A new fuzzy mathematical model for green supply chain network design

Transcription

1 Internatinal Jurnal f Indutrial Engineering Cmutatin 8 (07) 5 70 Cntent lit available at GrwingScience Internatinal Jurnal f Indutrial Engineering Cmutatin hmeage: A new fuzzy mathematical mdel fr green uly chain netwrk deign Mhen Sadegh Amalnick and Mhammad Mahdi Saffar * Schl f Indutrial Engineering, Cllege f Engineering, Univerity f Tehran, Tehran, Iran C H R O N I C L E A B S T R A C T Article hitry: Received Aril 06 Received in Revied Frmat June 6 06 Acceted July 06 Available nline July 5 06 Keywrd: Cled l uly chain netwrk deign Envirnmental timizatin Multi bective fuzzy rgramming Oeratinal rik CO Emiin The envirnmental change caued by indutrial activitie have urred a ignificant interet in deigning uly chain netwrk by cnidering envirnmental iue uch a CO emiin. The ivtal rle f taking uncertainty and rik int accunt in cled-l uly chain netwrk ha induced numeru reearcher and ractitiner t devel arriate deciin making tl t ce with thee iue in uch netwrk. T deign a uly chain regarding envirnmental imact under uncertainty f the inut data and t ce with the eratinal rik, thi aer re a multi bective ibilitic timizatin mdel. The red mdel minimize traditinal ct uch a ct f rduct himent, urchaing machine and n, a well a minimizing the envirnmental imact, and a a reult trike a balance between the tw bective functin. Furthermre, in rder t lve the red multi bective fuzzy mathematical rgramming mdel, an interactive fuzzy lutin arach i alied. Numerical exeriment are ued t rve the alicability and feaibility f the develed ibilitic rgramming mdel and the uefulne f the alied hybrid lutin arach. 07 Grwing Science Ltd. All right reerved. Intrductin The uly chain i a netwrk f ulier, rductin center, ditributin center, cutmer zne and channel between different layer rganized t rcure raw material and cnvert them t the finihed rduct and tranrt final rduct t cutmer zne in an efficient way (Pihvaee et al., 0). In tday market, a trategically deigned uly chain rvide cmanie with cmetitive advantage. The mt imrtant trategic deciin in uly chain management (SCM) i Suly chain netwrk deign that lay a ignificant rle in bth ecnmic and envirnmental erfrmance f the uly chain. Suly chain netwrk deign rblem cnit f determining the lcatin, caacitie and number f netwrk facilitie and the material flw between layer f uly chain (Mel et al., 009). The cncern abut envirnmental iue caued by indutrie activitie, reult in gvernmental legilatin t decreae the detructive envirnmental imact caued by factrie and rganizatin. In ther wrd, gvernment and cnumer ut reure n cmanie t reduce the envirnmental imact f their activitie and rcee (Ilgin & Guta, 00; Meade et al., 007). Hence, * Crrending authr. Tel.: m.affar@alumni.ut.ac.ir (M. M. Saffar) 07 Grwing Science Ltd. All right reerved. di: 0.567/.iiec

2 6 in recent year reearcher and ractitiner fcu mre n envirnmental uly chain management. The envirnmental uly chain management r green uly chain management integrate envirnmental aect int SCM including bth frward (frm rduct deign) and revere (t end-flife management f ued rduct) uly chain netwrk. The ultimate aim i t cnider envirnmental iue in deciin making acr the uly chain, eecially the trategic deciin (Srivatava, 007; Lintn et al., 007). A it i mentined earlier, the deign and develment f the lgitic netwrk i a trategic deciin, it mean it effect will remain fr everal year. Cnequently, arameter uch a demand f cutmer, tranrtatin ct, rductin ct and envirnmental ct may change (Meeetchdee & Shah, 007). Therefre, the critical arameter are quite uncertain. Aart frm that, ince etablihing and cling a facility i a time needed and ctly activity, changing the facility lcatin i imible within a hrt time. Therefre, the uly chain netwrk deign rblem huld be mdeled cnidering realitic aumtin t vercme the rblem caued by determinitic mathematical mdel. Althugh, the uncertainty iue i mre ignificant in revere lgitic netwrk becaue in revere uly chain netwrk the quantity f returned rduct have t be faced with larger degree f uncertainty, the relevant literature indicate that mt f the wrk aume that the arameter f the uly chain netwrk are determinitic.. Literature review Baed n literature review, the cmmn mdel f revere uly chain netwrk deign are rereented a mixed-integer rgramming (MIP) mdel. The variety f thee mdel are frm imle uncaacitated mdel t cmlex caacitated multi-tage mdel. The bective functin f thee mdel are mtly aimed at reducing the ct f netwrk deign. Mel et al. (009), and Klibi et al. (00) cnduct a urvey n uly chain netwrk deign rblem t demntrate future reearch directin. Three earate reearch tream are intrduced a fllw... Revere uly chain netwrk deign Revere uly chain netwrk deign rblem cnit f the lcatin f cllectin, recvery, recycling center and caacitie f thee center and material flw between the layer f uly chain (Dekker & Fleichmann, 00). A initial wrk in revere uly chain netwrk deign rblem, Krikke et al. (999) red mathematical mdel. They re a MILP mdel fr a tw-tage revere lgitic netwrk. A number f metaheuritic algrithm were ued t vercme the cmlexity f thee mdel (e.g. Lee et al., 009) and al heuritic (e.g. Ara & Aken, 008) algrithm are red. Fleichmann et al. (997) intrduced a cmrehenive urvey n the alicatin f mathematical mdeling in revere uly chain management. Barr et al. (998) reented a MILP mdel fr a and recycling netwrk lved by a heuritic algrithm. Jayaraman et al. (999) reented a MILP mdel fr revere uly chain netwrk deign baed n cutmer demand fr recvered rduct. The gal f the reented mdel wa t minimize the traditinal ct. In thi area everal year later reearcher have develed mre cmlex mdel uch a multi-rduct (e.g. Mutha & Pkharel, 009) and multi-bective (e.g. Fneca et al., 00). Jayaraman et al. (00) develed their reviu wrk t mdel the ingle rduct twlevel hierarchical lcatin rblem cnidering the revere lgitic eratin f hazardu rduct. They al extend a heuritic t lve large-ized rblem. Pati et al. (008) intrduced a mixed-integer gal rgramming mdel fr aer recycling uly chain netwrk deign. The aim f bective functin are: () minimizing the itive deviatin frm the ecified budget () minimizing the negative deviatin frm the minimum lanned wate cllectin and () minimizing the itive deviatin frm the maximum limit f wateaer. Uncertainty in the quantity f returned rduct i the imrtant factr that huld be included in the deign f revere lgitic netwrk. Accrding t thi iue, Lite and Dekker (005) develed the rir wrk dne by Barr et al. (998) a tchatic mixed-integer rgramming mdel fr a and recycling uly chain netwrk deign.

