A Game-theoretical Approach for Job Shop Scheduling Considering Energy Cost in Service Oriented Manufacturing

Transcription

1 06 Inernaonal Conferene on Appled Mehans, Mehanal and Maerals Engneerng (AMMME 06) ISBN: A Game-heoreal Approah for Job Shop Shedulng Consderng Energy Cos n Serve Orened Manufaurng Chang-le TIAN, Guang-hu ZHOU * and Feng-an CHANG Shool of Mehanal Engneerng, X an Jaoong Unversy, X an 70049, Chna *Correspondng auhor Keywords: Serve-orened manufaurng, Energy os, Job shop shedulng, Nash equlbrum, Non-ooperave game. Absra. In serve-orened manufaurng mode, a large amoun of enerprses open her workshops o provde manufaurng serve, and produon ousourng and usomer sasfaon are wo rual manners o make profs. In serve orened manufaurng workshops, jobs ome from dfferen usomers. Compeve relaonshp among usomers should be nevably aken no aoun owng o he openness haraers of workshops and neress maxmzaon pursu of eah usomer. Moreover, beause of nreasng energy pre, arbon ax poly, arbon label poly, mos of usomers and manufaurng ompanes are urgenly eager o redue energy onsumpon o save os. Based on above-menoned requremens, n hs paper, a non-ooperave game model for job shop shedulng based on ndvdual profs maxmzaon n serve orened manufaurng envronmen s gven. I akes usomer s os as opmal objeves n whh energy os of manufaurng proess and ransporaon proess are onsdered. Fnally, one ase s arred ou o valdae he raonaly of he proposed model. Inroduon Serve-orened manufaurng mode has emerged as a novel and promsng manufaurng paradgm, whh s beng wdely appled n he global manufaurng ndusry. In serve-orened manufaurng mode, produon ousourng and usomer sasfaon are wo rual manners o make profs and realze value nremen []. Conreely speakng, manufaurng frms are wllng o open her workshops o provde manufaurng serve o make exra money. I s obvous ha hgher sasfaon from eah usom s soure for hem o wn he profs. In radonal Make o Sok produon mode, he manufaurers, wh he purpose of opmzng her own global objeves (makespan, os and so on), are poenally nlned o gnore he neress of paral usomers. However, as serve-orened manufaurng mode sprngs up, produon mode has been ransformed o Make o Order. In hs mode, eah usomer who plans o ousoure her jobs o serve-orened manufaurng enerprses furher hghlghs her own opmal profs (he probable lowes os, he possble earles delvery dae). In order o aommodae o hs new produon paern and aheve hgher sasfaon from eah usom, manufaurers are oblged o pay muh more aenon o maxmze profs of jobs of eah usomer. These jobs are proessed n hs new open serve-orened manufaurng job shop wh dsrbued manufaurng resoures or serves. However, beause of he openness and fneness of manufaurng resoures, s neessary for manufaurers o make eah len onend for manufaurng resoures so ha he greaes benef of ndvdual ould be aheved. Moreover, wh dramaally hange of global lmae, energy onsumpon of manufaurng draw publ onern. Aordng o ehnology a of European Unon abou radng energy nensve produs, for hna, s anpaed ha abou 80% produs whh exeed a gven energy onsumpon would be kep ou of EU []. Thus, s mperave for manufaurers and eah len o hghlgh he energy onsumpon faor relaed o her neress. Shop shedulng no only ould qukly and reasonably alloae he lmed manufaurng resoures so as o mprove mahnng effeny, qualy and so on, bu also ould opmze he requremens of usomers.

