of the SCND aea. The emnde of ths pape s oganzed as follows. The elated woks ae evewed. Descpton and fomulaton of the poposed model ncludes the descpton and fomulaton of the poposed model. The numecal esults ae epoted n Results and dscusson. Fnally, Conclusons concludes ths pape and offes some dectons fo futhe eseach. Results and dscusson Computatonal esults In ode to evaluate the pefomance of the pesented model fo desgnng agle supply chan netwok, two test poblems ae andomly geneated accodng to the nfomaton specfed n Table 1 nsped fom lteatue. Inteested eades can each the detaled data set fo the two test poblems fom the authos. Custome sevce level s consdeed to be 75% (.e., csl = 0.75) n the two test poblems. It should be mentoned that openng and closng a faclty s a stategc decson, and a tmeconsumng and costly pocess. Theefoe, changng faclty locaton s mpossble n the shot un. On the othe hand, detemnng the quanttes of flow between the facltes of the netwok as a tactcal decson s moe flexble to change n the shot un (Pshvaee et al. 2009). Theefoe, stategc decsons (bnay vaables) should be detemned ndependently fom ealzatons, wheeas tactcal decsons can be changed and updated dung the ealzatons. The poposed model s solved by ILOG CPLEX 10.1 optmzaton softwae on a Pentum dual-coe 2.60-GHz Table 1 Data geneaton Paamete d k f g j Value ~Unf (100, 200) unt ~Unf (1,700,000,4,000,000) $ ~Unf (1,600,000,3,000,000)$ p ~Unf (120,150)$ mh j ~Unf (60,75) $ cs ~Unf (90,170)$ MI j ~Unf (80,100)$ MV ~Unf (90,110) unt DP ~Unf (400,550) unt CD ~Unf (10,500,14,500)$ α k ~Unf (4,000,6,000)$ a jn ~Unf (40,60)$ b jkn ~Unf (40,60)$ e kn ~Unf (90,130)$ ta kn ~Unf(10,16) day tc jkn ~Unf(6,12) day te k ~Unf(10,12) day caw ~Unf (2,000,5,000) unt cay j ~Unf (2,000,3,500) unt CPA1 m ~Unf (50,000,60,000)$ CPA2 jc ~Unf (30000,35,000)$ CPA j ~Unf (60,000,70,000)$ ~Unf, unfom dstbuton.

4 Babazadeh et al. Jounal of Industal Engneeng Intenatonal 2012, 8:19 Page 3 of 8 Table 2 Computatonal esults and complexty of pesented models Poblem sze K * I * J * N * R O.F.V Constants Vaables Run tme(s) 10*5*8 *3*2 16,015, *10*10 *3*2 22,917,570 1,578 1, O.F.V, objectve functon value. compute wth 4 GB RAM. To educe the complexty of detemnstc model, we elax the decson bnay vaables PA1 m, PA2 jc, and PA j as contnuous vaables. It should be noted that mnmzaton of the objectve functon and bnay vaables W and Y j n constants (8) to (14) assues that the elaxed vaables ae set equal to 0 o 1. Acqued esults llustated n Table 2 show that by nceasng the sze of the poblem n queston, objectve functon value (O.F.V) and complexty of the dscussed poblems ncease. Table 3 demonstates the shae of dffeent objectve functon components fo the poposed model n detals. As t s llustated n Table 3, the fxed fo openng facltes have the lagest shae n the objectve functon value fo both models. Theefoe, detemnng the numbe and locaton of facltes n each stage of the SCND pocess s the most mpotant stategc decson whch has effects on the oveall pefomance of the SCN. Moeove, the total of poducton, outsoucng, nventoy, and tanspotaton ae sgnfcant n the objectve functon. Ths s because the demand of customes must be satsfed based on pedefned custome sevce level epesentng upsteam of the supply chan management. Addtonally, the shae of outsoucng cost s lesse than poducton cost n the objectve functon value. It could be explaned by the lmtaton on the majoty of the poducts that could be outsouced (see constant 8 n Descpton and fomulaton of the poposed model ). As descbed n pevous sectons, allance between facltes n the supply chan netwok plays an mpotant ole n ntegaton and success of the agle supply chan. The model pays allance cost to mpove nfomaton and pocess ntegaton. In addton, although dscount ssue can mpove compettveness of the agle supply chan, ts amount should be balanced wth othe. As depcted n Fgue 1, senstvty analyss