3 .. Cled-l uly chain netwrk deign M. S. Amalnick and M. M. Saffar / Internatinal Jurnal f Indutrial Engineering Cmutatin 8 (07) 7 The deign f frward and revere lgitic netwrk ha a trng imact n the erfrmance f each ther. Thu, t avid the ub-timalitie caued by the earated deign, the deign f the frward and revere uly chain netwrk huld be integrated (Pihvaee et al., 00a; Fleichmann et al, 00). Salema et al. (007) tried t devel the Fleichmann et al. (00) mdel and uing tchatic mixed-integer rgramming arach under uncertainty. Lu and Btel (007) red a mixed-integer rgramming mdel including the bth frward and revere netwrk and their interactin imultaneuly. T lve the reented mdel a lagrangian-baed heuritic wa extended. Pihvaee et al. (00a) red a bi-bective mixed-integer linear rgramming mdel minimizing the ttal ct in a cled-l lgitic and maximizing the netwrk renivene. A memetic algrithm wa extended t lve the reented bi-bective MILP mdel. Thu, by integrated deign f frward and revere uly chain netwrk we al take the rfit reult and urt the whle life cycle f gd and rduct. General mdel (e.g. Wang & Hu, 00a) and cae-baed (e.g. K & Evan, 007) are red by reearcher. The imrecie nature f returned rduct caue a high degree f uncertainty in cled-l and revere uly chain netwrk deign rblem. T ce with thi uncertainty iue mt f the relevant aer alied tchatic rgramming arache (e.g. Pihvaee et al., 009; El-Sayed et al., 00). Becaue f the lack f hitrical data in real cae that i rarely available and the high cmutatinal cmlexity the ue f tchatic rgramming mdel eem t be imible in real cae. S, in recent year a few number f aer ued mre flexible arache uch a fuzzy rgramming (e.g. Wang & Hu, 00b)... Suly chain netwrk deign cnidering envirnmental iue Ilgin and Guta (00) reented a cmrehenive review n cmany' cnciu abut envirnment and rduct recycle and recvery; we have urveyed me affiliate aer that wrk n envirnmental uly chain netwrk deign. Since the end-f-life (EOL) gd and rduct have imrtant imact n envirnment thi ha make a need t extend and devel mdel fr revere uly chain (lgitic) netwrk deign. Additinally, a it een in relevant literature a thin art f wrk incrrate the envirnmental iue int uly chain netwrk deign deciin. Hug and Pitikul (005) reented a bi-bective mathematical rgramming mdel t cnit envirnmental imact in frward uly chain netwrk rblem. The red mdel maximizing the ttal rfit and mrever, minimize the envirnmental imact by alying LCA rincile. Fr electrnic equiment recycling netwrk a mdel wa reented by Quariguai Frta Net et al. (009) t minimize traditinal ct bective in additin t cumulative energy demand and wate. Frta Net et al. (008) red a bibective linear rgramming mdel fr frward uly chain netwrk deign cnidering envirnmental imact in Eurean ul and aer indutry. Hwever, the develed mdel i able t timize the quantity f flw between uly chain layer and ignre the ther deciin uch a determining the lcatin, number f facilitie and caacity f them. All f the mentined aer in the area f envirnmental uly chain netwrk deign avid the integrated deign f frward and revere netwrk and incrrating the envirnmental iue int deciin making mdel. Al, all f the abve mentined aer are incaable t mdel the uncertainty f arameter in uly chain netwrk deign rblem. Since uly chain netwrk deign and relevant MIP mdel belng t the cla f NP-hard rblem, great number f heuritic algrithm (e.g. Liteş & Dekker, 005) and meta heuritic uch a imulated annealing (e.g. Pihvaee et al., 00b), genetic algrithm (e.g. Min et al., 006), catter earch (e.g. Du & Evan, 008) tabu earch (e.g. Lee & Dng, 008) are alied and develed t lve thee mdel. T fill the literature ga, in thi aer we develed a ractical bi-bective fuzzy mathematical rgramming mdel fr uly chain netwrk deign rblem cnidering envirnmental factr that i able () t timize bth traditinal ct and envirnmental bective in the deign f the lgitic netwrk, () integrate the deign f frward and revere uly chain netwrk t neglect the ubtimalitie caued by earated deign f frward and revere lgitic () handle the uncertainty f arameter caued by incmletene r unavailability and imrecie nature f arameter.

4 8 Table Reviewed relevant article in uly chain netwrk deign Mdel ecificatin Obective Functin Oeratinal Rik Netwrk Deign Green Suly chain Revere arach Netwrk Flw Technlgy Tranrtati n Recycling Authr Ct CO emiin Fuzzine Multi rduct Multi Perid Caacity Cntraint Tardine Deficiency Prductin tranrtati n Revere ulier Ditributin Cllectin Recycling Recvery Recvery Frward backward Klibi et al. (00) Trabi & Haini (008) Pihvaee & Razmi (0) Pihvaee et al. (0) Pihvaee & Trabi (00) Wang et al. (0) Amin & Zhang (0) Chaabane et al. (0) Özkır (0) Sawik (0) Shaw et al. (0) Thi aer

