supply chain network design problem.

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1 Ieaioal Joual o Iusial Egieeig & Poucio Reseach (016) Decebe 016 Volue 7 Nube DOI: /ijie h://ijiepr..ius.ac.i/ Cosieig Picig Poble i a Dyaic a Iegae Desig o Susaiable Close-loo Suly Chai Newok Aash Nobai Ai Saa Kheikhah* & Maya Esaeili Aash Nobai Iusial Egieeig Deae Faculy o Egieeig Bu-Ali Sia Uivesiy Aisaa Kheikhah Iusial Egieeig Deae Faculy o Egieeig Bu-Ali Sia Uivesiy Maya Esaeili Iusial Egieeig Deae Faculy o Egieeig Al-Zaha Uivesiy KEYWORDS Suly Chai Newok Desig Susaiabiliy Log-e a Sho- e Decisios e-cosai Meho Ieialis Coeiive Algoih ABSTRACTT Flexible a yaic suly chai ewok esig oble has bee suie by ay eseaches uig as yeas. Sice iegaio o sho-e a log-e ecisios i saegic laig leas o oe eliable las i his ae a uli-objecive oel o a susaiable close-loo suly chai ewok esig oble is oose. The laig hoizo o his oel coais ulile saegic eios so ha he sucue o suly chai ca be chage yaically uig he laig hoizo. Fuheoe i oe o have a iegae esig seveal sho-e ecisioss ae cosiee besies saegic ewok esig ecisio. Oe o hese sho-e ecisios is eeiig sellig ice a buyig ice i he owa a evese logisics o suly chai esecively. Fially a augee e- cosai eho is use o aso he oble o a sigle-objecive oel a a ieialis coeiive algoih is esee o solve lage scale obles. The esuls aalysis iicaes he eiciecy o he oose oel o he iegae a yaic suly chai ewok esig oble. 016 IUST Publicaio IJIEPR. Vol. 7 No. 4 All Righs Reseve Aog iee saegic ecisios suly chai 1. Ioucio1 ewok esig (SCND) ca be egae as a The suly chai ca be cosiee as a esseial ecisios ae i SCM [3-4]. I a cobiaio o iee ogaizaios which SCND oble he ai issue is iig a seve cusoes i cooeaio wih each ohe. eicie iasucue o he eie suly chai Makig cooiaio aog hese iee so ha he low o goos a couicaio ebes a laig i he suly chai is oe bewee iee ebes o a suly chai ca o he ai issues o suly chai aagee be oe sily. Exesive aue o chagig (SCM) [1]. Cosieig he ie hoizo he he sucue o a suly chai akes SCND laig i SCM ca be caegoize io oble as a saegic ecisio i SCM [1 3 5]. saegic acical a oeaioal levels []. I I aiio o ewok esig o suly chai he coas wih acical a oeaioal ecisios ohe log-e ecisios such as eiig he saegic laig i SCM coais ecisios caaciy a echology o aciliies ca be wih log-lasig iluece o suly chai [3]. eee [6]. I oe o aa o chagig evioe ay * Coesoig auho: Aisaa Kheikhah aages ae ieese i esigig he ewok Eail: o a suly chai yaically so ha he Receive 4 ASil 016; evise 5 Novebe 016; accee 17 Ail 017 sucue o suly chai ca be chage wih Ieaioal Joual o Iusial Egieeig & Poucio Reseach Decebe 016 Vol. 7 No. 4

2 354 A. Nobai A. S. Kheikhah & M. Esaeili esec o he vaiaios o he ake. So ay eseachess cosiee yaic suly chai ewok esig i he ece yeas [7]. I also shoul be oe ha base o he ieacios exisig aog log-e a sho-e ecisios a he eecs o hesee ecisios o each ohe ay suly chai aages cosie acical a oeaioal ecisios besies he saegic suly chai ewok esig oble. Oe o hese sho-e ecisios less egae i he lieaue o SCND oble is icig. I he ece yeas iovig aeios o evioeal coce iceasig esisace wih olluig aciviies goveeal legislaioss associae wih social issues a ec ake ay is o coceae o ohe goals as well as hei ecooicc goals. Hece uig he las ecae susaiabiliy as a ew coce i which evioeal a social coces ae egae eee iee scoes o he suly chai such as SCND oble besies ecooic esiaios [8]. Accoigly he ai o his ae is oosig a oe coehesive oel o a yaic a iegae close-loo suly chai ewok esig oble i which evioeal social a ecooic coces ae egae siulaeously. Fo sake o yais a iegaio o ewok esig seveal saegic eios ae cosiee whee each o hese saegic eios cosiss o ulile sho-e eios i which acical a oeaioal ecisios shoul be eie. The sellig ice o oucs o cusoe zoes a buyig ice o use oucs o cusoe zoes ae wo o hese sho-e ecisios. Fially he oose suly chai ewok esig oble is oulae as a uli-objecive ixe-iege liea laig () oel. The coibuios o his ae ca be suaize as ollow: Cosieig ulile saegic eios o ake he yaic esig o suly chai ossible. Cosieig sellig ice o oucs usig liea ea ucios i owa logisics o he suly chai. Cosieig buyig ice o use oucs i evese logisics o suly chai usig liea acquisiio ucio. Poosig a levelig aoach o icig ecisios i owa a evese logisics o have a oel which siliies solvig he oose oel. Pacically he oose oel ca hel suly chais i seveal asecs o esig hei ewoks Cosieig Picig Poble i a Dyaic... oe eicie. O oe sie his oel akes chagig he sucue o suly chai ossible esecig seveal log-e a saegic eios. This hels aages o aa hei suly chai o he chagig coeiive ake. O he ohe sie iegaio o log-e a sho-e ecisios ca lea o oe ealisic laig because eiig he sucue o a suly chai wihou esecig acical a oeaioal ecisios a hei ieacios is o ossible uly. The oose oel also ecouages he cusoes o eu use oucs o suly chai usig cosieaio o iceive buyig ice o use oucs by which boh ecooic a evioeal goals o suly chai ca be aece osiively. Fially he cosieaio o susaiabiliy i he suly chai ewok esig oble hels aages o achieve a bee siuaio i a coeiive ake. The es o his ae is ogaize as ollows: he lieaue elae o SCND oble is eviewe i Secio. The close-loo suly chai ewok esig oble is eie i Secio 3 a a oel is use o oulae his oble. The soluio aoach o he oose oel is sae i his Secio oo. I Secio 4 he esuls o solvig he oel o a ueical exale a sesiiviy aalysis o aaees ae esee. Fially he coclusio a uue eseach suggesios ae give i Secio 5.. Lieaue Review The SCND oble has bee wiely suie by ay eseaches hough ece yeas [ 6]. Accoigly he elae lieaue ca be caegoize wih esec o iee asecs as show i Figue 1. Fig. 1. Classiicaio o SCND lieaue The SCND oble has bee wiely suie by ay eseaches hough ece yeas [ 6]. Accoigly he elae lieaue ca be Ieaioal Joual o Iusial Egieeig & Poucio Reseach Decebe 016 Vol. 7 No. 4