on demand of customes shows that the poposed model s senstve to demand of customes. Ths obsevaton can be explaned by the demand's effect on the oveall supply chan netwok. In othe wods, the confguaton of the supply chan netwok s constucted accodng to custome demands. The consdeed agle supply chan netwok n ths pape has a geneal stuctue that s able to suppot the aglty concepts besdes the tadtonal featues of the SCND aea and, theefoe, could be appled to dffeent knds of ndustes wth lead tme estcton such as food ndustes and semconducto ndustes. It can be concluded fom the acqued esults that the poposed model can be utlzed as a powe tool n pactcal cases wth less shotage and hgh degee of esponsveness. Conclusons In ths pape, we poposed a supply chan netwok desgn poblem fo a new maket oppotunty n an agle manufactung system. The poposed agle SCND model s able to ntegate poducton, outsoucng, dscount, flexblty, and dstbuton actvtes by consdeng the most mpotant factos of the agle supply chan. The expemental esults show the effcency of the poposed model n an agle supply chan netwok desgn. Also, t can be concluded fom the obtaned esults that the locatons of facltes n the supply chan netwok desgn ae a stategc decson, and theefoe, ntegaton of faclty locaton decsons wth othe decsons such as outsoucng, nventoy contol, poducton, etc. can mpove supply chan pefomance and esponsveness. Many possble futue eseach avenues can be defned fo futue eseach dectons. Fo example, addessng mult-poduct, mult-peod agle supply chan netwok desgn unde dffeent knds of opeatonal and dsupton sks s an attactve eseach decton wth sgnfcant pactcal elevance. Moeove, tme complexty s not addessed n ths pape; howeve, ths ssue mght be mpotant n lage-szed poblems that the commecal solves faled to solve; theefoe, developng effcent exact, o heustc soluton methods can be nteestng n ths aea. Methods Related woks In ths secton, we concsely evew some SCND model developed ecently. Melo et al. (2009) pesented a geneal evew on supply chan netwok desgn to dentfy basc featues that such models must captue to suppot Table 3 Shae of dffeent components of objectve functons Poblem sze K * I * J * N * R Fxed Poducton Outsoucng Inventoy Tanspotaton Allance Shotage Dscount amount 10*5*8 *3*2 13,403,300 1,220,666 30,400 12, , , ,076 15*10*10 *3*2 19,142,810 1,764,269 30,700 18,269 1,145, ,050 12,168 36,309

5 Babazadeh et al. Jounal of Industal Engneeng Intenatonal 2012, 8:19 Page 4 of 8 Allance between facltes Indect shpment Dect shpment Poducton cente Custome zones Fgue 1 Objectve functon vs. demand mean. Dstbuton cente Tanspotaton mode decson makng nvolved n stategc supply chan plannng and to suppot a vaety of futue eseach dectons. Othe nteestng evews n ths feld can be found n Dullaet et al. (2007) and Snyde (2006). Most of the pesented models n the lteatue focus on mnmzaton of total and gnoe othe objectves such as esponsveness and flexblty, whch ae effectve n the success of supply chan management. Zanjan Faahan et al. (2010) gave a compehensve evew on mult-ctea faclty locaton poblems n the SCND. The study shows that only appoxmately 8% of pesented models have consdeed esponsveness as a detemnng facto n SCND. You and Gossmann (2008) developed a esponsve b-objectve MINLP model by consdeng demand uncetanty and economc cteon. The model was able to detemne the safety stock levels to confont uncetanty. They used E-constant method to poduce Paeto font. Rajabalpou Cheshmehgaz et al. (2011) pesented a mult-objectve, multstage, flexble model to desgn logstcs netwok wth the am of mnmzng esponse tme and cost ctea. The effcent mult-objectve evolutonay algothm based on genetc algothm (GA) was poposed. Ross and Jayaaman (2008) developed a MILP model to detemne the locaton of the coss-docks n the SCND. Also, they utlzed smulated annealng and Tabu seach to solve the pesented model. Am (2006) pesented a MILP