5 M. S. Amalnick and M. M. Saffar / Internatinal Jurnal f Indutrial Engineering Cmutatin 8 (07) 9 Al, thi wrk ue an efficient lutin arach that i making a reanable tradeff between traditinal ct and envirnmental bective. Thu, amng the exiting wrk in the relevant literature the earlier mentined rertie, differentiate thi wrk frm ther wrk. In a hrt ntice, the ga amng mt relevant aer have been rereented in Table and thi aer indicate the ga it fill. El-Sayed et al. (00) develed a tchatic mixed integer rgramming mdel t integrating bth frward and revere uly chain netwrk deign under demand and returned rduct uncertainty. The bective functin i t maximize the ttal rfit. Hwever, there are tw mar drawback in uing tchatic arach: () fr uncertain arameter there i nt enugh hitrical data in many real cae, therefre, fr thee arameter we can rarely btain the exact and actual randm ditributin. Mrever, the chance cntraint increae ignificantly the cmutatinal cmlexity and () in mt f relevant reviu aer that wrk n revere uly chain netwrk deign, the uncertainty f arameter in thi rblem are mdeled thrugh cenari baed tchatic rgramming. S a large number f cenari ued in rerting the uncertain arameter lead t cmutatinally cmlex rblem. Fuzzy et thery a an arriate alternative rvide an arriate frame wrk t handle variu kind f uncertainty (Negita et al., 978). T the bet f ur knwledge that gain frm urveying the relevant literature, thi reearch i a rimary wrk alying the ibilitic timizatin arach in green cled-l uly chain netwrk deign area. Hwever, a few aer aly fuzzy timizatin arach fr frward and revere uly chain netwrk deign (e.g. Selim & Ozkarahan, 008; Pihvaee & Trabi, 00). Wang and Shu (007) red a ibilitic mdel fr the uly chain netwrk deign f a new rduct and mrever they alied a genetic algrithm t find near timal lutin. There are ther reearch wrk uing fuzzy arach in the cntext f lgitic lanning at tactical and eratinal level (e.g. Trabi & Haini, 008). The bective f thi reearch wrk i t devel a multi-bective ibilitic timizatin mdel fr a cled-l uly chain netwrk deign that integrate the deign f bth frward and revere uly chain netwrk under uncertain demand, returned rduct, caacitie, ct and delivery time. The bective f cncerned mdel include ttal ct minimizatin and minimizing the ttal tardine f delivered rduct. The main cntributin f thi reearch wrk that differentiate thi wrk frm the related exiting ne in the literature; can be ummarized a fllw: Pring an efficient and realitic new uly chain netwrk deign mdel that deign bth frward and revere uly chain imultaneuly mrever integrate the trategic deciin with tactical deciin in the cntext f cled l uly chain that cnider envirnmental imact in rductin center, recvery center, recycle center and himent. Thu, by thi red integrated mdel we can al avid the ub-timalitie caued by earated deign f the frward uly chain and revere uly chain and the earated deign between trategic deciin making rce and tactical level. T the bet f ur knwledge that gained frm urveying in the relevant literature there i n wrk cnidering bth f thee integratin and including envirnmental factr in a ingle mdel fr multi rduct and multi erid netwrk. (i.e. Pihvaee et al., 00a; Lee & Dng, 008) nly integrated the frward and revere uly chain but ignring the integratin f the trategic deciin and tactical level, And Pihvaee and Trabi (00) hwever cnidered bth f thee integratin but ignring the envirnmental factr and the red mdel frmulate uly chain fr ingle rduct hwever it eem mre realitic that uch a vat uly chain can rduce different kind f rduct with different demand and different rce time and rductin ct. On the ther hand, me reearch wrk (ee Shen, 007) integrate deciin making rcee in trategic level and tactical level but ignre integrating frward and revere uly chain deign. Pring a ibilitic rgramming timizatin mdel which handle different urce f uncertainty influencing cled-l uly chain by intly cntaining incmletene and imrecie nature f arameter. Deite the cae-baed mdel(e.g. Pihvaee & Razmi, 0) r reearch aer that nly mdel the recvery r recycling rce (e.g. Fleichmann et al., 00; Lee & Dng, 008; Üter et al., 007), thi aer reent a general and realitic netwrk that it can handling bth recvery and recycling rcee

6 50 with different technlgy in revere netwrk and al can cnider different tye f rductin technlgy in frward netwrk, and therefre can be ued t the different kind f indutrie (with ingle rduct r multi rduct) uch a vehicle (e.g. Üter et al., 007) and electrnic indutrie (e.g. Lee & Dng, 008). Mrever, ur red mdel al cntain a ecnd gru f cutmer that called recycled material cutmer. Ntably, many reviu wrk nly cnider the rduct cutmer and ignre the ecnd gru f cutmer. T the bet f ur knwledge it i the firt wrk that deign a general and realitic cled l uly chain netwrk cnidering envirnmental imact in rductin activitie, himent activitie, recvering and recycling rce imultaneuly and additinally integrate trategic deciin rce and tactical level. Briefly, thi wrk re a general and ractical and al realitic multi-bective ibilitic mdel fr integrating frward/revere uly chain netwrk deign envirnmentally that i able t: () integrate the deign f frward and revere netwrk in uly chain, a well a integrate trategic deciin level uch a facility lcatin and with tactical deciin like material flw ne at each erid, () a a general netwrk can handle recvery and recycling rcee with different technlgy in revere netwrk fr multi rduct uly chain,() a a facility f revere uly chain cnider the cutmer f recycled material,() allw t arriate trade-ff between tw imrtant bective functin,the cnventinal ttal ct and ttal CO emiin (a an imrtant envirnment factr) thrugh the different rcee(rductin, recvery, recycling and himent) in frward and revere uly chain and finally (5) handle different ytem uncertaintie and envirnment uncertaintie influencing the deign f cledl uly chain by cnidering incmletene r unavailability f arameter and imrecie nature f arameter that ued in the ibilitic rgramming arach. The rganizatin f thi aer i then a fllw. The cncerned rblem i defined in Sectin. And the multi-bective fuzzy mathematical rgramming mdel reented in thi ectin. The interactive lutin methd i reented in Sectin. The cmutatinal reult intrduced in ectin 5. Finally, the me directin fr future tudie and cncluding remark are reented in Sectin 6.. Prblem definitin The cled l uly chain netwrk reented in thi aer i a multi echeln, multi rduct and multi erid uly chain netwrk tye that include, ulier, rductin center, ditributin center, cutmer zne, cllectin center, recvery and recycle center and material cutmer. A new rduct, rduced by rductin center, i tranferred t the given cutmer zne via ditributin center t atify the demand f each cutmer zne and al the demand f cutmer mut be atified in each erid. Nted that the fuzzy ercentage f manufactured rduct in rductin center are wreck, and ince it aumed that the damage rduct cannt recgnize in netwrk, firt they delivered t the cutmer and then the cutmer turn them back t the cutmer zne and therefre the brand f cmany decreae and we define it a failure ct. If the caacity f rductin center i nt enugh fr manufacturing the needed rduct, they can urchae frm ulier and the urchaed rduct hied t the rductin center fr final acking. The fuzzy ercentage f urchaed rduct are wreck and likewie the fuzzy ercentage f them are hied t the rductin center with delay, and a it aumed in the mdel that all f demand mut be atified, the cutmer wait fr receiving the rduct and a enalty give t the cutmer, we define thi enalty a hrtage ct. Nted that cnequently the hrtage ct i a fuzzy arameter. The lcatin f ulier, rductin center, cutmer zne and material cutmer, are fixed and redefined. We al cnider multile caacity level fr ditributin center in each candidate lcatin. Ntably, ince different caacity fr facilitie in uly chain netwrk ha trng influence n the uly chain netwrk ct and it envirnmental imact, it i vital t cnider thi iue in mdeling (ee Amiri, 006). The tructure f cnidered cled l uly chain netwrk i illutrated in Fig.. In the revere flw, the ued rduct, which are deficient and are required t be fixed r recycled, cllected frm cutmer zne and in cllectin center they categrized in the