3 Cosieig Picig Poble i a Dyaic caegoize wih esec o iee asecs as show i Figue Base o suly chai logisics The is gou iclues eseaches which have cosiee owa logisics i SCND oble [9-17]. I coas he seco gou cosiss o eseaches i which he evese logisics o he suly chai is cosiee solely i SCND [18- ]. The las gou egae boh owa a evese logisics siulaeously i SCND oble [3-3]. I shoul be oe ha i he ece yeas he evese logisics have bee aee i he suies because o he ioace o evioeal issues [33]. Fo a oe coehesive suy i his aea oe ca ee o [34]. -. Base o ube o objecivee ucios I his ae he lieaue o SCND ca be caegoize io wo gous. The is oe suie sigle objecive SCND oble which iclues oe ha iey ece o elae eseaches []. The seco gou iclues eseaches which cosie uli-objecive oels o SCND oble. Fo a oe coehesive suy i his aea oe ca ee o [5]. Oe o he ai coces has bee aee wiely i he lieaue o SCND oble is susaiabiliy [35-36]. Base o [37] os o eseaches suie he susaiable SCND oble cosieig oly ecooic a evioeal coces [ ] while social coces have bee cosiee oly by a ew eseaches [ ]. Fo a oe coehesive suy i he susaiable SCND oble oe ca ee o [34]. -3. Base o ube o saegic eios The is gou iclues eseaches which evaluae SCND oble hough a sigle saegic eio i which he chages o he ewok is o ossible [7]. I coas he seco gou coais eseaches i which he sucue o suly chai ca be vaie uig ulile saegic eios [ ]. -4. Base o ecisios ie hoizo The is eseaches o SCND oble ivesigae oly saegic a log-e ecisio i esigig he suly chai ewok. I coas he seco gou cosiee iegae SCND oble i which acical a oeaioal ecisios ae also egae besiess saegic a log-e ecisios. A coehesive suy has bee esee by [40]. A. Nobai A. S. Kheikhah & M. Esaeili 3555 Aog suies which esee iegae SCND oble oly a ew oes (such as [41]) cosiee ulile saegic a acical eios siulaeously. The oel esee i [41] eveloe by seveal eseaches [7 13]. Soe eseaches cosiee icig ecisios i owa logisics ewok esig [ ]. The buyig ice-eee acquisiio ucios i evese logisics have bee cosiee by seveal eseaches oo [ ]. Oly a ew woks cosiee icig ecisios i owa a evese logisics siulaeously [30]. As iicae i Table 1 oly a ew eseaches ivesigae he SCND oble yaically a hough seveal saegic eios. While esecig he chagig evioe he uchageable a saic esig o a suly chai ca gaually lea o he ailue o suly chai i he coeiive ake. I ca also be obseve i Table 1 ha ew eseaches cosiee icig ecisios i owa a evese logisics siulaeously. This ae aes o ese a oe coehesive oel o a yaic SCND oble i which acical a oeaioal ecisios such as icig have bee iegae wih saegic ecisios. Also he esee levelig aoach o sellig a buyig ice siliies he aheaical oel. 3. Poble Deiiio I his ae he ewok esig oble o a close-loo suly chai which ais o ee he ake o sellig soe oucs is cosiee. The coiguaio o his suly chai is iicae i Figue. I owa logisics o his suly chai auacues ovie hei aw aeial o sulies a ouce ulile oucs. The hese oucs ae asoe o cusoe zoes via isibuio cees. I evese logisics collecio cees collec use oucs o cusoe zoes a aso he o ecovey cees which ivesigae use oucs a caegoize he o ecoveable a uecoveablee oucs. The is gou will be ecovee a asoe o isibuio cees agai while he lae will be asoe o isosal cees. Ieaioal Joual o Iusial Egieeig & Poucio Reseach Decebe 016 Vol. 7 No. 4