model to coodnate poducton and dstbuton actvtes. Addtonally, the pesented model was able to detemne the optmum numbe, locaton, and capacty of facltes that should be opened. Altpamak et al. (2006) developed a SCND model n a pactcal case and then poposed a GA by usng poty-based encodng to escape fom nfeasble solutons. Thanh et al. (2008) poposed a dynamc MILP model fo the faclty locaton n the SCND. The poposed model ncludes stategc and tactcal decsons. As yet, among the numeous SCND models, whch ae pesented to desgn SCN n an effcent way and mpove supply chan management, aglty as a wnnng facto n today's tubulent makets has been omtted. Howeve, n ecent yeas, some studes have ted to consde the aglty concepts n SCND. Bachlaus et al. (2008) pesented an ntegated mult-objectve MILP model to ntegate poducton, dstbuton, and supply chan actvtes as stategc decsons consdeng aglty as a key desgn cteon. They defned aglty ndex n thee levels ncludng low, medum, and hgh fo each faclty, whch should be satsfed n constants. Addtonally, they used flexblty as avalable capacty of each faclty, whch should be maxmzed n objectve functon. Pan and Nag (2010) developed a obust optmzaton appoach to deal wth demand uncetanty n supply chan netwok n agle manufactung. The pesented model was able to consde allance, whch s one of the mpotant factos of agle supply chan, between opened facltes. They poposed an effcent heustc based on a k-shotest path algothm to solve the pesented model n lage scales. Howeve, the model doesn't cove dstbuton centes and delvey tme to custome as well as one faclty whch should be detemned n any echelon of supply chan netwok, and the obust optmzaton s based on scenaos. Hasan et al. (2011) pesented a closed-loop supply chan netwok fo peshable goods unde uncetanty of demand and puchasng. Aglty can be seen as handlng poducts n the lfetme peod. They used a bounded-box obust optmzaton appoach to confont uncetanty n the model and solved t usng LINGO. Descpton and fomulaton of the poposed model The concened agle supply chan netwok n ths pape s a mult-echelon and dect acyclc netwok, whch

6 Babazadeh et al. Jounal of Industal Engneeng Intenatonal 2012, 8:19 Page 5 of 8 ntegates the poducton, outsoucng, flexblty, dscount, safety stock, shotage, and dstbuton actvtes. In each echelon, thee ae some canddate facltes whch should be detemned to desgn the netwok n queston. The dscussed echelons ae lnked togethe wth a fowad shpment of poducts and backwad flow of nfomaton n a pull system. As t s shown n Fgue 2, the fnshed poducts manufactued n plants and semfnshed poducts, whch have been outsouced, ae shpped to dstbuton centes o dectly shpped to custome zones afte pocessng n plants. The dect shpment of poducts ncludes shppng the poducts fom poducton centes to the custome zones dectly, whle ndect shpment of poducts ncludes the shppng of goods fom poducton centes to the dstbuton centes and then to the custome zones. Snce dect shpment of poducts has hghe wth espect to ndect shpment, and thee ae budget lmtatons n ths pocess, we assume that only a cetan amount of poducts can be dectly shpped. All dect and ndect shpments ae pefomed n seveal tanspotaton modes ncludng land, sea, and/o a. Usng dffeent tanspotaton modes mpoves the flexblty and esponsveness of the supply chan netwok n the sense that when utlzng a specal tanspotaton mode s not possble, the othes could be effcently used. Also, n ctcal condtons, the poducts could be delveed n maxmum allowable tme by usng faste tanspotaton modes to mpove esponsveness. Some of the fnshed poducts n poducton centes shpped to dstbuton centes ae stoed, and the est ae shpped to custome zones accodng to custome needs. It should be noted that agle supply chans ty to satsfy all custome demands; howeve, some custome needs may be not satsfed n the eal wold. Theefoe, shotage can occu based on pedefned custome sevce level. To