7 M. S. Amalnick and M. M. Saffar / Internatinal Jurnal f Indutrial Engineering Cmutatin 8 (07) 5 recverable r unrecverable gru by quality teting and diaembly activitie. The recverable rduct are hied t recvery center and craed rduct are hied t recycling facilitie. The recvered rduct then return t the ditributin center a t be ditributed amng cutmer zne. On the ther hand, craed rduct, after rceing in the recycle center and cnverting t the raw material, are hied in t the material cutmer t be ld a raw material and gain incme fr the netwrk. The cncerned netwrk in thi aer ha a general tructure which i able t handle bth recvery activitie and recycling activitie (a it can be een Fig.) and therefre can be ued by different kind f indutrie and firm uch a vehicle indutrie (e.g. Mel et al., 009) and electrnic indutrie (e.g. Du & Evan, 008). Becaue f incmletene r unavailability f data in real wrld rblem, eecially in trategic deciin rce, mt f the data embedded in uch frward and revere uly chain netwrk deign rblem have an imrecie nature. Thu, fr mdel the lack f knwledge abut thee ill-knwn data and arameter are reented by fuzzy number decribed by their ibility ditributin (ee Pihvaee et al., 009; Hann & Hitchcck, 009). By including multile erid in the red mdel we culd cnider a deciin hrizn and thu the flw quantitie between different layer f cled-l uly chain belnging t different echeln f uly chain are determined accrding t demand f cutmer zne, return and ther arameter at each erid. Aart frm that, thi mdel cnider multi cmmdity t endw different rganizatin and indutrie rducing multi rduct with the efficacy and alicability. Mrever, a mentined befre, thi mdel enable indutrie t trike a fair balance between ecnmic timizatin and envirnmental iue. Thi btained by cnidering CO emiin factr a an bective functin t be timized.by alying thi arach we can integrate the trategic level lcatin deciin rce and the tactical material flw deciin with cnidering revere flw and envirnmental factr (ee Frta Net et al., 008). Under abvementined aumtin the deciin t be addreed in, include determining lcatin and the number f required ditributin center, cllectin center, recvery and recycle center and the number f machine with uitable technlgy t be urchaed in rductin, recvery and recycle center, a well a aggregated material flw between cled l uly chain netwrk nde and their crrending tranrtatin mde. A mentined earlier, ur mdel incrrate the deciin abut tranrtatin mde and rductin technlgie in the trategic lgitic netwrk deign rblem. Our mtivatin fr uch incrratin ge back t ignificant imact f tranrtatin mde and rductin technlgie n ttal envirnmental imact a well a ttal ct f lgitic netwrk. Al, the integratin f uch tactical deciin with the trategic netwrk deign ne enure t ecae frm the ub timality reulting frm earated deciin making fr the tactical and trategic level deciin (ee Pihvaee et al., 00a; Shen, 007). Furthermre, when creating uch a green lgitic netwrk, it i imrtant t rvide an ecnmic and envirnmental trade-ff fr the deciin maker. Fr thi rean, it i mre deirable t frmulate bth f envirnmental and ecnmic aect a deign bective rather than cntraint. Therefre, the ultimate gal culd be exreed a determining the rblem deciin while making a reanable tradeff between thee tw cnflicting bective and atifying the ytem cntraint. The ther aumtin ued in the develed netwrk deign frmulatin are a fllw: Demand f each kind f rduct mut be atified and all f the returned rduct frm cutmer zne mut be cllected. In the frward flw f netwrk each kind f rduct are hied thrugh a ull mechanim. In the revere ide f netwrk returned rduct are hied thrugh a uh mechanim. The himent ytem ha different mde f tranrtatin with different ct and CO emiin. Lcatin f ulier, rductin center (lant), cutmer zne and material cutmer are fixed and redefined. A redefined ercent f reviu erid demand f each cutmer zne i aumed a returned rduct frm related cutmer zne in the current erid. A redefined ercent f returned rduct i aumed a recverable rduct.

8 5 Withut l f generality, multi rduct with different ecificatin (like rductin ct, demand, recvery ct, rate f return, fractinal rate, vlume and etc.) are mved thrugh the netwrk. The tructure f cnidered cled l uly chain netwrk i illutrated in Fig.. Sulier (i) Prductin center Ditributin center (r) Cutmer zne (k) Recvery center (m) Material cutmer (v) Recycle center (n) Cllectin center (q) Fig.. The integrated uly chain netwrk The fllwing ntatin are ued in the frmulatin f the red mdel:.. Indice and Set i Index f ulier i 0,,, I Index f different art 0,,, J r Index f candidate lcatin fr the ditributin center r 0,,, R v Index f fixed lcatin fr the material ctumer zne v,,, V k Index f fixed lcatin fr the ctumer zne k,,, K q Index f candidate lcatin fr the cllectin center q,,, Q m Index f candidate lcatin fr the recvery center m,,, M n Index f candidate lcatin fr the recycle center n,,, N z Index f caacity level available fr ditributin center z,,, Z l Index f different technlgie available fr rductin center l,,, L Index f different technlgie available fr recvery center,,, O Index f different technlgie available fr recycle center,,, S Index f available tranrtatin mde =,,,P t Index f time erid t=,,,t.. Parameter Ct.. Fixed Ct z H r Fixed ct f ening ditributin center r with caacity level z h q Fixed ct f ening cllectin center q r m Fixed ct f ening recvery center m f n Fixed ct f ening recycle center n

9 M. S. Amalnick and M. M. Saffar / Internatinal Jurnal f Indutrial Engineering Cmutatin 8 (07) 5.. Purchaing Technlgy l C Purchaing ct er machine with l technlgy in the lant C m C n Purchaing ct er machine with technlgy at recvery center m Purchaing ct er machine with technlgy at recycle center n.. Oerating l h Prducing ct er unit rduced in the lant with technlgy l m n Remanufacturing ct er unit at recvery center m with technlgy Recycling ct er unit at recycle center n with technlgy.. Shiing T i c r a rk b kq v qm mr w qn V nv Caacity Tranrtatin ct fr hiing ne rduct unit frm ulier i with tranrtatin mde Tranrtatin ct fr hiing ne rduct unit frm lant t ditributin center r with tranrtatin mde Tranrtatin ct fr hiing ne rduct unit frm ditributin center r t ctumer zne k with tranrtatin mde Tranrtatin ct fr hiing ne rduct unit f returned rduct frm cutmer zne k t cllectin center q with tranrtatin mde Tranrtatin ct fr hiing ne rduct unit f recverable rduct frm cllectin center q t recvery center m with tranrtatin mde Tranrtatin ct fr hiing ne rduct unit f recvered rduct frm recvery center m t ditributin center r with tranrtatin mde Tranrtatin ct fr hiing ne rduct unit f cllected rduct frm cllectin center q t recycle center n with tranrtatin mde Tranrtatin ct fr hiing ne recycled unit frm recycle center n t material ctumer zne v with tranrtatin mde.. Time l Ti Available time fr ne machine with l technlgy in the lant l Pt Time needed fr rducing ne rduct unit with l technlgy in the lant TM Available time fr ne machine with technlgy in the recvery center PTM Time needed fr recvering ne rduct unit with technlgy in recvery center TN Available time fr ne machine with technlgy in the recycle center PTN Time needed fr recycling ne rduct unit with technlgy in recycle center.. Vlume and Oerating C i Caacity f ulier i fr rducing art z VR r Available vlume fr keeing art f ditributin center r with caacity level z

