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1、?27?1?2012?2?JOURNAL OF SYSTEMS ENGINEERINGVol.27 No.1Feb.2012?1,2,?2,?2,?1,?2(1.?,?200245;2.?,?200093)?:?,?,?,?.?,?.?:?;?;?;?:F406;TP29?:A?:10005781(2012)01005209Research on three-level supply chain coordinated planning withquantity discountMA Hui-min1,2,YE Chun-ming2,ZHANG Shuang2,XU Sheng-liang1,
2、XU Meng-jun2(1.Business School,Shanghai Dianji University,Shanghai 200245,China;2.Business School,University of Shanghai for Science and Technology,Shanghai 200093,China)Abstract:The problem of coordinated planning in manufacturing supply chain network with multi-supplier,multi-location plants,multi
3、-distributor,multi-product,multi-period and restricted capacity is studied.Amodel whose object is to minimize the total costs of production costs,production inventory costs,setup costs,transportation costs,ordering costs,material inventory costs and material purchasing costs under the systemcapacity
4、 restriction is put forward.A method based on knowledge evolution algorithm is proposed to solvethis problem.The example is presented.Simulation results of this paper demonstrates the effective of themodel and the method.Key words:three-level supply chain;coordinated planning;quantity discount;knowl
5、edge evolution algorithm1?,?,?,?,?1.?,?,?.?,?,?,?.?:20100603;?:20110518.?:?(09YJC630152);?(20093120110008);?(S30504);?(09YS486);?(10XKJ01).?1?:?53?.?2?,?,?;?3?,?;?4?;?5?,?;?6?,?;?7?,?;?8?,?,?;?9?.?.?;?,?;?,?.2?2.1?F?,J?,?I?,?,?.?1?.?T?,?,?,?1.?,?,?0.?.?1?Fig.1The structure of a three-level supply ch
6、ain network?,?:?,?,?,?,?.2.2?,?Min(T?t=1F?f=1I?i=1(PifQift+SifYift+HifIift)+I?i=1J?j=1T?t=1F?f=1UijftVjfEi+T?t=1I?i=1(GiXit+R(Oit)+KiWit)(1)54?27?s.t.Iif,t1+Qift Iift=J?j=1Uijft,i=1,2,.,I;t=1,2,.,T;f=1,2,.,F(2)Uijft=ZijftDijt,i=1,2,.,I;t=1,2,.,T;f=1,2,.,F;j=1,2,.,J(3)Wi,t1+Qit Wi,t=F?f=1Qift,i=1,2,.
7、,I;t=1,2,.,T(4)R(Oit)=rinOit,DISi,n1?Oit pk,j,r,fn,h,i,t0,?(n=1,2,.,N;h=1,2,.,Hn;i=1,2,.,I;k=1,2,.,K;t=1,2,.,T;j=0,1,.,J;r=0,1,.,R;f=0,1,.,F),(28)?R(0,1)?0,1?.2)?pbk,j,r,fn,h,i,t?,?k=0,?pbk,j,r,fn,h,i,t=xk,j,r,fn,h,i,t,?pbk,j,r,fn,h,i,t?(29)?.?gbk,j,r,fn,i,t?,?(30)?.pbk,j,r,fn,h,i,t=?pbk1,j,r,fn,h,i
8、,t,f(xk,j,r,fn,h,i,t)f(pbk1,j,r,fn,h,i,t)xk,j,r,fn,h,i,t,?,(29)gbk,j,r,fn,i,t=min(pbk,j,r,fn,h,i,t),(30)3)?1?:?57?,?(31)?.zk,j,r,fi,t=N?n=1gbk,j,r,fn,i,t/N,(i=1,2,.,I;k=1,2,.,K;t=1,2,.,T;j=0,1,.,J;r=0,1,.,R;f=0,1,.,F).(31)3.2.4?xk,j,r,fn,h,i,t?,?;?xk,j,r,fn,h,i,t?,?.3.2.5?(32)?(33)?.pk+1,j,r,fn,h,i,
9、t=0.5+c1(pk,j,r,fn,h,i,t 0.5)+c2(0.5 pbk,j,r,fn,h,i,t)+c3(0.5 gbk,j,r,fn,i,t)+c4(0.5 zk,j,r,fi,t),(32)g(pk+1,j,r,fn,h,i,t)=1,1?pk+1,j,r,fn,h,i,tpk+1,j,r,fn,h,i,t,0 pk+1,j,r,fn,h,i,t 10,pk+1,j,r,fn,h,i,t?0.(33)3.2.6?.?,?3.1?.4?,?2?5?.?,?,?.?2?Table2Production demand of each distribution center in eac
10、h period?1?2?3?123456123456123456117151613131817201215112018141319161621018181710141710161111181411161719183191814201911131013141319101519141715419141518111620141312121615151414131151513161613131414171316121220111414156181816201912121611151913121513161512?3?Table 3The original model parametersPifSif
