Genetic Algorithm Approach for Multiobjective Green Supply Chain Design

Transcription

1 Genei Algorihm Approah for Muliobjeive Green Supply Chain Design Li-Chih Wang,, Ming-Chung Tan, I-Fan Chiang, Yin-Yann Chen 3, Sheng- Chieh Lin, Shuo-Tsung Chen Deparmen of Indusrial Engineering and Enerprise informaion Tunghai Universiy Taihung, 40704, Taiwan, ROC Tunghai Green Energy developmen and managemen Insiue (TGEI) Tunghai Universiy Taihung, 40704, Taiwan, ROC. 3 Deparmen of Indusrial Managemen Naional Formosa Universiy Yunlin Couny, 63, Taiwan, ROC. Absra. This paper applies muli-objeive genei algorihm (MOGA) o solve a losed-loop supply hain nework design problem wih muli-objeive susainable onerns. Firs of all, a muli-objeive mixed ineger programming model apuring he radeoffs beween he oal os and he arbon dioxide (CO ) emission is developed o akle he muli-sage losed-loop supply hain design problem from boh eonomi and environmenal perspeives. The muli-objeive opimizaion problem raised by he model is hen solved. Finally, some experimens are made o measure he performane. Keywords: muli-objeive, genei algorihm, losed-loop, supply hain, mixed ineger Inroduion Reen years, arbon asse beame a riial subje o global enerprises. Global enerprises need o provide effeive energy-saving and arbon-reduion means o mee he poliies of Carbon Righ and Carbon Trade (Subramanian, e al., 00). In his senario, forward and reverse logisis have o be onsidered simulaneously in he nework design of enire supply hain. Moreover, he environmenal and eonomi impas also need o be adoped and opimized in supply hain design (Gunasekaran, e al., 004; Srivasava, 007). Chaabane, e al. (0) inrodue a mixed-ineger linear programming based framework for sus-

2 Names of he auhors ainable supply hain design ha onsiders life yle assessmen (LCA) priniples in addiion o he radiional maerial balane onsrains a eah node in he supply hain. The framework is used o evaluae he radeoffs beween eonomi and environmenal objeives under various os and operaing sraegies in he aluminum indusry. This paper applies muli-objeive genei algorihm (MOGA) o solve a losed-loop supply hain nework design problem wih muli-objeive susainable onerns. Firs of all, a muli-objeive mixed ineger programming model apuring he radeoffs beween he oal os and he arbon dioxide emission is developed o akle he muli-sage losed-loop supply hain design problem from boh eonomi and environmenal perspeives. Then, he proposed MOGA approah is used o deal wih muli-objeive and enable he deision maker o evaluae a greaer number of alernaive soluions. Based on he MOGA approah, he muliobjeive opimizaion problem raised by he model is finally solved. The remainder of his paper is organized as follows. Seion II inrodues he muli-objeives losed-loop supply hain model and he proposed MOGA. Experimens are ondued o es he performane of our proposed mehod in Seion III. Finally, onlusions are summarized in Seion IV. Muli-Objeive Closed-Loop Supply Chain Design. Problem saemen and model formulaion This seion will firsly propose a muli-objeives losed-loop supply hain (MOCLSCD) model o disuss he relaionship of forward and reverse logisis, he plan loaions of forward and reverse logisis, he apaiy of losed-loop logisis, and arbon emission issues. Nex, deision makers have o deermine he poenial loaion and quaniy of produion and reyling unis in forward and reverse logisis, furhermore, design he apaiy and produion ehnology level. Figure inludes poenial omponens of he forward and reverse logisis. Based on he proposed muli-objeive genei algorihm (MOGA) approah, he muli-objeive opimizaion problem raised by he model is finally solved. The assumpions used in his model are: () The number of usomers and suppliers and heir demand are known. () Seond marke is unique. (3) The demand of eah usomer mus be saisfied. (4) The flow is only allowed o be ransferred beween wo onseuive sages. (5) The number of failiies ha an be opened and heir apaiies are boh limied. (6) The reovery and disposal perenages are given.