2 Therefore, n shop shedulng wh lmed shop resoures, how o maxmze eah usomer s ore neress onsderng energy onsumpon based on her ompeve relaonshp would be a new fous. In order o response o lmae hange, a grea many of leraures akng no energy and arbon emssons aoun abou job shop shedulng problems. He e al. [3] proposed an energy-responsve opmzaon mehod o opmze mahnng operaons and he dle energy onsumpon of mahne ools. Zhang e al. presened a model of low-arbon shedulng of he flexble job shop, esablshed a quanave arbon fooprn model of mul-job proessng, and pu forward hree arbon effeny ndaors. Song e al. [5] nrodued energy onsumpon faors no flexble job-shop shedulng problem wh manenane aves, amng a mnmzng maxmum ompleon me, oal produon energy oss and oal energy oss of manenane smulaneously. Sok e al. [6] esablshed a mul-objeve shop floor shedulng usng monored energy daa desrbed by energy-plannng daabase nludng relaed mahng operaons, proessng mahnes, and proessng parameers. All n all, an be learly seen ha hough many of sholars dsussed job shedulng ssue allowng for he envronmenally frendly faors, few sholars ondued sudy of shop shedulng n onsderng of energy onsumpon based on ompeve relaonshp among jobs. In vew of new haraerss of job shop shedulng, a non-ooperave game model for job shop shedulng s gven. Compared wh radonal shedulng model, he proposed novel shedulng model drven by he demands of lens, onenraes on he ompeve relaonshps o aan maxmum of profs of eah usomer. The goal of hs model s he oal os nvolvng energy os n manufaurng proess and ransporaon proess, manufaurng os, ransporaon os and penaly os under he onsran of due-dae. To ge he opmal shedulng resuls, a gene algorhm s adoped o fnd an approxmae Nash equlbrum (NE) pon of he model. Model Desrpon Energy Consumpon Model In a serve orened manufaurng workshop, here are N jobs need o be proessed and eah job has n sequened operaons. The produon of an operaon nvolves many manufaurng aves. These manufaurng aves, suh as sar and sop proess, ung proess, ools hangng proess and ransporaon proess, are losely relaed o he energy onsumpon. However, n hese proesses, he proess of sar and sop and he proess of ools hange susan a shor perod of me whh s dfful o measure hese mes. So, an average negraed power s used o alulae he energy onsumpon whn he omprehensve proess me. The manufaurng energy onsumpon CE of operaon j of job s shown n Eq. () j CE = P () j j jk Obvously, he manufaurng energy onsumpon CE of job ould be expressed n Eq. () CE n = CEj () j= The ransporaon proess energy onsumpon CE of job s alulaed wh Eq. (3) n = v j, j j= CE P p (3) Where jk denoes he proessng me of operaon j of job on mahne k, P j denoes he average negraed power of operaon j of job on mahne k, P v denoes he power of vehles,

3 p j, j denoes ransporaon me beween mahne j and j. Therefore, he energy onsumpon of job s he sum of energy onsumpon of manufaurng proess and ransporaon proess, as shown n Eq. (4) CE = CE + CE (4) Non-ooperave Game Model for Job Shop Shedulng The whole framework of he model s shown n Fgure, here are N usomers and eah usomer has one Job whh nludes a sequene of operaons. These Jobs need o proess n he workshop G, whh nludes r dsrbued mahnes and g vehles used o ranspor job. Eah usomer hoose s sraegy s by dedng mahne for eah operaon so ha s own payoff aheve he bes. The payoff of usomer affeed no only by s own sraegy bu also oher N- usomers seleable sraeges beause of varous proess sequenes. In hs model, he players refer o he jobs submed by relaed usomer, he sraeges of eah job refer o he seleable mahnes relaed o he operaons of hs job, and he payoff of eah job refers o oal os. Job Job Job N Job Job Job N Sraeges profes Job Job Job N Nash profes Payoff Payoff Payoff N Fgure. The framework of he model. The non-ooperave model s made up of players, sraeges, and payoffs. The proposed model an be desrbed as he form G ( W, H, Y).Spefally n hs model, W represens players, namely N usomers. H represens sraegy adoped by eah player ha s he seleable mahnes for eah usomer, ha s X, X = X X X n, X denoes sraegy se of J. Y represens he se of payoffs funon for players. For hs model, eah player has s pay-off funon, ha s: Manufaurng os pay-off funon: n n a d b d U ( x) = = rk jk + r max{0,( )} + r max{0,( )} + p p k, k + j= k= (5) Energy os pay-off funon: n n ( ) = j jk r + v j, j r j= j= (6) U x P q P p q The oal payoff funon s: U = U + U (7) x = x,, xn x X and subje o: Where ( )

4 d ( x) = (8) s ( x ) + ( x ) = ( x ) (9) jk jk jk p, =,, N. j =, n. k =,, M (0) s jk ( j+ )(k + ) k, k + s ( x ) ( x ),, q =, N. j =, n, l =, n. k =, m () Where jk qlk q mahne k, s jk denoes he sar me of O j on mahne k, jk denoes he ompleon me of O j on denoes he fnsh me of job, d denoes he due dae of job, r k denoes he proess pre on mahne k, r denoes he un pre of ask due o pospone delvery me, b un pre of ask due o nvenory os aused by delvery me n advane. r elery, p denoes he pre of ransporaon of job. a r he q denoes he pre of Equaon (8) ensures he onsran of delvery of J n serve orened manufaurng envronmen. Formula (9), (0) ensure he onsran ha one operaon mus be proessed only on one mahne a a me. And nequaly () guaranees he onsran ha one mahne mus proess only one operaon a a me. In a word, eah player wans o mnmze s payoff-funon value and nrease opponen s payoff-funon value. s he ore of he model o balane he neress of eah player o oban opmal shedulng resul. For hs non-ooperave game model for job-shop shedulng, n he Nash Equlbrum pon, he opmal shedulng resul sasfes he followng nequaly (). Therefore, he problem seekng he opmal shedulng resul wll be ransformed no he queson, namely alulang he Nash equlbrum pon of he model. U ( x, x, x, x, x +,, x ) U ( x, x, x, x, x +,, xn ) N x X, =,,N () Smulaon Case Frs, a smulaon ase s desgned. The nal relaed daa s gven n Table. In erms of eah ell n he Table, onans hree groups of daa, and a group of daa s enrled by a par of quadrae parenheses. The upper group daa means he seleable mahne ools of operaon O, he seond se of daa means he proessng me orrespondng o he seleable mahne, and he hrd se of daa means he proessng power orrespondng o he seleable mahne. Furhermore, ransporaon me beween wo mahnes s shown n Table. The number,, 8 lsed n he frs olumn and n he frs row respevely represens he ID of eah mahne. Eah elemen n Table denoes ransporaon me alulaed by he rao of he ransporaon dsane and ransporaon speed beween mahnes. In addon, he proessng pre of eah mahne s shown n Table 3. In addon, Table 4 gves he dealed parameers of eah job, nludng he delvery dae, ardness penaly, earlness penaly, and pre of ransporaon. j