10 5 CO Emiin.. Shiing t i CO equivalent emiin er rduct unit hied frm ulier i by tranrtatin mde r CO equivalent emiin er rduct unit hied frm rductin center t ditributin center r by tranrtatin mde J rk CO equivalent emiin er rduct unit hied frm ditributin center r t ctumer zne k by tranrtatin mde kq CO equivalent emiin er rduct unit hied frm ctumer zne k t cllectin center q by tranrtatin mde qm CO equivalent emiin er rduct unit hied frm cllectin center q t recvery center m by tranrtatin mde qn CO equivalent emiin er rduct unit hied frm cllectin center q t recycle center n by tranrtatin mde mr CO equivalent emiin er rduct unit hied frm recvery center m t ditributin center r by tranrtatin mde nv CO equivalent emiin er recycled unit hied frm recycle center n t material ctumer zne v by tranrtatin mde.. Oerating L CO equivalent emiin er rduct unit rduced by the lant with technlgy l l CO equivalent emiin er rduct unit recvered with technlgy CO equivalent emiin er rduct unit recycled with technlgy Rate q i De i kt r kt Fr Other i e C v Exected defect rate f ulier i in quality f art Exected delay rate f rduct tye urchaed frm ulier i Exected defect rate f the lant fr quality f art Rate f return ercentage rduct tye frm cutmer zne k at the time erid t The quantity f returned rduct tye frm cutmer zne k at the time erid t Rate f recverable ercentage rduct tye Quantity f material er unit rduct tye Ct er rduct unit urchaed frm ulier i Per unit failure ct fr the art Per unit hrtage ct fr the art Price er unit f recycled rduct red by material cutmer v

11 M. S. Amalnick and M. M. Saffar / Internatinal Jurnal f Indutrial Engineering Cmutatin 8 (07) 55 d kt V Demand f ctumer zne k fr rduct at time erid t Vlume f ne unit f rduct Deciin Variable.. Shiing x it y rt rkt kqt M qmt I qnt mrt U nvt Quantity f rduct art urchaed frm ulier i and tranfer t rductin center by tranrtatin mde at time erid t Quantity f rduct unit hied frm rductin center t ditributin center r by tranrtatin mde at time erid t Quantity f rduct unit hied frm ditributin center r t cutmer zne k by tranrtatin mde at time erid t Quantity f returned rduct unit hied frm cutmer zne k t cllectin center q by tranrtatin mde at time erid t Quantity f cllected rduct unit hied frm cllectin center q t recvery center m by tranrtatin mde at time erid t Quantity f cllected rduct unit hied frm cllectin center q t recycle center n by tranrtatin mde at time erid t Quantity f recvered rduct unit hied frm recvery center m t ditributin center r by tranrtatin mde at time erid t Quantity f recvered rduct hied frm recycle center n t material ctumer zne v by tranrtatin mde at time erid t.. Oerating and Purchaing l z t Quantity f rduct manufactured in the lant with technlgy l at time erid t l NM Number f urchaed machine with l technlgy in the lant m mt NM m i nt NN n Quantity f cllected rduct in recvery center m that recvered with technlgy at time erid t Number f urchaed machine with technlgy in recvery center m Quantity f cllected rduct in recycle center n that recycled with technlgy at time erid t Number f urchaed machine with technlgy in recycle center n.. Binary Variable = if a ditributin center with caacity level z i ened at lcatin r; 0, therwie z r = if a cllectin center i ened at lcatin q; 0, therwie z q m = if a recvery center i ened at lcatin m; 0, therwie n = if a recycle center i ened at lcatin n; 0, therwie

12 56 It huld be nted that arameter with a tilde n indicate arameter tainted with uncertainty. Thee cefficient are etimated by uitable ibility ditributin. In term f the abve ntatin, the cncerned rblem can be frmulated a fllw... Mdel Frmulatin Obective Functin A mentined in earlier, tw cnflicting bective functin are cnidered in the frmulatin f cled l uly chain netwrk deign rblem: () minimizatin f cnventinal ttal ct and () minimizatin f ttal envirnmental imact (CO emiin).. Firt Obective: Ct Obective The ttal ct f green cled l uly chain netwrk deign cntain the fixed ening ct f facilitie like ditributin center, recvery and recycle center and cllectin center, and variable rceing like rducing, recycling and reairing ct, and tranrtatin ct f flw between netwrk facilitie, and al urchaing machine in lant, recvery center and recycle center and hrtage r failure enalty that huld give t the cutmer (i.e., Ttal ct = Fixed ening ct + Tranrtatin+ Prceing ct+ Purchaed machine ct+ hrtage and failure ct). Thu, the firt bective functin can be frmulated a fllw. Min W= x. q. x. e De. x. x. T it i i it i it it i t i t i t i t l l l l l z z z. h NM. C z.. e y. c H. t t rt r r r l t l l t r t r z r k t i. a. b h. Z M. v rkt rk kqt kq q q qmt qm k q t q q m t I. w r. m. C. NM. qnt qn m m mt m m m mrt mr q n t m m t m m r t U V. f. i. C. NN U. C. () nvt nv n n nt n n n nvt v n v t n n t n n v t It huld be nted that the tranrtatin ct between netwrk facilitie are calculated by multilying the tranrtatin ct f ne unit f hiing rduct er unit f ditance (i.e., ne kilmeter) by the crrending ditance between tw facilitie.. Secnd Obective: Ttal Envirnmental Imact (CO emiin) The ttal CO emiin in the cncerned cled l uly chain, cme frm rceing activitie (uch a rducing unit, recvery and recycle activitie) and hiing art between different layer f uly chain. S, the ecnd bective functin can be frmulated a fllw.