3 Tile of your paper 3 Figure. The sruure of susainable losed-loop supply hain. The indies, inpu parameers, and deision variables are defined as follows: Indies s Index for maerial suppliers ( s,..., S) i Index for forward produion sages ( i,..., I) () i Se of poenial forward produion unis in eah sage i ( ( i),..., Num( i) ) (i,k) Poenial forward produion uni k in sage i, where k () i Index for end usomers (,..., C) j Index for reyling sages ( j,..., J ) ( j) Se of poenial reyling unis in eah sage j ( ( j),..., Num( j) (j,p) Poenial reyling uni p in sage j, where p ( j) l Index for apaiy expansion levels ( l,..., L) Index for ehnology levels (,..., T ) Parameers Cos relaed parameers p, sm p Purhasing os from maerial supplier and seondary marke rm s d ( jp, ) j Disposal os in poenial reyling uni p of sage j s, s, ( i, k)( i, k ) s k Transporaion os in forward logisis m, ( i, k ) m Produion os using ehnology level a poenial produion uni k in sage i and poenial reyling uni p in sage j s, s, ( j, p) s ( i, k) Transporaion os in reverse logisis b, ( ik, ) ( jp, ) b Fixed insallaion os of poenial produion and reyling uni, ( i, k ) l Capaiy expansion os of eah apaiy level using eah ehnology ype a poenial produion l and reyling uni Capaiy relaed parameers l ( i, k ) l Expanded apaiy amoun of apaiy level l using ehnology level a poenial produion uni k in sage i l l Expanded apaiy amoun of apaiy level l using ehnology level a poenial reyling uni p in sage j Supply & Demand relaed parameers

4 4 Names of he auhors rm s s Supply quaniy of supplier s sm s j Supply quaniy of seondary marke in eah sage j of reverse supply hain d r Demand quaniy of usomers Reyling quaniy of usomer Environmen relaed parameers pe, ( i, k ) pe Carbon emissions quaniy of insalling poenial produion uni k in sage i using ehnology level and insalling poenial reyling uni p in sage j using ehnology level pue, ( i, k) pue Carbon emissions quaniy of ehnology level a poenial produion uni k in sage i and reyling uni p in sage j e, e, ( i, k)( i, k ) e k Carbon emissions quaniy in forward logisis e, e, e ( i, k ) Carbon emissions quaniy in reverse logisis ( j, p) Logisi relaed parameers, ( i, k )( i, k ), k ;, ( j, p), ( i, k ) Minimum ransporaion quaniy in forward logisis and in reverse logisis Raio relaed parameers re Reyling perenage of usomer Disposal perenage of poenial reyling uni p in sage j dis ( jp, ) re ji Reovery perenage from sage j of reverse supply hain o sage i of forward supply hain Deision Variables Coninuous Variables,, ( i, k)( i, k ) k Transporaion quaniy in forward logisis,, ( i, k) Transporaion quaniy in reverse logisis ( j, p) p ( jp, ) Purhasing quaniy of poenial reyling uni p in sage j from seondary marke D ( jp, ) Disposal quaniy of poenial reyling uni p in sage j Binary Variables X, if poenial reyling uni k in sage i is open; X 0, oherwise. ( i, k) ( i, k) X, if poenial reyling uni p in sage j is open; X 0, oherwise. AC, if exising produion uni k in sage i expands apaiy level l using ehnology ; AC 0, oherwise. ( i, k) l ( i, k) l AC, if poenial reyling uni p in sage j expands apaiy level l using ehnology ; AC 0, oherwise. l l TA, if supplier s ships o exising produion uni k in firs sage of forward supply hain; TA 0, oherwise. TA, if exising produion uni k in sage i ships o exising produion uni k in sage i; A 0, oherwise. ( i, k)( i, k ) ( i, k)( i, k ) TA, if exising produion uni k in las sage of forward supply hain ships o usomer ; TA 0, oherwise. k TA, if usomer ships o poenial reyling uni p in firs sage of reverse supply hain; TA 0, oherwise. TA, if poenial reyling uni p in sage j ships o poenial reyling uni p in sage j ; TA 0, oherwise. ( j, p) ( j, p) TA, if poenial reyling uni p in sage j ships o exising produion uni k in sage i; TA 0, oherwise. ( i, k) ( i, k) k