5 Table. Soure daa of he smulaon ase. J J J J 3 J 4 J 5 J 6 J 7 J 8 operaons [,5] [3,] [3,5] [4,] [,6] [3,6] [3,7] [7, 6] [,8] [,6] [] [5,8] [7,7] [,5] [,8] [9,8] [5,3] [3,] [4,6] [8,5] [,6] [4,6] [8,6] [3,5] [,7] [8,7] [5,3] [,3] [5,4] [,5] [7,5] [4,] [8,7] [,7] [7,7] [4,7] [,8] [7,5] [] [3] [4,7] [9,5] [7,7] [5] [6] [3] [8] [,] [3,7] [3,] [,7] [7,5] [,5] [5,8] [,3,7] [5,8,7] [5,4,3] [,,4] [8,7,6] [5,3,4] [8,7] Table. The ransporaon me beween wo mahnes. [,3,8] [5,6,6] [,3,3] [3,6] [,7] [3,5] [,8] [,] [,7 [9,8] [,8] [8,6] [,6] [4,] [5,8] [6] [3] Mahne Table 3. The proessng pre of eah mahne per hour. Mahne Pre(RMB/hour) Table 4. The dealed parameers of eah job. J J J3 J 4 J5 J6 J7 J8 Job Delvery dae(/h) Tardness penaly (RMB/h) Earlness penaly (RMB/h) Pre of ransporaon (RMB/h) 3 3

6 J Table 5. The payoff value of jobs n s and he equlbrum generaon. s generaon / RMB payoff The equlbrum generaon / RMB J J 39 4 J J J J J J Compared wh he s generaon, os of eah job noably derease n Equlbrum generaon and eah usomer s wllng o hange her sraegy, so an approxmae NE s found and aepable. Summary In hs paper, foremos, he haraerss of shop shedulng n serve-orened manufaurng envronmen s elaboraed and s dsnon wh radonal shedulng s denfed. In addon, he energy onsumpon onsdered n he arle nludes wo ypes, namely he energy onsumpon of ung proess and he energy onsumpon of ransporaon proess among mahnes. More mporanly, based on hose haraerss, a novel non-ooperave game model for job shop shedulng n serve-orened manufaurng envronmen s pu forward, whh akes he faors of energy os no aouns. Fnally, a ase s appled o demonsrae he raonaly and feasbly of he proposed model. Insead of fousng on overall energy onsumpon, from he perspeve of usomers, redung os s possble. The nex sep for hs researh feld wll pay more aenon o he mehod n how o alloae he dle energy onsumpon o usomers n serve-orened manufaurng envronmen. Aknowledgemen Ths researh s suppored by he Naonal Naural Sene Foundaon of Chna (gran no ). Referenes [] Lang, P., Sun, Y. & L, W.,Year.Serve-orened manufaurng nformaon sysem: Conep, arheure and fous of fuure researhed. Inernaonal Conferene on Serve Sysems and Serve Managemen. [] hp://xh.xhby.ne/mp/hml/008-08/8/onen_8436.hm. [3] He, Y., L, Y., Wu, T. & Suherland, J.W.An energy-responsve opmzaon mehod for mahne ool seleon and operaon sequene n flexble mahnng job shops,journal of Cleaner Produon, 87 (05), Zhang, C., Gu, P. & Jang, P. Low-arbon shedulng and esmang for a flexble job shop based on arbon fooprn and arbon effeny of mul-job proessng, Proeedngs of he Insuon of Mehanal Engneers Par B Journal of Engneerng Manufaure, 9 (04),

7 [5] Song, W.J., Zhang, C.Y., Ln, W.W. & Shao, X.Y.Flexble job-shop shedulng problem wh manenane aves onsderng energy onsumpon,appled Mehans & Maerals,5 (04), [6] Sok, T. & Selger, G.Mul-objeve shop floor shedulng usng monored energy daa, Proeda CIRP, 6 (05), Zhou, G., Jang, P. & Huang, G.Q.A game-heory approah for job shedulng n neworked manufaurng,the Inernaonal Journal of Advaned Manufaurng Tehnology, 4 (009),