13 M. S. Amalnick and M. M. Saffar / Internatinal Jurnal f Indutrial Engineering Cmutatin 8 (07) 57 l l min W xit. ti zt. L yrt. r rkt. J rk i t l t r t r k t. M. I. kqt kq qmt qm qnt qn k q t q m t q n t m. i.. U. () mt nt mrt mr nvt nv m t n t m r t n v t Cntraint r x it C, i,, t, rkt i d kt,,, t k, l l l l Z. Pt NM. Ti, l, t, t l x z = y,, t, it t rt i l r rt mrt m k q y, r,, t, rkt kqt rkt kt. d k ( t ), k,, t, M I, q,, t, kqt qmt qnt k m n. M, q,, t, kqt qmt k m M qmt q r mrt, m,, t, m M,, m, t, mt q qmt Caacity f ulier cntraint Demand atifactin cntraint Prceing time in rductin center cntraint Plant flw balance cntraint Ditributin center flw balance cntraint Cutmer zne flw balance cntraint Cllectin center flw balance cntraint Recverable ercentage cntraint Recvery center flw balance cntraint Prceing n each art hied in t recvery center cntraint () () (5) (6) (7) (8) (9) (0) () () Fr. I U, n,, t, qnt nvt q v i I,, t, n, nt q qnt Recycle center flw balance Prceing n each art hied in t recycle center cntraint () ()

14 58. V VR., r, t, z z rkt r r k z m mt. PTM TM. NM m, m,, t, Ditributin center caacity cntraint Prceing time in recvery center cntraint (5) (6) i nt. PTN TN. NN n, n,, t, z, r, r z kqt M. zq, q k t M NM M., m, qmt m m q t I i M., n, qnt nt n q t t Deciin variable cntraint (nn-negativity and binary retrictin) z, z,, 0,, r, z, q, m, n, r q m n x, y,,, M, I, Z,,, i, t, r, k, q, m, n, U it rt rkt kqt qmt qnt mrt nvt 0,, n, v, t, l l z, NM,m, NM,i,NN Z, l,, t,, m,, n. t mt m nt n Prceing time in recycle center cntraint Oening ditributin center with unique caacity cntraint Cllectin center cntructin cntraint Recvery center cntructin cntraint Recycle center cntructin cntraint (7) (8) (9) (0) () () () () Cntraint () enure that the caacity cntraint f all ulier are cnidered. Cntraint () enure that all cutmer demand mut be atified. Cntraint (5) guarantee that the rduct in the factry are nt mre than rductin caacity accrding t the available time f all technlgie. Cntraint (6), (7), (8), (9), (0), () and () trike a balance between what arrive and what leave in rductin center, ditributin center, cutmer zne, cllectin center, recvery center, and recycle center. Cntraint (0) al calculate the rate f deficiency in cmmditie in cutmer zne. Cntraint () and () aure that ne tye f technlgy in each center recver r recycle all cmmditie. Cntraint (5), (6), (7) define the caacity cntraint in ditributin, recvery, and recycling center. Cntraint (8) enure if ditributin center en in any lcatin, it can cntruct with nly ne caacity level. And finally cntraint (9), (0), () enure that n cmmdity i ent t a ditributin, recvery, r recycling center unle they are exit and al n machine urchaed fr recvery and recycle center unle they are exit.. The lutin methd Accrding t the uncertainty claificatin decribe in (Pihvaee & razmi, 0) in the uly chain netwrk deign rblem we are facing imrecie arameter, therefre, in the red uly chin netwrk deign mdel, ibilitic rgramming arach i alied t handle the uncertain arameter. In ibilitic rgramming arach each ill-knwn arameter in red mdel ha it ibility ditributin. The ibility ditributin fr each uncertain cefficient demntrate the ibility degree f ccurrence f ible value. It i neceary t exlained that the ibility ditributin i (5)

15 M. S. Amalnick and M. M. Saffar / Internatinal Jurnal f Indutrial Engineering Cmutatin 8 (07) 59 mtly ecified baed n exert knwledge r available data. Thu, the red uly chain netwrk deign mdel i a multi-bective ibilitic mixed integer rgramming, t lve the red mdel a tw-haed arach i alied. In the literature, t cnfrnting with ibilitic rgramming mdel a number f methd have been reented (e.g. Jiménez et al., 007; Lai & Hwang, 99). Amng the red methd in the literature, baed n detail belw the Jimenez et al. (007) methd i chen t handle the red mdel. Firt the Jimenez et al. methd can urt variu kind f memberhi functin uch a traezidal, triangular and al nnlinear memberhi functin ymmetric and aymmetric frm. Secnd t lve fuzzy linear rblem thi methd i cmutatinally efficient becaue it can retain linearity f red mdel and d nt increae inequality cntraint and al the number f bective functin. On the ther hand everal arache have been reented in the literature t lve the multi-bective rgramming mdel. Becaue f their ability in meauring and editing the atifactin degree f each bective functin, the mtly ued arache in thi dmain are fuzzy rgramming methd. Fuzzy rgramming arache vary frm reliminary arache (ee Lai & Hwang, 99; Sakawa et al., 987; Zimmermann, 978) t mre advanced methd (ee Trabi & Haini, 008; Li et al., 006). Fr lving red multi bective mdel we have alied -cntraint methd that it i ne f the fuzzy lutin methd. The main advantage f thi methd cmared with ther riri methd exlained ubequently. Baed n Hwang et al. (979) decritin, the -cntraint methd i knwn a a generatin methd r teriri that i able t reare uitable icture f whle Paret timal et fr manager and deciin maker. Then baed n Paret timal the deciin maker can elect the mt arriate lutin. Thu, accrding t cmrehenive infrmatin, all f the lutin are dicvered and the manager can make a deciin mre cnfidently. We refer the intereted reader t Ehrgtt (005) fr mre infrmatin n -cntraint methd. Briefly, in the firt te, t cnvert the red mdel int an equivalent auxiliary cri mdel the methd f Jimenez et al. (007) i alied. In the ecnd te, we have alied -cntraint methd (Ehrgtt, 005) t find the arriate lutin. The auxiliary cri mdel f the cnidered rblem baed n Jimenez et al. (007) methd can be frmulated a fllw... Auxiliary Cri Mdel m in W = i t i x m m m i i i qi qi q i e e e.. xit. it t i t De De De T T T. xit. xit. i t m m m i i i i i i m l l l m m l h hh l l l e e e zt. NM. C zt.. l t l l t m m z z z cr cr cr Hr Hr Hr z y rt.. r r t r z

16 60 m m ark ark ark bkq b kq bkq. kqt. rkt r k t k q t m m hq hq h q qm v vqm vqm. Zq M qmt. q q m t I m m wqn wqn wqn rm rm r m.. m qnt q n t m m m m m m mr mr mr m mt. Cm. NM m mrt. m t m m r t v v v. m m nv nv nv U fn fn f n nvt n n v t n n t m Cv Cv C v Cn.NN n Unvt.. n n v t m n n n. i nt. m m l l l ti ti ti L L L l min W = xit. zt. i t l t y m m r r r J rk J rk J rk. rkt. rt r t r k t m m kq kq kq qm qm qm. M qmt. kqt k q t q m t m m qn qn qn I qnt. mmt. q n t m t m m mr mr mr. mrt. nt n t m r t n v t ubect t i U. m nv nv nv nvt