5 Tile of your paper 5 Muli-Objeive Closed-Loop Supply Chain Design (MOCLSCD) Problem: The purpose of he MOCLSCD model aims o idenify he rade-off soluions beween he eonomi and environmenal performanes under several logisi onsrains. The eonomi objeive, F PC BC MC CEC TC DC, is measured by he oal losed-loop supply hain os. The environmenal objeive, F PCOE BCOE TCOE, is measured by he oal arbon (CO ) emission in all he losed-loop supply hain. Eonomi objeive ( F ):The eonomi objeive inludes he following oss. Toal maerial purhasing os (PC) rm () sm p p P ss, () k () s jj p ( j) Toal insallaion os (BC) b X b X (3) ii k ( I ) ( i, k ) ( i, k ) jj p ( J ) ( j, p ) ( j, p ) Toal produion os (MC) (4) m (5) ss k () T (, k) (6) m (7) (8) C p () T (, p) j I i k ( i) k ( i) T J j p ( j) p ( j) T m jj p ( j) ii k ( i) T ( i, k) ( i, k) Toal apaiy expansion os (CEC) (9) l AC ii k ( j) T (0) ll ( i, k) l ( i, k ) l ( i, k) l Toal ransporaion os (TC) l () s () ss k () m ( i, k)( i, k ) ( i, k)( i, k ) m ( j, p) ( j, p) l AC jj p ( j) T ll l l l s ( ) ( ) ( i, k)( i, k ) i k i k i (3) ( i, k)( i, k ) J (4) s C p () (5) s ( ) (, )(, ) ( j, p)( j, p) j p j p j p j p ( j, p) (6) s jj p ( j) ii k ( i) ( i, k) ( i, k) Toal disposal os (DC) (7) d D jj p ( j) ( j, k) ( j, k) Environmenal objeive ( F ): The environmenal objeive inludes following. Toal produion arbon emission (PCOE) (8) pue s S k () T (, k) s k ( i) k I (9) pue( i, k )( i, k ) ( i, k )( i, k ) (0) pue C p () T (, p) i k ( i) k ( i) T J () pue( j, p) ( j, p) j p ( j) p ( j) T () pue ( ) ( ) ( i, k) jj p j ii k i T ( i, k) Toal insallaion arbon emission (BCOE) pe X pe X (3) ii k ( I ) ( i, k ) ( i, k ) jj p ( J ) ( j, p ) ( j, p )

6 6 Names of he auhors Toal ransporaion arbon emission (TCOE) I (4) e (5) e i k i k i k i k ss C kφ() pψ() ikφ( i) (6) k Φ( i) (, )(, ) (, )(, ) (9) (, )(, ) (, )(, ) J (7) e (8) e j pψ( j) p Ψ( j) j p j p j p j p e kφ( I ) C k k Consrains Maerial supply onsrains rm sm (30), k Φ() ss s S (3) P ( j, p ) s j, j J, p Ψ( j) Flow onservaion onsrains (3),, i, k Φ ss jj pψ j j p i k k Φ i i, ki, k (33) e jj pψ( j) ii kφ( i) ( i, k) ( i, k),,, k Φ i i, k i, k jj pψ j j p i k k Φ i i, k i, k k ΦI i, k, i k j J p Ψ j j, pi, k C k i I k I C, C k Φ( I ) k (36), p Ψ( j) r C P D,,,, Ψ Φ,,, C j p p j j p j p j p ii k i j p i k j p pψ j j, p j, p j, p pψ j j, p j, p j, p ii kφi j, pi, k,,,, Ψ( ) p Ψ j j p P D j J p J j p j, p j, p ii k i j, p i, k, i, I, k Φ( i ) (34), Φ (35) (37) (38) (39) {}, Ψ() P D j,, J, p Ψ( j) C pψ( j) re,, ji,,,, {}, Ψ j p i k j p j p (40) D dis P,, j {}, p Ψ. (4) D dis jp P (, )(, ),, j,, J, p Ψ( j ). j p j p jp (4) P D i I j p kφi C (43) re P,,, D,,,,,, Ψ( ) k Φ i j p i k ji i I j J p j p Ψ j j, p j, p j p j p Capaiy expansion and limiaion onsrains (44) l AC, i {}, k Φ() (45) (46) (47) (48) ss jj pψ j j, pi, k T ll i, kl i, kl l AC, i,, I, k Φ( i ) k i i, k i, k jj pψ j j, pi, k T ll i, kl i, k l AC X i I k i T ll i k l ( jp, ),,, Φ( ) P l AC, j {}, p Ψ() (, ),, C j p T ll j pl j pl j p l ( jp, ) P l AC, j,, J, p Ψ( j ) p Ψ j j, p j, p j, p T ll j, pl j, pl (49) AC X, j J, p Ψ( j ) T ll, Transporaion onsrains (50) TA TA M, s S, k ()