11、HifaifbifiEiGiKif=1f=2f=1f=2f=1f=2f=1f=2f=1f=2122654411211412291244223845311811832261432314833410310824102921413624412010831132512513933512010922271112614924412810132172022?c1=c2=2,?100,?58?27?1 000;?N=9,Hn=11,K=1 000,c1=0.8,c2=0.05,c3=0.045,c4=0.095.?Intel Core2,2.4GHz?20?,?34 679,?34 818.65,?120.5
12、1,?0.003 5,?61s;?34 812,?35 035.05,?184.37,?0.005 3,?72s.?.?6?8?.?4?Table 4The distance from plants to distribution centers and the plant capacityVjfCftfj=1j=2j=3t=1t=2t=3t=4t=5t=616321 5001 5001 5001 5001 5001 50022461 5001 5001 5001 5001 5001 500?5?Table5Discount list of raw materials?1?2?3?4?10,1
13、00)10100,200)8200,300)6300,)520,80)1280,150)11150,220)9220,)830,90)1190,180)10180,300)8300,)740,70)1470,140)12140,210)11210,)1050,80)1380,170)11170,290)9290,)860,120)15120,230)14230,300)12300,)10?6?Table 6Lot-sizing of purchasing raw materials?12345612830000028001850003850188000426200000517500083061
14、310014100?7?Table7Lot-sizing of production of each plant?1?2?123456123456119100000920000022508600055099000385018800000000046400000198000005175000830000000652007700790064005?.?;?1?:?59?.?8?Table8The transportation number of each product from each plant to each distribution center?1?2?3?12345612345612
15、3456100000017201215112018141319161620000000016000141116171918?3191814201911131013141319101519141715?400000020000001515140001515131616131314141713161212201114141560000001200151901215131615121171516131318000000000000210181817101417100111118000000?3000000000000000000?41914151811160141312121600014131125
16、0000000000000000006181816201912016110013000000?:1?,?,?,?.?J.?,2009,18(3):123127.Ma Huimin,Ye Chunming,Xu Shengliang,et al.Research on multi-location plants capacitated lot-sizing problem based on particleswarm optimization algorithm J.Operation Reseach and Management Science,2009,18(3):123127.(in Ch
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20、in,Wang Ningsheng.Study on three-stage supply chain integrated planning based on GAJ.A Journal ofNanjing University of Aeronautics&Astronautics,2004,36(5):550555.(in Chinese)8 Syarif A,Yun Y S,Gen M.Study on multi-stage logistic chain network:A spanning tree-based genetic algorithm approach J.Comput
21、ers&Industrial Engineering,2002,43(2):299314.9?.?J.?,2009,24(03):329334.Dai Daoming.Coordination pricing and capacitated lot sizing problem in the case of market segmentationJ.Journal of SystemsEngineering,2009,24(03):329334.(in Chinese)10?,?,?.?J.?,2009,26(9):32823284.Ma Huimin,Ye Chunming,Zhang Sh
22、uang.Knowledge evolution algorithmJ.Application Research of Computers,2009,26(9):32823284.(in Chinese)11 Ma Huimin,Ye Chunming,Zhang Shuang.Knowledge evolution algorithm for capacitated lot sizing problemC/Proceedingof the Second International Joint Conference on Computational Sciences and Optimization.Piscataway:IEEE Service Center,60?27?2009:9991002.?:?(1981),?,?,?,?,?,?:?,E-mail:;?(1964),?,?,?,?,?,?:?,E-mail:;?(1980),?,?,?,?,?:?,E-mail:;?(1982),?,?,?,?,?:?,E-mail:;?(1988),?,?,?,?:?,E-mail:.*2011?(?)?