17 M. S. Amalnick and M. M. Saffar / Internatinal Jurnal f Indutrial Engineering Cmutatin 8 (07) 6 r m m C i C i C i C i.., i,, t, x it m m d kt d kt d kt d kt rkt. +.,, t, k, m m m m l l l l l l l l l Pt Pt Pt Pt l Ti Ti Ti Ti Z t... NM..., l, t, l x z = y,, t, it t rt i l r rt mrt m k q y, r,, t, rkt m m rkt r kt rkt r kt kqt.., k,, t, M I, q,, t, kqt qmt qnt k m n m m... kqt M qmt, k m q,, t, m m... kqt M qmt, k m q,, t, M qmt q r mrt, m,, t, m M,, mt,, mt q qmt Fr. I U, n,, t, qnt nvt q v i I,, t, n, nt q qnt. V VR., r, t, z z rkt r r k z m m m m PTM PTM PTM PTM TM TM TM TM m mt NM m, m,, t, m m m m PTN PTN PTN PTN TN TN TN TN i nt NNn, n,, t, z, r, r z

18 6 M. z, q, kqt q k t M NM M., m, qmt m m q t I i M., n, qnt nt n q t t z, z,, 0,, r, z, q, m, n, r q m n x, y,,, M, I, Z,,, i, t, r, k, q, m, n, U it rt rkt kqt qmt qnt mrt 0,, n, v, t, nvt l l t mt m nt n z, NM,m, NM,i,NN Z, l,, t,, m,, n. 5. Cmutatinal exeriment T illutrate the validity f the reented mdel in thi reearch wrk and the alicability and uefulne f the alied hybrid lutin, everal numerical exeriment are examined and the reult are rereented in thi ectin. Becaue f the lack f data in thee mdel tw tet rblem with different ize are deigned baed n exert knwledge and available data gathered by Pihvaee and Trabi (00). The ize f tet rblem are hwn in Table. Table The ize f tet rblem Sulier Ditributin center Cutmer center Cllectin center Recvery center Recycle center Raw material cutmer Part tye Prductin technlgie Recvery technlgie Recycling technlgie Tranrtatin mde Caacity level Time erid Size T Z P S O L J V N M Q K R I S M The urce f randm generatin f the mt likely value hwn in Table. Ntably, cxi i tranrtatin ct f ne unit f hiing art er unit f ditance with tranrtatin mde and al gxi i amunt (Kg) f CO emiin f ne unit f hiing art er unit f ditance with tranrtatin mde. Baed n Lai and Hwang (99) decritin, fr rducing triangular fuzzy arameter firt the mt likely (c m ) value fr each cefficient generated by uing unifrm ditributin hwn in Table, and then tw number (r, r) are chen between (0., 0.8) randmly, and timitic int (c ) and eimitic int (c ) are calculated a fllw: c ( r). c m (6) c ( r ). c m (7)

19 M. S. Amalnick and M. M. Saffar / Internatinal Jurnal f Indutrial Engineering Cmutatin 8 (07) 6 Table Surce f randm generatin f the mt likely value arameter Randm ditributin arameter Randm ditributin z H r Unifrm (80000,60000) i Unifrm (,) h q Unifrm (80000,60000) C i Unifrm (,5) Z= U (80,00) Unifrm (00000,00000) z r Z= U (00,0) m VR r Z= U (0,0) f n Unifrm (50000,0000) V Unifrm(.,.7) P= U (0.08,0.) l C Unifrm (8000,000) cxi P= P= U (0.,0.) U (0.,0.6) P= U (0.6,0.8) P= U (.5,) C m Unifrm (000, 000) gxi P= P= U (,.5) U (.5,) P= U (,.5) C n Unifrm (000, 000) l L Unifrm (600,800) l h Unifrm (, 5) Unifrm (600, 800) m Unifrm (, ) Unifrm (600,800) n Unifrm (,) De i q i Unifrm (0.,0.) TM,TN Ti l, Unifrm (00,00) kt Unifrm (0.75,0.85) l Pt Unifrm (,.5) Unifrm(0.8,0.85) PTN PTM Unifrm(0.6,0.8) Fr Unifrm(0.7,0.8) e Unifrm(0,0) Unifrm(0,0) C v Unifrm(,) d kt Unifrm(80,50)

20 6 It huld be nted that fr calculating tranrtatin ct between tw facilitie f uly chain netwrk firt, fr each facility, we generate tw randm number uing unifrm ditributin between (0,00), and they indicate the length and width f crrending facility in crdinate (Amiri, 006). Secnd, we calculate the Euclidean ditance between tw facilitie. Third, tranrtatin ct between facilitie, fr each tranrtatin mde are calculated by multilying the crrending cxi (i.e., ne kilmeter) by the crrending Euclidean ditance between tw facilitie. Fr calculating the amunt f CO that emitted by each tranrtatin mde we can al multily the gxi by crrending Euclidean ditance between tw facilitie. T lve and analyze the erfrmance f the red ibilitic mdel, all f the mathematical mdel are cded in GAMS.. timizatin ftware and all tet are carried ut n an Intel cre i7.70ghz cmuter with GB RAM and the reult fr S ize rblem are rert in Table and fr M ize rblem are rert in Table 5. T carry ut the -cntraint methd, the CO emiin bective i ued a a ide cntraint and the ct bective i ket in the mdel a bective functin. In rder t erfrmance teting, different minimum accetable feaibility degree (i.e., level: 0.7, 0.8 and 0.9) are alied and the behavir f the bective functin baed n different level hwn in Fig. (fr S ize rblem) and Fig. (fr M ize rblem). A it can be een in Table and 5 ix Parettimal lutin are generated fr each level by the aid f the -cntraint methd (Ehrgtt, 005).A they are indicated in Fig. and Fig. when the minimum accetable feaibility degree ( level) i augmented the value f ct bective functin and CO emiin bective functin increae. Thu, a the manager decided t face uncertainty iue with a higher cnfidence level, the value f bth ct and CO emiin are al augmented becaue t atify demand and ther cntraint in higher level, need mre reurce. Accrding t the deciin maker and manager reference the value f level can be varied. By tudying the number f cntructed facilitie in Table and 5 we can btain that the firt bective functin fr minimizing the ttal ct ha a tendency tward lgitic netwrk centralizatin. Thu, at higher atifactin degree f ct bective functin cmared with lwer ne, le number f ditributin, cllectin, recvery and recycle center i ened. On the ther hand, the CO emiin bective functin t minimize the ttal CO emiin (envirnmental imact) ha a tendency tward decentralized uly chain netwrk. The reult culd be imly exlained when the ecnd bective i mre imrtant cmared with the firt ne fr deciin maker (in decentralized netwrk), becaue mre facilitie f uly chain netwrk are ened (cmared with centralized cnfiguratin), t tranrt rduct between tw facilitie, mre and rbably hrter ath are available therefre le CO emitted frm hiing activitie.