4 356 A. Nobai A. S. Kheikhah & M. Esaeili Cosieig Picig Poble i a Dyaic... Tab. 1. Lieaue o SCND oble Re [8] [9] [1] C [17] [18] [19] [10] [] C Logisics o Suly Chai Nube o Objecive Fucios FL 1 FL 1 CLSC RL 1 RL 1 RL > FL CLSC 1 [3] CLSC 1 [0] [11] [4] RL FL CLSC [5] CLSC [1] [6] FL CLSC 1 1 [13] [7] FL CLSC > > [14] [15] [6] [8] FL FL FL CLSC [] CLSC > [16] [9] FL CLSC > [31] CLSC Cue ae CLSC > Ecooic Susaiabiliy Coces Evioeal Social Nube o Tacical a Saegic Peios Mulile Tacical Peio Mulile Saegic Peio Moel Locaio Saegic Techology Caaciy Sulie Selecio Decisio Vaiables Poucio Tacical Assige/ Shie MINLP MINLP MINLP MINLP NLP NLP MIP MINLP MINLP MINLP HA: Heuisic Aoach MH: Mea-heuisic Aoach LM: Lagagia Meho CS: Coecial Solve e-cm: Ɛ-Cosai Meho Soage Sellig Pice Buyig Pice Soluio Aoach HA HA HA MH MH MH LM HA LM MH e-cm CS e-cm LM CS e-cm MH LM LM MH H MH MH CS CS e-cm Ieaioal Joual o Iusial Egieeig & Poucio Reseach Decebe 016 Vol. 7 No. 4

5 Cosieig Picig Poble i a Dyaic Fig.. Coiguaio o close-loo suly chai ewok I his ae i is assue ha i aiio o ew ea suly chai hee is a exisig suly chai which sells he sae oucs i cusoe zoe a achieves a oio o he ake shae cosequely. Regaig his exisig suly chai he ew ea suly chai ca achieve oly a seciie oio o eas. To iegae sho-e a log-e ecisios i is assue ha he laig hoizo cosiss o seveal saegic eios so ha each saegic eio iclues ulile acical eios (as show i Figue 3). Fig. 3. Relaioshi aog saegic a acical eio A. Nobai A. S. Kheikhah & M. Esaeili 357 exese i oe o iove he sucue o suly chai a he eaie buge ca be ivese wih a eeie iees ae. The ai o his ewok esig oble is iig a eicie iasucue o suly chai so ha he oi o suly chai is axiize he ube o ueue use oucs is iiize a job oouiies ceae by he suly chai ae axiize. The ohe assuios o his SCND oble ae as ollows: The oeial locaios o aciliies ae eeie. Oee aciliies cao be close uig ex saegic eios. The oeial oios o iovig he caaciy o auacues ae eeie. The ea ucio o each ouc ees liealy o sellig ice. The acquisiio ucio o each use ouc ees liealy o buyig ice. The shoage ca occu as los sales. Recovee oucs i ecovey cees ca be eceive by isibuio cee ae oe acical eio. All he aaees cosiee i owa a evese logisics ae eeiisic Noaios Table iicaes all oaios aaees a ecisio vaiables use i he oose aheaical oel. I is also assue ha a seciie buge is assige o each saegic eio which ca be Tab.. Noaios aaees a ecisio vaiables Ses Ex o : Caaciy exasio o caaciy oio o S: Sulies ( s S ) a auacue M: Mauacues ( M ) ax Ca : Maxiu isallable oucio D: Disibuio cees ( D ) K: Cusoe zoes ( k K ) caaciy o auacue ax C: Collecio cees ( c C ) Ca : Maxiu soage caaciy o R: ecovey cees ( R ) isibuio cee ax C : Disosal cees ( c C ) Ca c : Maxiu collecig caaciy o P : Raw aeials ( P) collecio cee c P: Poucs ( P ax ) Ca : Maxiu ecovey caaciy o L: Level o sellig ice (l L ) ecovey cee L : Level o Buyig ice ( l L) U : Uilizaio ae o auacue O: Caaciy oios o auacues ( o O ) B N: Nube o saegic eios ( N ) : Assige buge o saegic eios T: Nube o acical eios ( T ) IR : Iees ae o ivesig i Saegic eios Paaees FO i : Fixe cos chage i saegic eio : Quaiy o equie aw aeial o Ieaioal Joual o Iusial Egieeig & Poucio Reseach Decebe 016 Vol. 7 No. 4