acheve flexblty and deal wth dsupton sks, the plants can pefom outsoucng and use dffeent tanspotaton modes to delve new poducts to customes. It s wothy to note that because of the Fgue 2 Stuctue of the concened agle supply chan netwok. keepng ndependency, the maxmum amount of outsouced poducts should be estcted so that the supply chan netwok wll be able to espond to custome needs effectvely when some of the supples ae dsupted. Dsupton of supples could occu because of natual dsaste o othe ssues such as teost attacks and labos stke. As mentoned n pevous sectons, allance between facltes s a key facto to mpove aglty of the supply chan. Ceatng allance between opened facltes, selected to fom the agle supply chan netwok, enables facltes to shae the nfomaton, mpove oganzatonal educatons, leveage oganzatonal sklls, and patcpate n new poduct development. Theefoe, we assume that the supply chan netwok pays a cetan cost to ceate allance between opened facltes n dffeent echelons. As egads delvey tme to customes playng an ncedble ole n mpovng esponsveness to customes, we assume that all costume demands should be met n the expected tmes. Anothe mpotant ssue n SCND s detemnng the capacty of facltes whch should be opened. Most of the pevously pesented models consde fxed capactes fo facltes, wheeas detemnng the capacty of facltes s often dffcult n pactce (Wang et al. 2009). Theefoe, t s assumed that the capacty level of facltes s detemned as a decson vaable to avod addtonal and useless. The followng notaton s used n the fomulaton of the poposed model. Indces I,M Index of canddate locatons fo plants (,m =1,..., I) J,C Index of canddate locatons fo dstbuton centes (j,c =1,..., J) K Index of fxed locatons of customes (k =1,..., K) N Index of tanspotaton modes (n =1,..., N) R Index of capacty levels ( =1,..., R) Paametes d k Demand of custome k f Fxed cost of openng plant wth capacty level g j Fxed cost of openng dstbuton cente j wth capacty level p Poducton cost pe unt of poducts at plant CPA1 m Pocess and nfomaton (allance) ntegaton cost between plants and m CPA2 jc Pocess and nfomaton ntegaton cost between dstbuton centes j and c CPA j Pocess and nfomaton ntegaton cost between plants and dstbuton cente j CD Dscount amount by plant to customes

7 Babazadeh et al. Jounal of Industal Engneeng Intenatonal 2012, 8:19 Page 6 of 8 α k Penalty cost pe unt of unsatsfed demand of custome k mh j Mateal handlng and nventoy cost pe unt of poducts at dstbuton cente j oc Outsoucng cost pe unt of poducts at plant a jn Unt tanspotaton cost fom plant to dstbuton cente j by mode n fo poduct p b jkn Tanspotaton cost pe unt of poducts fom dstbuton cente j to custome k by mode n e kn Tanspotaton cost pe unt of poducts fom plant to custome k by mode n ta kn Delvey tme fom plant to custome k by mode n tc jkn Delvey tme fom dstbuton cente j to custome k te k Expected delvey tme of custome k MI j Mnmum nventoy whch should be held n dstbuton cente j MV Maxmum amount of poducts whch can be outsouced n plant DP Mnmum amount equed that plant offes dscount to customes csl Pecentage of pedetemned custome sevce level caw Capacty wth level fo plant cay j Capacty wth level fo dstbuton cente j mn f w þ gj y j þ X ðp xu þ oc v Þ j þ X mh j In j þ X a jn x jn j j n þ X b jkn Q jkn þ X e kn L kn j k n k n þ 1 2 CPA1 mpa1 m þ 1 2 CPA2 jcpa2 jc m6¼ j c6¼j þ CPA j PA j þ X α k δ k X CD λ S:t: j k ð1þ L kn þ Q jkn þ δ k d k 8k ð2þ n j n δ k ð1 cslþd k 8k ð3þ λ d k 8; k DP X x jn þ X j n x jn ¼ X n k In j X y j MI j8j L kn ¼ X k n X Q jkn þ In j 8j n ð4þ ðxu þ v Þ ð5þ ð6þ ð7þ Decson vaables v X w MV 8 ð8þ xu Quantty of poducts poduced at plant In j Quantty of poducts held at dstbuton cente j v Quantty of poducts outsouced at plant δ k Quantty of unsatsfed demand of custome k x jn Quantty of poducts shpped fom plant to dstbuton cente j by mode n Q jkn Quantty of poducts shpped fom dstbuton