21 Table Paret-timal lutin accrding t the different level fr S ize rblem M. S. Amalnick and M. M. Saffar / Internatinal Jurnal f Indutrial Engineering Cmutatin 8 (07) 65 α level Obective functin value Satifactin degree Slvin Number f cntructed center Paret g time CO emiin (Kg) Ditributi Cllecti Recver Ct μ(w) μ(w) (ec) Recycle Prductin Tranrtatin Recvery Recycle n n y E E+0.5E+05.78E E+05.75E+0.86E+05.69E E+05.5E+0.68E+05.59E E+05.E+0.5E+05.57E E E E E+05 9.E+05 9.E+05 9.E E+05.08E+06.05E+06.0E+06.0E E E+05.E+0.68E E E+0 5. E+0.95 E+0.8 E+0. E+0 6.7E+0 5.8E+0 5.6E+0 5.E+0 5.8E+0.59E+0.E+05.E+05.56E+05.9E+05.8E+05.96E+05.9E+05.9E E+05.7E+05.6E+05.E+05.E+05.5E+05.5E+05.5E+05.95E+05.87E+05.8E+05.8E+05.80E+05.79E+05.5E+05.06E+05.99E+05.97E+05.9E+05.9E

22 66 Table 5 Paret-timal lutin accrding t the different level fr M ize rblem α level Obective functin value Satifactin degree Slvin Number f cntructed center Paret g time CO emiin (Kg) Ditributi Cllecti Recver Ct μ(w) μ(w) (ec) Recycle Prductin Tranrtatin Recvery Recycle n n y 7.E E E+06.E+07.9E E E+07.7E+06.86E+07.68E E+06 8.E+07.5E+06.67E+07.57E E E+07. E+06.57E+07.5E E E+07. E+06.50E+07.50E E E E+06.5E+07.E E E E+06.56E+07.99E E E E+06.9E+07.87E E E E+06.8E+07.8E E E E+06.07E+07.76E E E+07.8 E+06.9E+07.68E E E+07. E+06.90E+07.60E E+06.E E+06 5.E+07.5E E+06.07E E+06.97E+07.0E E+07.0E E+06.78E+07.99E E+07.0E E+06.9E+07.9E E E E+06.7E+07.85E E E+07.78E+06.0E+07.79E

23 M. S. Amalnick and M. M. Saffar / Internatinal Jurnal f Indutrial Engineering Cmutatin 8 (07) 67 Al it can be een in Fig. and Fig., the ct bective functin and CO emiin bective functin are in cnflict with each ther. It mean that increaing in ne f them lead t decreaing anther ne and vice vera. Ttally, it can be cncluded that the -cntraint methd i arriate and qualified methd fr lving the auxiliary cri mdel f uly chain netwrk deign rblem. Ntably if the number f bective functin are mre than tw, the ther MCDM methd uch a analytic hierarchy rce can be alied t et the bective weight Ct E+06.0E+06.0E+06.50E+06.60E+06.70E+06.80E+06.90E+06 CO Emiin (kg) α=0.7 α=0.8 α=0.9 Fig.. Senitivity Analyi f Different α Level fr "S" Size Prblem.50E+07.0E+07.0E+07 Ct.0E+07.0E+07.00E E+06 α=0.7 α=0.8 α= E E E+06.0E+08.0E+08.60E+08.80E+08.00E+08 CO Emiin (kg) Fig.. Senitivity Analyi f Different α Level fr "M" Size Prblem A it can be een in Fig. baed n available data the rean f mre than half CO emiin are rductin activitie. It huld be cnidered by deciin maker that if le CO emiin i mre deirable, it i lgical that invet n rductin center and urchaed machine with le rate f CO emiin. In ther language, baed n available data it eem the mt imrtant factr in air llutin i rductin activitie, invetigate n imrving rductin technlgy i ne f the iue that huld be cnidered by exert and reearcher.

24 68 % 59% 6% % 6. Cncluin Recycle Recvery Fig.. CO Emiin Percentage In recent year, envirnmental iue have becme an imrtant tic and reearcher invetigated rblem cnidering envirnmental imact. The deign f uly chain netwrk cnidering envirnmental imact i a very critical and cmlex deciin that frm in an uncertain and dynamic envirnment. Deite the at relevant aer, thi wrk integrate the deign f bth frward uly chain and revere uly chain beide cnidering the envirnmental imact in the uly chain. Since mt f the arameter in cled l uly chain netwrk have imrecie nature, a ibilitic rgramming arach i ued t mdel cled l uly chain. T lve the red mdel, an interactive fuzzy lutin arach i alied by cmbining Jimenez et al. (007) methd and cntraint (Ehrgtt, 005) methd. The effectivene f the develed fuzzy timizatin mdel a well a the uefulne f the alied lutin arach i invetigated thrugh randmly generated tet rblem. A it eem in the literature, the uly chain netwrk deign cnidering envirnmental aect i till carce. Thu, many ible future wrk directin can be defined in thi area. Fr examle addreing ther uly chain netwrk deign rblem uch a tactical and eratinal lanning rblem are attractive invetigate avenue with ignificant ractical relevance. Scial aect i nt addreed in thi wrk, hwever it i an imrtant iue regarding the uly chain utainability, hence anther attractive future reearch directin i incrrating the cial iue int uly chain lanning timizatin mdel. Since uly chain netwrk deign belng t the cla f NP-hard rblem eecially in large ized, develing efficient exact, heuritic r metaheuritic lutin methd can be aealing in thi cntext. Reference Amin, S. H., & Zhang, G. (0). A multi-bective facility lcatin mdel fr cled-l uly chain netwrk under uncertain demand and return. Alied Mathematical Mdelling, 7(6), Amiri, A. (006). Deigning a ditributin netwrk in a uly chain ytem: Frmulatin and efficient lutin rcedure. Eurean Jurnal f Oeratinal Reearch, 7(), Ara, N., & Aken, D. (008). Lcating cllectin center fr ditance-and incentive-deendent return. Internatinal Jurnal f Prductin Ecnmic, (), 6-. Barr, A. I., Dekker, R., & Schlten, V. (998). A tw-level netwrk fr recycling and: a cae tudy. Eurean Jurnal f Oeratinal Reearch, 0(), 99-. Chaabane, A., Ramudhin, A., & Paquet, M. (0). Deign f utainable uly chain under the emiin trading cheme. Internatinal Jurnal f Prductin Ecnmic, 5(), 7-9. Dekker, R., & Fleichmann, M. (Ed.). (00). Revere lgitic: quantitative mdel fr cled-l uly chain. Sringer. Du, F., & Evan, G. W. (008). A bi-bective revere lgitic netwrk analyi fr t-ale ervice. Cmuter & Oeratin Reearch, 5(8), Ehrgtt, M. (005). Multicriteria timizatin (Vl. ). Berlin: Sringer. El-Sayed, M., Afia, N., & El-Kharbtly, A. (00). A tchatic mdel fr frward revere lgitic netwrk deign under rik. Cmuter & Indutrial Engineering, 58(), -.

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