6 358 A. Nobai A. S. Kheikhah & M. Esaeili 1 o oeig aciliy i saegic eio FA o : Fixe cos o auacue chage i saegic eio 1 o aig oucio caaciy oio o i saegic eio FCCC o : Fixe cos o auacue o oeae ue caaciy oio o i saegic eio FOC i : Fixe oeaig cos o aciliy i PC : Vaiable cos o oucig oe ui o ouc a auacue HC : Vaiabl e cos o holig oe ui o ouc a isibuio cee IC : Vaiable cos o isecig oe ui o ouc a ecovey cee RC : Vaiable cos o ecoveig oe ui o ouc a ecovey cee SC : Vaiable k cos o shoage oe ui o ouc a cusoe zoe TC : Vaiable s cos o asoig oe ui o aw aeial bewee sulie s a auacue TC : Vaiable i j cos o asoig oe ui o ouc bewee aciliies i a j BC : Buyig c s os o oe ui o aw aeial o sulie s J i : Nube o job oouiies ceae ue o oeig aciliy i MaxDe : Maxiu achievable ake shae o cusoe zoe k o ouc i acical eio o saegic eio De : Dea o cusoe zoe elae o ea suly chai o ouc i acical eio o saegic eio De l: Dea o cusoe zoe elae o ea suly chai o ouc i acical eio o saegic eio base o sellig ice level l IP : Buyig k l ice o ouc i cusoe zoe k a ice level l i acical eio o saegic eio Re k l : The aou o eue ouc o cusoe zoe k i acical eio o saegic eio base o iceive ice levell Decisio vaiables OM : 1 i auacue is oe uig Cosieig Picig Poble i a Dyaic... ouce oe ui o ouc U : Usage ae o soage caaciy o isibuio cee o soe oe ui o ouc U : Usage ae o oucio caaciy o auacue o ouce oe ui o ouc A : Nube o eliveies o auacue o isibuio cee A : Nube o eliveies o ecovey cee o isibuio cee : Reu ae o use ouc collece ee a wihou buyig o cusoe zoe : Elasiciy coeicie o sellig ice i ea ucio o cusoe zoe k o ouc : Elasiciy coeicie o buyig ice i acquisiio ucio o cusoe zoe o ouc : Recovea able acio o eue ouc P : Sellig ice o ouc o cusoe zoe k i acical eio o saegic eio P l: Sellig ice o ouc o cusoe zoe k a ice level l i acical eio o saegic eio : Peceage o ake shae o exisig suly chai Dea : Poeial ea o cusoe zoe k o ouc i acical eio o saegic eio ouc o cusoe zoe k i acical eio o saegic eio l : 1 i buyig ice level l is use o buyig aiioal use ouc o cusoe zoe k i acical eio o saegic eio Q : Quaiy o ouc ouce by auacue i acical eio o saegic eio H : Aou o ouc hel by isibuio cee i acical eio o saegic eio s : Aou o aw aeial shie o sulie s o auacue i acical eio o saegic eio i j : Aou o ouc shie o aciliy i o aciliy j i acical eio o saegic eio S l: Shoage o ouc base o ice level l i cusoe zoe k i acical eio o Ieaioal Joual o Iusial Egieeig & Poucio Reseach Decebe 016 Vol. 7 No. 4

7 Cosieig Picig Poble i a Dyaic saegic eio OD : 1 i isibuio cee is oe uig saegic eio OC c : 1 i collecio cee c is oe uig saegic eio OR : 1 i ecovey cee is oe uig saegic eio : 1 i caaciy oio o is isalle a O o auacue i saegic eio : 1 i sellig ice level l is use o sellig k l 3-. Sellig ice-eee ea ucio I he las ecaes vaious ice-eee ea ucios have bee iouce i he lieaue. I his ae oe o he os coo ea ucios is use o cosie he A. Nobai A. S. Kheikhah & M. Esaeili 359 saegic eio UB : Use buge i saegic eio SB : Se buge i saegic eio o exe he ewok o suly chai Cos : Toal oeaioal ixe cos o suly chai Cos chai Cos Fixe Va oal Icoe : Toal oeaioal vaiable cos o suly : Toal cos o suly chai oal : Toal icoe o suly chai elaioshi aog eas a sellig ice o oucs. The use ea ucio ca be oulae by Eq. (I) i which heee is a liea elaioshi bewee ea a ice. Figue 4( (a) iicaes his ice-eee ea ucio. De 1 Dea Cosieig he exisig suly chai he ew ea ca achieve oly a oio o oal ea ( Dea ) which equals MaxDe k. The icoe o sellig oucs o cusoe zoes equals P whi k ich akes a ixe-iege oliea ogaig (MINLP) oel. Hece i his ae i oe o have a liea elaioshi aog ecisio vaiables a levelig aoach siila o [7] is alie o sellig ice. I his ae seveal iscee levels o sellig ice is cosiee i each cusoe zoe as show i Figue 4(b). Assuig L as he ube o ice levels he sellig ice o each level l ca be calculae by Eq. (II). l 1 MaxDe P l (II) L 1 k Fig. 4. Pice-eee ea ucio P MaxDe P (I) So he icoe o sellig oucs o each ice level equals P k l De l. k l S l which akes a oel Buyig ice-eee acquisiio ucio I his ae i is assue ha he ube o eue oucs i evese logisics ees liealy o buyig ice o use oucs which ca be oulae by Eq. (III). Re IP (III) D k whee D k iicaes he oal ube o oucs eue eee o cusoe zoes a IPk iicaes he oal ube o bough oucs. Base o Eq. (III) i ca be obseve ha iceasig he buyig ice leas o ceasig he ube o eue oucs as show i Figue 5(a). Ieaioal Joual o Iusial Egieeig & Poucio Reseach Decebe 016 Vol. 7 No. 4

8 360 A. Nobai A. S. Kheikhah & M. Esaeili Cosieig Picig Poble i a Dyaic... Fig. 5. Buyig ice-eee acquisiio ucio lea o euig use oucs oe ha Accoig o eioe acquisiio ucio he saisie ea. oal cos o buyig exa use oucs equals o IP IP which leas o a MINLP k IPkl kl 1 D k l L oel. The sae as he eioe aoach o k (V) sellig ice (Secio 3.) a levelig aoach is 3-4. Maheaical oel alie o buyig ice as show i Figue 5(b). The objecivee ucios a cosais o he Assuig L as he oal ube o buyig ice oose oel ae as ollows: levels he buyig ice associae wih levell l ca be calculae usig Eq. (IV) Objecive ucios l 1 1 MaxDe - Ecooic objecive ucio IP l (IV) L Maxiizaio o oal oi is cosiee as he 1 is objecivee ucio which ca be oulae Fially he oal cos o buyig oucs o each as Eq. (1). ice level equals IP k l IP l. Max OF1 Icoeoal Cosoal IRNUB N (1) Sice i is assue ha shoage ca occu i The oal icoe o he suly chai ca be cusoe zoes so Eq. (V) shoul be ae o calculae by Eq. (1-1). he oose oel as a exa cosai. This cosai eves selecig buyig ices which Icoeoal Pk ldek l l Pk lsk l (1-1) N T kk P l L kk P l L Toal cos o suly chai iclues ixe a vaiable cosss which ca be oulae by Eq. (1-) a Eq. (1-3) esecively. CosFixe Cos Va FOC OM N M N D FC C o O o N T oo N BCs s 0 N T ss M P FOC OD N cc 0 N T M P FOC OC PC c Q c N R FOC 1 1 HC H 0 N T D P M A R A SCk S l k IPk l l 0 N T kk P ll 0 N T kk P l L IC RC c TCs s 0 N T cc R P 0 N T ss M P TC TC 0 N T M D P 0 N T D kk P TC c c TCc c 0 N T ss M P 0 N T cc R P TC 0 N T RDP OR (1-) (1-3) Ieaioal Joual o Iusial Egieeig & Poucio Reseach Decebe 016 Vol. 7 No. 4