7 Tile of your paper 7 (5) TA TA M i I k i k i i, k i, k i, k i, k i, k i, k i, k i, k,,,, Φ( ), Φ( ) (5) TA TA M, k Φ( I), C (53) TA TA M, C, p Ψ() k k k k (54),,,, Ψ( ), Ψ( ) j, p j, p TA j, p j, p j, p j, p TA M j J p j p j j, p j, p (55) TA TA M, j J, p Ψ j, i I, k Φ( i) j, p i, k j, p i, k j, p i, k j, p i, k Domain onsrains,,,,, P, D, N 0 s( i, k ) ( i, k )( i, k ) ( i, k ) ( j, p) ( i, k ), (56) s S, i I, k ( i), C, j J, P ( j) (57) X,,,,,,, AC( i, k ) l AC l TAs ( i, k ) TA( i, k )( i, k ) TA( i, k ) TA TA( j p), TA( i, k ) 0, s S, i I, k ( i), C, j J, P ( j). Muli-Objeive Genei Algorihm In his seion, a novel muli-objeive genei algorihm (MOGA) wih idealpoin non-dominaed soring is designed o find he opimal soluion of he proposed MOCLSCD model. Firs of all, he proposed ideal-poin non-dominaed soring for non-dominaed se is as follows. min min a. Calulae F F F F ( F, F) x i (, ) and he disane dis max min max min x F F F F i F F beween ( F, F ) and zero, where x i ( F, F) is an elemen in nondominaed se; F and F are he highes values of he firs and x i max seond max objeives among experimens; min F are F he lowes values of he firs min and seond objeives among experimens. b. Sor he disanes disx i, i. whih leads o he proposed MOGA in he following.. Chromosome represenaion for iniial populaion: The hromosome in our MOGA implemenaion is divided ino hree segmens namely Popen, Papaiy, and Pehnology, aording o he sruure of he proposed MOCLSCD model. Eah segmen is generaed randomly.. Flow assign and finess evaluaion: The flow assign beween wo sages depends on he values of he wo objeives F, F. Respeively, he flow wih minimum values of F, F simulaneously will be assigned firsly. On he poin of his view, he proposed ideal-poin non-dominaed soring is performed again on he prioriy of flow assign. The finess values of F and F are hen alulaed. 3. Crossover operaors: Two-Poin Crossover is used o reae new offsprings of he hree segmens Popen, Papaiy, and Pehnology.

8 8 Names of he auhors 4. Muaion operaors: The muaion operaor helps o mainain he diversiy in he populaion o preven premaure onvergene. 5. Seleion/Replaemen sraegy: The seleion mehod adops he mehod suggesed by Horn e al. (994) and Deb (00). 6. Sopping rieria: There are wo sopping rieria proposed. Due o he ime onsrains in he real indusry, he firs sopping rierion of he proposed MOGA approah is he speifiaion of a maximum number of generaions. The algorihm will erminae and obain he near-opimal soluions one he ieraion number reahes he maximum number of generaions. In order o searh beer soluions wihou ime-onsrain onsideraion, he seond sopping rierion is he onvergene degree of he bes soluion. While he same bes soluion has no been improved in a fixed number of generaions, he bes soluion may be onvergen and hus he GA algorihm is auomaially erminaed. 3 Experimenal resuls This seion gives he experimenal resuls. As an example, we implemen he MOGA approah on he MOCLSCD model wih 4 sages, 4 failiies in eah sage, 4 apaiy levels, and 4 ehnology levels. By 00 ieraions of MOGA, we obain he minimum os dollars and arbon emission kg. 4 Conlusions In his work, we firsly proposed a muli-objeives losed-loop supply hain (MOCLSCD) model. Nex, a novel muli-objeive genei algorihm (MOGA) wih ideal-poin non-dominaed soring is used o solve he model. Referenes Chaabane, A., Ramudhin, A. and Paque, M. (0). Design of susainable supply hains under he emission rading sheme. Inernaional Journal of Produion Eonomis, 35(), Deb, K. (00). A Fas and Eliis Muliobjeive Genei Algorihm: NSGA-II. IEEE Transaions on Evoluionary Compuaion, Vol. 6, No.. Gunasekaran, A., Pael, C. and MGaughey, R. E. (004). A framework for supply hain performane measuremen. Inernaional Journal of Produion Eonomis, 87(3),

9 Tile of your paper 9 Horn, J., Nafpliois, N., and Goldberg, D.E. (994). A Nihed Pareo Genei Algorihm for Muliobjeive Opimizaion. presened a he IEEE World Congress on Compuaional Inelligene. Subramanian, R., Talbo, B. and Gupa, S. (00), An approah o inegraing environmenal onsideraions wihin managerial deision-marking. Journal of Indusrial Eology, 4(3), Srivasava, S. K. (007). Green Supply-Chain Managemen: A Sae-of-he-Ar Lieraure Review. Inernaional Journal of Managemen Reviews, 9(),