cente j to custome k by mode n L kn Quantty of poducts shpped dectly fom plant to custome k by mode n W 1 f plant wth capacty level s opened; othewse, 0 y j 1 f dstbuton cente j wth capacty level s opened; othewse, 0 PA1 m 1 f pocess and nfomaton ntegaton s pefomed between plant and plant m; othewse, 0 PA2 jc 1 f pocess and nfomaton ntegaton s pefomed between dstbuton cente j and dstbuton cente c; othewse, 0 PA j 1 f pocess and nfomaton ntegaton s pefomed between plant and dstbuton cente j; othewse, 0 λ 1 f plant gves dscount to customes, othewse, 0 PA1 m X PA1 m X PA2 jc X PA2 jc X PA j X PA j X w 8; m 6¼ ð9þ w þ X y j 8j; c 6¼ j ð11þ y j þ X w 8; j y j 8; j y c w m 18; m 6¼ ð10þ 18j; c 6¼ j ð12þ PA j X w þ X y j 18; j L kn ta kn L kn te k 8; k; n Q jkn tc jkn Q jkn te k 8j; k; n λ X xu X w 8 w caw 8 ð13þ ð14þ ð15þ ð16þ ð17þ ð18þ ð19þ

8 Babazadeh et al. Jounal of Industal Engneeng Intenatonal 2012, 8:19 Page 7 of 8 x jn X y j cay j 8j n x jn þ L kn X j n k n X xu LB w caw 8 X L kn UB k n X w 18 X y j 18j w U8 xu ; In j ; v ; x jn ; L kn ; Q jkn ; δ k 0 8; j; k; n ð20þ ð21þ ð22þ ð23þ ð24þ ð25þ ð26þ w ; y j ; λ ; PA1 m ; PA2 jc ; PA j 2 f0; 1g8; j; ; m; c ð27þ Objectve functon (1), whch mnmzes the total, ncludes fxed openng, poducton cost, outsoucng cost, nventoy holdng cost, tanspotaton and pocessng, allance between opened facltes, and shotage as well as the amount of dscount, s maxmzed to mpove compettveness of the agle supply chan netwok. Coeffcent (1/2) s consdeed to avod ecalculaton of allance between opened facltes n the same echelon. Constant (2) ensues that all demands of customes ae not satsfed, and shotage s possble. Constant (3) mposes the maxmum allowable shotage based on pedefned custome sevce level. Constant (4) s nequalty fo decson makng on gvng dscount to customes. It should be noted that snce the dscount amount s maxmzed n the objectve functon to mpove the competency of supply chan netwok, the bnay vaable λ gves the value 1 when the customes puchase the cetan amount of poducts specfed to gve dscount (.e., DP ). Constants (5) and (6) ae the flow balances at the plants and waehouses, espectvely. Constant (7) mposes the mnmum nventoy whch should be stoed as safety stocks n opened waehouses. Constant (8) assues that the amount of outsouced poducts doesn't exceed a cetan amount to assue ndependency. Constant (9) expesses that to ceate allance between the poducton centes of the agle supply chan netwok, the poducton centes should be detemned among the canddate locatons wth specfed capactes n advance. Constant (10) quaantnes the ceaton of allance between opened poducton centes n the fst echelon. Fo example, assume a poducton cente wth capacty level 2 s establshed n locaton 3 (.e., w (3,2) = 1), and anothe poducton cente wth capacty level 1 s establshed n locaton 4 (.e., w(4,1) = 1), so the allance between these poducton centes wll be ceated (.e., PA1(3,4) 1+1 1). Note that the PA1 s a bnay vaable and so wll be equal to 1. Constants (11) and (12) ae the same as constants (9) and (10) to ceate allance between opened dstbuton centes n the second echelon. Constants (13) and (14) expess that to ceate allance between poducton and dstbuton centes n dffeent echelons, they should be selected fo establshng among the canddate locatons n advance. Constant (15) ensues that when the poducton cente and dstbuton cente ae establshed n dffeent echelons, the allance wll be ceated between them. Constants (16) and (17) ensue that all the poducts ae delveed to customes n the maxmum allowable delvey tme. Restcton (18) expesses that only opened plants ae allowed to gve dscount to customes. Constants (19) and (20) ae capacty constants n any faclty. Constant (21) ensues that only opened plants can send poducts to waehouses and custome centes. Constant (22) expesses the utlzaton of lowe-bound pecentage of the capacty of opened plants. Constant (23) expesses the lmtaton on the total numbe of poducts dectly sent to customes. Constants (24) and (25) ensue that any faclty can be opened, at most, n one of the capacty levels. Fnally, constants (26) and (27) enfoce the bnay and non-negatvty estctons on coespondng decson vaables. Competng nteests The authos declae that they have no competng nteests. Authos' contbutons RB poposed the mathematcal model and solved t. JR managed the study and was esponsble fo ntegatng and evsng the manuscpt. RG patcpated n the desgn of the study. Acknowledgments We would lke to thank fom anonymous efeees fo the constuctve and valuable comments that mpoved the contents of the pape substantally. All authos ead and appoved the fnal manuscpt. Receved: 10 Mach 2012 Accepted: 12 August 2012 Publshed: 30 August 2012 Refeences Altpamak F, Gen M, Ln L, Paksoy T (2006) A genetc algothm appoach fo mult-objectve optmzaton of supply chan netwoks. ComputInd Eng 51: Am A (2006) Desgnng a dstbuton netwok n a supply chan system: fomulaton and effcent soluton pocedue. Eu J Ope Res 171: Am F (2011) Sgnfcance of lean, agle and leagle decouplng pont n supply chan management. Jounal of Economcs and Behavoal Studes 3(5): Bachlaus M, Mayank KP, Chetan M, Rav S, Twa MK (2008) Desgnng an ntegated mult-echelon agle supply chan netwok: a hybd taguchpatcle swam optmzaton appoach. J Intell Manuf 19: Chstophe M, Lowson R, Peck H (2004) Ceatng agle supply chans n the fashon ndusty. Intenatonal Jounal of Retal & Dstbuton Management 32(8): Dullaet W, Baysy O, Goetschalckx M, Raa B (2007) Supply chan (e)desgn: suppot fo manageal and polcy decsons. Eu J Tansp Infastuct Res 7(2):73 91

9 Babazadeh et al. Jounal of Industal Engneeng Intenatonal 2012, 8:19 Page 8 of 8 Hasan A, Zegod SH, Nkbakhsh H (2011) Robust closed-loop supply chan netwok desgn fo peshable goods n agle manufactung unde uncetanty. Int J Pod Res. do: / Hason A, Hoek R, Chstophe M (1999) Ceatng the Agle Supply Chan. Insttute of Logstc &Tanspot, London Ln CT, Chu H, Chu PY (2006) Aglty ndex n the supply chan. Int J Pod Econ 100(2): Mason-Jones R, Naylo JB, Towll DR (2000) Engneeng the leagle supply chan. Intenatonal Jounal of Agle Manufactung Systems 2(1):54 61 Melo MT, Nckel S, Saldanha-da-Gama F (2009) Faclty locaton and supply chan management: a evew. Eu J Ope Res 196: Pan F, Nag R (2010) Robust supply chan desgn unde uncetan demand n agle manufactung. Comput Ope Res 37: Pshvaee MS, Jola F, Razm J (2009) A stochastc optmzaton model fo ntegated fowad/evese supply chan netwok desgn. J Manuf Syst 28: Rajabalpou Cheshmehgaz H, Ishak Desa M, Wbowo A (2011) A flexble thee-level logstc netwok desgn consdeng cost and tme ctea wth a mult-objectve evolutonay algothm. J Intell Manuf. do: /s Ross A, Jayaaman V (2008) An evaluaton of new heustcs fo the locaton of coss-docks dstbuton centes n supply chan netwok desgn. Comput Ind Eng 55: do: /j.ce Snyde LV (2006) Faclty locaton unde uncetanty: a evew. IIE Tans 38(7): Thanh PN, Bostel N, Peton O (2008) A dynamc model fo faclty locaton n the desgn of complex supply chans. Int J Pod Econ 113: Wang S, Watada J, Pedycz W (2009) Value-at-sk-based mult-stage fuzzy faclty locaton poblems. IEEE tansactons on ndustal nfomatcs 5: You F, Gossmann IE (2008) Desgn of esponsve supply chans unde demand uncetanty. Comput Chem Eng 32: Zanjan Faahan R, Steade Sef M, Asga N (2010) Multple ctea faclty locaton poblems: a suvey. Appl Math Model 34: do: / x-8-19 Cte ths atcle as: Babazadeh et al.: Supply chan netwok desgn poblem fo a new maket oppotunty n an agle manufactung system. Jounal of Industal Engneeng Intenatonal :19. Submt you manuscpt to a jounal and beneft fom: 7 Convenent onlne submsson 7 Rgoous pee evew 7 Immedate publcaton on acceptance 7 Open access: atcles feely avalable onlne 7 Hgh vsblty wthn the feld 7 Retanng the copyght to you atcle Submt you next manuscpt at 7 spngeopen.com