9 Cosieig Picig Poble i a Dyaic A. Nobai A. S. Kheikhah & M. Esaeili 361 The oi o ivesig uexee buge equals IRNUBN. - Evioeal objecive ucio Miiizaio o oal ueue oucs o cusoe zoes is he seco objecive ucio o he oose oel whichh ca be oulae by Eq. (). Mi OF () N T D kk P - Social objecive ucio Maxiizaio o job ceaio as a social esosibiliy is cosiee as he hi objecive ucio o he oose oel whichh ca be calculae usig Eq. (3). NT NT NT NT Max OF 3 JOM J OD JOC c c JOR (3) M k D N T kk cc P cc kc R Cosais Q 0 H s ss P Q 0 D 1 H k M R kk 1 T H H k M R kk 1 c 0 cc D 1 T c 0 1 cc D 1 c c 0 c C cc l 1 0 ll S l l De l l 0 k S l lde l 0 D ll ll l 1 0 ll IP l l 1 k ll D kc k IP l l cc D ll kc c c 0 kk R 1 OM OM 0 1 OD OD 0 1 OCc OC c c 0 1 OR OR SB FO OM OM FO OD M D FOc OCc OCc FO OR OR cc R SB SB UB UB B IR UB B OD M oo 1 o o FA O N (4) (5) (6) (7) (8) (9) (10) (11) (1) (13) (14) (15) (16) (17) (18) (19) (0) (1) () (3) (4) Ieaioal Joual o Iusial Egieeig & Poucio Reseach Decebe 016 Vol. 7 No. 4

10 36 A. Nobai A. S. Kheikhah & M. Esaeili Cosieig Picig Poble i a Dyaic... UB IR 1UB 1 N Oo OM 0 oo U Q U Ex o o P 0 NoO Exo O ax o Ca 0 N o O U H U U P M P A R P ax U kc OC c Cac c 0 kk P ax U c ORCa 0 cc P OM OD OCc OR Oo l l Q H s i j S l UB 0 x O 0 0 Eq. (4) assues ha each auacue ovies suicie aw aeials i each acical eio. Eq. (5) iicaes ha ouce oucs will be asoe o isibuio cees. Eq (6) a Eq. (7) iicae he balace o goos o isibuio cees a Eq. (8) a Eq. (9) assue he balace o goo aog isibuio cees a ecovey cees. Eq. (10) assues he low o goos aog ecovey cees a isosal cees. Selecig oly oe ice level i each acical eio is guaaee by Eq. (11). Base o Eq. (1) shoage i each cusoe zoe shoul be less ha oal ea. Eq. (13) iicaes ha su o e ea a shoage o each ouc equals oal ea o elae cusoe zoe. Eq. (15) is he exa cosai which eves selecig buyig ices which lea o euig use oucs oe ha e ea. The balace o goos o each cusoe zoe a collecio cee is cosiee by Eq. (16) a Eq. (17). Eqs. (18)-( 1) guaaee ha he oee aciliies cao be close hough ex saegic eios. Eq. () cosies he assige buge o each saegic eio whichh ca be use o oe aciliies a icease he caaciy o auacues. Eqs. (3)-(5) liis su o exee a uuse buge o assige buge o each eio. Eq. (6) iicaes ha each auacue ca acivae a os oe caaciy oio uig each saegic eio. This ac ha he auacues cao ocee oe ha hei caaciy is cosiee via Eq. (7). Eq. (8) liis he oal acivae caaciy o each auacue o axiu allowable isallable caaciy. The caaciy liiaios o ohe A 01 OD Ca ax 0 (5) (6) (7) (8) (9) (30) (31) (3) aciliies ae sae by Eqs. (9)-(31). Fially he ecisio vaiables ae cosiee i Eq. (3) Soluio aoach I his ae a e-cosai aoach is use i oe o ake a sigle-objecive oel. Also a ieialis coeiive algoih is esee o lage size obles Sigle-objecive oel I oe o have a sigle-objecive ucio oel a e-cosai aoach is use i his ae. Accoigly he oble is eoulae as a sigle-objecive ucio oel wih esec o objecive ucio wih os ioiy a he ohe objecive ucios ae cosiee as cosais [4]. Eq. (33) iicaes he eoulaio o oose oel. ax OF1 ( x) ax OF1 ( x) OF() x OF3() x s.. s.. OF ( x) e (33) Cosai s OF 3( x) e3 Cos ais whee e i is he esilo o ih cosai. Fially he ceae sigle-objecive oel shoul be solve o iee values o e i. I his ae o iove he eoace o soluio aoach a augee e-cosai eho is use [4]. Eq. (34) iicaes he oulaio o oose oel wih esec o his eho. Ieaioal Joual o Iusial Egieeig & Poucio Reseach Decebe 016 Vol. 7 No. 4

