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1、AK是一家空调制造商，其面临的需求增长很快。预计2001年，其全国的需求在南部将为180,000单位，在中部为120,000单位，在东部为110,000单位， 在西部为100,000单位。Dryice在设计物流网络时，有四个备选的地点：NewYork, Atlanta, Chicago和San Diego。在这四个地点建厂，工厂的生产能力将要么为 200,000单位，要么为400,000单位。工厂的年固定运营成本及从工厂所在地生 产出产品并运往四个销售区域的生产和运输的单位成本如表所示。请为该设施网络的设计建立模型，并请对模型作简要说明。设定变量如下表所示：其中M11 M12等一系列值为0.1
2、变量，即可得到如下式子：New YorkAtlantaChicagoSan DiegoAnnual fixed cost of 200,000-u nit pla nt$6 millio nM11$5.5 millionM12$5.6millio nM13$6.1 millio nM14Annual fixed cost of 400,000-u nit pla nt$10 millio nM21$9.2millio nM22$9.3 millionM23$10.2 millio nM24East$211 x11$232 x12$238 x13$299 x14South$232 x21$212
3、 x22$230 x23$280 x24Midwest$240 x31$230 x32$215 x33$270 x34West$300 x41$280 x42$270 x43$225 x44min =6000000*m11 + 10000000*m21+211*x11+232*x21+240*x31+300*x41+5500000* m12+9200000*m22+232*x12+212*x22+230*x32+280*x42+5600000*m13+9300000*m 23+238*x13+230*x23+215*x33+270*x43+6100000*m14+10200000*m24+29
4、9*x14+2 80*x24+270*x34+225*x44;m11*200000+m21*400000=x11+x21+x31+x41;m12*200000+m22*400000=x12+x22+x32+x42;m13*200000+m23*400000=x13+x23+x33+x43;m14*200000+m24*400000=x14+x24+x34+x44;x11+x12+x13+x14=110000;x21+x22+x23+x24=180000;x31+x32+x33+x34=120000;x41+x42+x43+x44=100000;bin (m11); bin(m21); bin(
5、m12); bin (m22); bin(m13); bin (m23); bin(m14) ;bin (m24);通过运行LINGO得到如下结果：LINGO Solver Status LINGOlrSolver StatusModelILPGlobal OptVariablesonlinear： it a gers:2403uibili ty：0tr at ions：131Extended SolverStatusSolverB-and-EBest1.294Se+00SObJ Bmmd:1.2948006Steps：0Active：0State?j ectiva1 2943e+00aCon
6、straints otL： onliMar:-Nonzer osotal： online ar:Generator Men cry Used （X22-ELapsd Ewitim* （Kh：mn）： ss00:00:00VjidataGlobal optimal solutio n found.Objective value:0.1294800E+09Exte nded solver steps:0Total solver iterati ons:131VariableValueReduced CostM110.000000-6200000.M210.000000-0.1440000E+08X
7、110.0000000.000000X210.00000041.00000X310.00000031.00000X410.000000136.0000M120.000000-2500000.M221.000000-6800000.X12110000.00.000000X22180000.00.000000X32110000.00.000000X420.00000095.00000M130.000000-5400000.M230.000000-0.1270000E+08X130.00000021.00000X230.00000033.00000X330.0000000.000000X430.00
8、0000100.0000M141.0000006100000.M240.0000000.1020000E+08X140.00000027.00000X240.00000028.00000X3410000.000.000000X44100000.00.000000RowSlack or SurplusDual Price10.1294800E+09-1.00000020.000000-61.0000030.000000-40.0000040.000000-55.00000590000.000.00000060.000000-272.000070.000000-252.000080.000000-
9、270.000090.000000-225.0000如下表:New YorkAtlantaChicagoSan DiegoAnnual fixed cost of 200,000-u nit pla nt$6 millio n(0)$5.5 millio n(0)$5.6millio n(0)$6.1 millio n(1)Annual fixed cost of 400,000-u nit pla nt$10 million(0)$9.2millio n(1)$9.3 millio n(0)$10.2 millio n(0)East$211 (0)$232(110000)$238(0)$299(0)South$232(0)$212 (180000)$230(0)$280(0)Midwest$240(0)$230(110000)$215(0)$270(10000)West$300(0)$280(0)$270(0)$225(100000)总成本为：$129480000