11 Cosieig Picig Poble i a Dyaic sl sl 3 ax z=1( x) Rage Rage3 s.. ( x) sl e (34) 3( x) sl3 e3 sli 0 (4) (3) whee Rage i iicae age o vaiaios o each objecive ucio. Base o [4] hese ages ca be calculae usig ayo able achieve via lexicogahy eho. Sl i iicaes slack o sulus vaiable o each objecive ucio. Usig Eq. (3) i e-cosai eho lea o oe o-oiae soluios a ecisio ake ca choose aog he [4] Aoxiae soluio aoach To solve lage size oble aoxiae eho such as ea-heuisic aoaches ca be A. Nobai A. S. Kheikhah & M. Esaeili 3633 use. I his ae a ieialis coeiive (ICA) aoach is esee Ieialis coeiive algoih The ieialis coeiive algoih is oe o he well-kow oulaio-base evoluioay algoihs has bee iouce by [43]. The ses o ICA ae as ollows: - Se 1: Iiializaio o he eies The is se is geeaigg N iiial couies which iclue N couies as ieialiss a i he ohe ae coloies. The sucue o soluio eeseaio is iicae i Figue 6 which iclues a 1 M D C R veco a he value o each cell is a iscee ube bewee 0 o N. This value iicaes he saegic eio i which he elae aciliy is oee a he zeo value eas he aciliy cao be oee uig he laig hoizo. The ohe ecisio vaiables ae eeie base o his veco. o Fig. 6. Soluio eeseaio x ~ U 0 (37) The he ube o coloies seize by each ieialis ca be calculae wih esec o he ~ U (38) owe o each ieialis. Eq. (35) calculaes he whee U. is a coiuous ao vaiable wih owe o each ieialis. Uio isibuio is isace aog coloy z P (35) a is ieialis a a ae wo Ni z aaees. i i1 - Se 3: Chagig osiio o coloy a whee z i is iess ucio o ih ieialis ieialis I a coloy eaches a bee osiio ahe ha which ca be calculae usig Eq. (34) a P i is is elaive ieialis he osiio o his coloy he owe o elae ieialis. The ube o a ieialis shoul be exchage. coloies o each ieialis ca be calculae - Se 4: Couig oal owe o usig Eq. ( 36). eies NC oupn col (36) The oal owe o each eie ca be calculae - Se : Movee o coloies owa usig Eq. (39). ieialis TP Pieia ( alis ) ea Pcoloies (39) The coloies o each ieialis will ove whee is less ha 1 a TP is oal owe o owa hei ieialis egaigg a eviaio. h eie. The value o ovee a eviaio ca be - Se 5: Coeiio aog eies calculae usig Eq. (37) a Eq. (38) I his se he os oweul eie seizes he esecively. weakes coloy o weakes eie. Ieaioal Joual o Iusial Egieeig & Poucio Reseach Decebe 016 Vol. 7 No. 4

12 364 A. Nobai A. S. Kheikhah & M. Esaeili - Se 6: Eliiaig eies wihou coloy I a eie loses all coloies i shoul be eliiae o he coeiio. - So cieio Cosieig Picig Poble i a Dyaic... I oly oe eie eais i he coeiio he algoih will be soe ohewise go o se. Figue 7 iicaes he lowcha o oose algoih. Fig. 7. Flowcha o ICA chaaceisicss o ueical exales ae 4. Nueical Resuls iicae i Table 3. I shoul be oe ha i all I his secio seveal ueical exales ae ueical exales i is assue ha L 5 a use o evaluae he oose oel. I his ae oe o hesee ueical exales is solve exacly usig a e-cosai eho a L 5. The aoly. ohe aaees ae geeae sesiiviy aalysis is cosiee. The Tab. 3. Chaaceisic o ueical exales Poble No. S M D K C R C' P' P O N T P P P P P P P P P P sigle-objecive oel usig Eq. (34). Table Exac solvig aoach Cosie a SCND oble o P3 which is chaaceisic is iicae i Table 3. Fis his iicaes axiu a iiu o seco a hi objecive ucios egaig lexicogahy eho. oble is oulae usig Eqs. (1)-(3). The he uli-objecive oel is asoe o a Tab. 4. Vaiaio o seco a hi objecive ucios Miiu value Maxiu value Rage o Nube o o objecive ucio o objecive ucio vaiaio esilos e 1 e e 3 OF OF hee iee levels ae cosiee o seco To solve he oose we use GAMS 4.5 sowae i which CPLEX solve is se. Also a hi objecive ucios. Table 5 iicaes he esuls o solvig oel o iee values Ieaioal Joual o Iusial Egieeig & Poucio Reseach Decebe 016 Vol. 7 No. 4

13 Cosieig Picig Poble i a Dyaic o e i. The oiu value o each objecive ucio egaless he ohe objecive ucios ca be obseve i Table 5 oo. Tab. 5. No-oiae soluios o ueical exale # Soluio Oiu OF1 value OF value OF3 value Sesiiviy aalysis To evaluaee he oose oel oe accuaely a sesiiviy aalysis is cosiee o soe aaees. - Sesiiviy aalysis o buge aaee A. Nobai A. S. Kheikhah & M. Esaeili 365 Figue 8(a) iicaes he vaiaio o ecooic a social objecive ucios wih esec o he vaiaio o he buge. Accoigly i ca be obseve ha iceasig he buge iceases he oi. I shoul be oe ha he gowh ae o oi will be ecease gaually because he ea o cusoe zoes ae ixe. So oly a oio o buge is equie o ee eas a he eaie buge ca be ivese. The covegece o e ea i Figue 8(a) cois his ac. Also Figue 8(a) iicaes ha ceasig o he buge leas o iceasig job oouiies ill he ea is e coleely. The eceage o use buge a ece o acivae o aciliies ae iicae i Figue 8(b). I ca be obseve i Figue 8(b) ha he eceage o he use buge will ecease gaually egaig ixe ea. I ac he exa buge will be ivese i ohe ojecs. The covegece i he ece o acivae aciliies assues his ac. Fig. 8. Sesiiviy aalysis o buge ae iicae i Figue 9 i which boh icease - Sesiiviy aalysis o ea aaee via iceasig he ea. The vaiaio o he ecooic objecive ucio a oal e ea wih esec o he ea Fig. 9. Sesiiviy aalysis o ea Figue 10(a) iicaes he eec o chagig - Sesiiviy aalysis o elasiciy o oi. Accoigly i ca be coclue coeicie o sellig a buyig ice ha iceasig i he elasiciy coeicie o sellig ice leas o a ecease i oi. Base Ieaioal Joual o Iusial Egieeig & Poucio Reseach Decebe 016 Vol. 7 No. 4

14 366 A. Nobai A. S. Kheikhah & M. Esaeili o Eq. (I) iceasig o euces he ossible age o oucs' icig a cosequely he e ea will be ecease Cosieig Picig Poble i a Dyaic... as show i Figue 10(b). I ac eeig he eas usig low ice is o eecive ecooically. Fig. 10. Sesiiviy aalysis o sellig ice coeicie euig use oucs a ecooic objecive Figue 11( (a) iicaes he eec o chage i ucio wih esec o chagig ae o eceage o eue a bough iicae i Figue 11( (b) a Figue 11(c) oucs. Base o Figue 11-a he iluece o esecively. I ca be obseve ha ceasig o he chages i elasiciy coeicie o buyig eceases buyig cos o use oucs a ice o eue a bough oucs is o cosieable. The vaiaios o he oal cos o iceases oi. Fig. 11. Sesiiviy aalysis o buyig ice coeicie Ieaioal Joual o Iusial Egieeig & Poucio Reseach Decebe 016 Vol. 7 No. 4

15 Cosieig Picig Poble i a Dyaic - Eec o yaic icig o oi I oe o coae yaic icig aoach wih saic oe seveal ueical exales which hei chaaceisic is iicae i Table 6 is use. The ecooic objecivee ucio o hese ueical exales is calculae o boh A. Nobai A. S. Kheikhah & M. Esaeili 367 o yaic icig echais a saic icig echais. I shoul be oe ha i saic icig aoach a cosai which eves chagig ices uig laig hoizo is ae o he oel. The esuls ae iicae i Figue 1. Tab. 6. Chaaceisic o ueical exales Poble No. S M D K C R C' P' P O L L' N T P P P P P wih esec o he size o he obles. Hece i Base o Figue 1 i ca be obseve ha he oi i case o yaic icig is oe ha sees ha yaic icig aoach is oe ecooic. saic case. Also his ieece will be icease OF1 o yaic icig OF1 o saic icig 0 P1 P P3 P4 P5 Fig. 1. Poi o yaic a saic icig aoach.4. Aoxiae aoach I his secio ueical exales ae solve usig ICA. I his ae he aaees o oose algoih ae ajuse usig Taguchi eho [44 45]. Base o Taguchi eho hee iee levels ae cosiee o aaees o ICA i his ae [46]. Table 7 iicaes hesee levels. The L7 Taguchi esig is cosiee o oose algoih usig Miiab sowae. Figue 13 iicaes he values o he sigal o oise o iee levels o aaees. Sice bigge value o he sigal o oise is esiable he oiu level o aaees is highlighe i Table 7. Tab. 7. Level o ICA aaees Paaee Level o Paaee Low Meiu High Poulaio size Nube o ieialiss Max I Movee ao ube Deviaio coeicie Iac aco o coloy Mea o SN aios Mai Eecs Plo (aaa eas) o SN aios Nube o oulaio Nube o ieialis Maxiu geeaio Rao vaiable Iluece coeicie Deviaio coeicie Sigal-o-oise: Lage is bee 3 1 Fig. 13. Taguchi esuls o ICA To evaluaee he eiciecy o ICA each ueical exale is oele usig Eq. (34). The he sigle-objecive oel is solve usig boh GAMS a ICA. The esuls o solvig ueical exales usig GAMS a ICA ae iicae i Table 8. 3 Ieaioal Joual o Iusial Egieeig & Poucio Reseach Decebe 016 Vol. 7 No. 4

16 368 A. Nobai A. S. Kheikhah & M. Esaeili Tab. 8. Resuls o solvig ueical exales via GAMS a ICA Poble No. P1 P P3 P4 P5 P6 P7 P8 P9 P10 I ca be obseve ha usig GAMS i secos leas o o soluio o P10 while he ICA achieves a soluio which iicaes he caabiliy o he oose algoih. Also coaig he esuls o GAMS a ICA iicaes ha hee is o sigiica ieecee aog he exac a aoxiae aoaches. I ac he oose ICA ca achieve acceable ea oiu soluios. Figue 14 iicaes he ecooic objecive ucios o each ueical exale solve by GAMS a ICA GAMS NA P1 P P3 P4 OF e-c Cosai ICA P5 P6 P7 P8 P9 P10 CPU ie o ICA Fig. 14. Resuls o ueical exale o ICA a GAMS 5. Coclusio I his ae a iegae uli-objecive oel o a close-loo SCND oble was esee. Fo sake o yais seveal saegic eios wee egae which ae chagig he sucue o suly chai ossible. Also icig ecisios i boh owa a evese logisics wee cosiee. Fially a augee e- cosai eho was use o ake sigle- objecive oel a a ieialis GAM ICA Cosieig Picig Poble i a Dyaic... coeiive algoih was esee o solve lage size obles. Sice he susaiable SCND oble is aee wiely uig las ecaes so eseig ohe objecive ucios o cosie evioeal a social coces is suggese as a exesio o his ae. Also cosieig uceaiy i he oose oel leas o oe ealisic a eliable esuls. Reeece [1] Choa S. & Meil P. Suly chai aagee: saegy laig a oeaios New Jesey: Peice Hall (007). [] Melo M. T. Nickel S. & Salaha-a-Gaa F. Faciliy locaio a suly chai aagee a eview Euoea joual o oeaio eseach Vol. 196 (009) PP [3] Sichi-Levi D. Kaisky a P. Sichi- he Levi E. "Desigig a aagig suly chai: coces saegies & cases New Yok: McGaw-Hill F. Ge M. Li L. & Paksoy (1999). [4] Aliaak T. A geeic algoih aoach o uli- chai objecivee oiizaio o suly ewoks Coues & Iusial Egieeig Vol. 51 (006) PP [5] Makui A. Tavakkoli-Moghaa R. & Ghoi-Avili M. A owa/evese suly chai ewok esig cosieig he isuio obabiliy o isibuio a collecio/isecio cees Ieaioal Joual o Iusial Egieeig & Poucio Maagee Vol. 6 (015) PP [6] Zajiaii Faahai R. Rezaou S. Deze T. & Fallah S. Coeiive suly chai ewok esig: A oveview o classiicaios oels soluio echiques a alicaios Oega Vol. 45 (014) PP [7] Faahi M. Mahoochi M. Govia K. & Moaa Husseii S.M. Dyaic suly chai ewok esig wih caaciy laig a uli-eio icig Tasoaio Ieaioal Joual o Iusial Egieeig & Poucio Reseach Decebe 016 Vol. 7 No. 4

17 Cosieig Picig Poble i a Dyaic Reseach Pa E Vol. 81 (015) PP [8] Ahi P.. & Seacy C. A aalysis o eics use o easue eoacee i gee a susaiable suly chais Joual o Cleae Poucio Vol. 86 (015) PP [9] Zhag S. O a oi axiizig locaio oel Aual o Oeaios Reseach Vol.103 No.1 (001) PP [10] She J.M. A oi-axiizig suly chai ewok esig oel wih ea choice lexibiliy Oeaios Reseach Lees Vol. 34 No. 6 (006) PP [11] Naguey A. & Naguey L.S. Susaiable suly chai ewok esig: a uli-cieia esecive Ieaioal Joual o Susaiable Egieeig Vol. 3 No. 3 (010) PP [1] Pishvaee M.S. Razi J. & Toabi S.A. Robus ossibilisic ogaig o socially esosible suly chai ewok esig: A ew aoach Fuzzy Ses a Syses Vol. 06 (01) PP [13] Bai H. Bashii M. & Hejazi T.H. Iegae saegic a acical laig i a suly chai ewok esig wih a heuisic soluio eho Coues & Oeaios Reseach Vol. 40 No. 4 (013) PP [14] Moa B. Goes M.I. Cavalho A. & Babosa-Povoa A. P. Towas suly chai susaiabiliy: ecooic evioeal a social esig a Plaig Joual o Cleae Poucio Vol. 105 (014) PP [15] Ahai-Javi A.. & Ghaali R. A eicie oiizaio oceue o esigig a caaciae isibuio ewok wih ice-sesiive ea Oiizaio a Egieeig Vol. 15 No. 3 (014) PP [16] Ahai-Javi A. & Hoseiou P. Icooaig locaio iveoy a ice ecisios io a suly chai isibuio ewok esig oble Coues & A. Nobai A. S. Kheikhah & M. Esaeili 369 Oeaios Reseach Vol. 56 (015) PP [17] Govia K. Jaaia A. & Noubakhsh V. Bi-objecive iegaig susaiable oe allocaio a susaiable suly chai ewok saegic esig wih sochasic ea usig a ovel obus hybi uli- & objecivee eaheuisic Coues Oeaios Reseach Vol. 6 (015) PP [18] Aas N. Akse D. & Goul Taugu A. Locaig collecio cees o iceive- olicy eee eus ue a ick-u wih caaciae vehicles Euoea Joual o Oeaioal Reseach Vol. 191 No. 3 (008) PP [19] Aas N. & Akse D. Locaig collecio cees o isace- a iceive- eee eus Ieaioal Joual o Poucio Ecooics Vol. 111 No. (008) PP [0] Dehghaia F. & Masou S. Desigig susaiable ecovey ewok o e-o-lie oucs usig geeic algoih Resouces Cosevaio a Recyclig Vol. 53 (009) PP [1] Tuzkaya G. Gulsu B. & a Osel S. A ehoology o he saegic esig o evese logisics ewoks a is alicaio i he Tukish whie goos iusy Ieaioal Joual o Poucio Reseach Vol. 49 No. 15 (011) PP [] Tavakkoli-Moghaa R. Jaaazaeh B. & Molla-Alizaea ew uli-objecive oel o a Zavaehi S. Desigig ocuee-oucio-isibuio ewok esig oble i a gee suly chai by a gaviaioal seach algoih Ieaioal Joual o Iusial Egieeig & Poucio Maagee Vol. 6 (015) PP [3] Neo J.Q.F. Bloeho-Ruwaa J. va Nue J.. & va Heck E. Desigig a evaluaig susaiable logisics ewoks Ieaioal Joual o Poucio Ecooics Vol. 111 No. (1998) PP Ieaioal Joual o Iusial Egieeig & Poucio Reseach Decebe 016 Vol. 7 No. 4

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