运筹学实验一线性规划求解、运输问题、整数规划求解

西华大学上机实验报告课程名称：运筹学年级/专业：2009水利水电工程实验成绩：指导教师：施浩然姓名：丁冬冬实验日期：2011年11月实验名称：线性规划求解、运输问题、整数规划求解学号：312009080801417实验学时：3一、实验目的掌握线性规划求解的基本方法，熟悉灵敏度分析的步骤和内容；掌握运输问题的模型，概念，求解方法；掌握整数规划的算法。在熟悉lingo软件基本功能基础上，能熟练操作，正确完成模型求解过程及分析过程。二、实验内容或设计思想1．lingo软件和运筹学实验软件的安装及菜单熟悉了解.2．lingo软件和运筹学实验软件应用内容之：任选几种不同类型的LP输入计算程序，运行求解；完成产销平衡的运输问题求解；求解任一整数规划。三、实验环境与工具计算机，lingo软件，运筹学软件四、实验过程或实验数据1、用lingo求解线性规划某家具公司制造书桌、餐桌和椅子，所用的资源有三种：木料、木工和漆工。生产数据如下表所示：

每个书桌每个餐桌每个椅子现有资源总数木料7单位6单位1单位46单位漆工4单位2单位1.5单位20单位木工2单位1.5单位0.5单位8单位成品单价50单位30单位20单位

若要求桌子的生产量不超过5件，如何安排三种产品的生产可使利润最大？用DESKS、TABLES和CHAIRS分别表示三种产品的生产量，建立LP模型。max=50*desks+30*tables+20*chairs;7*desks+6*tables+chairs<=46;4*desks+2*tables+1.5*chairs<=20;2*desks+1.5*tables+.5*chairs<=8;tables<=5;Globaloptimalsolutionfound.Objectivevalue:272.0000Totalsolveriterations:2VariableValueReducedCostDESKS0.0000006.000000TABLES1.6000000.000000CHAIRS11.200000.000000RowSlackorSurplusDualPrice1272.00001.000000225.200000.00000030.00000012.0000040.0000004.00000053.4000000.0000002、用LINGO软件计算运输问题6个发点8个收点的最小费用运输问题。产销单位运价如下表。单位销地运价产地B1B2B3B4B5B6B7B8产量24953858255A35219743357A476731127143A52395726541A65522814352销量3537253241364338

使用LINGO软件，编制程序如下：model:sets:warehouses/wh1..wh6/:capacity;vendors/v1..v8/:demand;links(warehouses,vendors):cost,volume;endsetsmin=@sum(links:cost*volume);@for(vendors(J):@sum(warehouses(I):volume(I,J))=demand(J));@for(warehouses(I):@sum(vendors(J):volume(I,J))<=capacity(I));

data:capacity=605551434152;demand=3537223241324338;cost=626742954953858252197433767392712395726555228143;enddataendGlobaloptimalsolutionfound.Objectivevalue:638.0000Totalsolveriterations:16VariableValueReducedCostCAPACITY(WH1)80.000000.000000CAPACITY(WH2)55.000000.000000CAPACITY(WH3)57.000000.000000CAPACITY(WH4)43.000000.000000CAPACITY(WH5)41.000000.000000CAPACITY(WH6)52.000000.000000DEMAND(V1)35.000000.000000DEMAND(V2)37.000000.000000DEMAND(V3)25.000000.000000DEMAND(V4)32.000000.000000DEMAND(V5)41.000000.000000DEMAND(V6)36.000000.000000DEMAND(V7)43.000000.000000DEMAND(V8)38.000000.000000COST(WH1,V1)8.0000000.000000COST(WH1,V2)2.0000000.000000COST(WH1,V3)6.0000000.000000COST(WH1,V4)7.0000000.000000COST(WH1,V5)4.0000000.000000COST(WH1,V6)2.0000000.000000COST(WH1,V7)9.0000000.000000COST(WH1,V8)5.0000000.000000COST(WH2,V1)4.0000000.000000COST(WH2,V2)9.0000000.000000COST(WH2,V3)5.0000000.000000COST(WH2,V4)3.0000000.000000COST(WH2,V5)8.0000000.000000COST(WH2,V6)5.0000000.000000COST(WH2,V7)8.0000000.000000COST(WH2,V8)2.0000000.000000COST(WH3,V1)5.0000000.000000COST(WH3,V2)2.0000000.000000COST(WH3,V3)1.0000000.000000COST(WH3,V4)9.0000000.000000COST(WH3,V5)7.0000000.000000COST(WH3,V6)4.0000000.000000COST(WH3,V7)3.0000000.000000COST(WH3,V8)3.0000000.000000COST(WH4,V1)7.0000000.000000COST(WH4,V2)6.0000000.000000COST(WH4,V3)7.0000000.000000COST(WH4,V4)3.0000000.000000COST(WH4,V5)11.000000.000000COST(WH4,V6)2.0000000.000000COST(WH4,V7)7.0000000.000000COST(WH4,V8)1.0000000.000000COST(WH5,V1)2.0000000.000000COST(WH5,V2)3.0000000.000000COST(WH5,V3)9.0000000.000000COST(WH5,V4)5.0000000.000000COST(WH5,V5)7.0000000.000000COST(WH5,V6)2.0000000.000000COST(WH5,V7)6.0000000.000000COST(WH5,V8)5.0000000.000000COST(WH6,V1)5.0000000.000000COST(WH6,V2)5.0000000.000000COST(WH6,V3)2.0000000.000000COST(WH6,V4)2.0000000.000000COST(WH6,V5)8.0000000.000000COST(WH6,V6)1.0000000.000000COST(WH6,V7)4.0000000.000000COST(WH6,V8)3.0000000.000000VOLUME(WH1,V1)0.0000006.000000VOLUME(WH1,V2)37.000000.000000VOLUME(WH1,V3)0.0000003.000000VOLUME(WH1,V4)0.0000004.000000VOLUME(WH1,V5)41.000000.000000VOLUME(WH1,V6)2.0000000.000000VOLUME(WH1,V7)0.0000004.000000VOLUME(WH1,V8)0.0000004.000000VOLUME(WH2,V1)0.0000002.000000VOLUME(WH2,V2)0.0000007.000000VOLUME(WH2,V3)0.0000002.000000VOLUME(WH2,V4)14.000000.000000VOLUME(WH2,V5)0.0000004.000000VOLUME(WH2,V6)0.0000003.000000VOLUME(WH2,V7)0.0000003.000000VOLUME(WH2,V8)0.0000001.000000VOLUME(WH3,V1)0.0000005.000000VOLUME(WH3,V2)0.0000002.000000VOLUME(WH3,V3)14.000000.000000VOLUME(WH3,V4)0.0000008.000000VOLUME(WH3,V5)0.0000005.000000VOLUME(WH3,V6)0.0000004.000000VOLUME(WH3,V7)43.000000.000000VOLUME(WH3,V8)0.0000004.000000VOLUME(WH4,V1)0.0000005.000000VOLUME(WH4,V2)0.0000004.000000VOLUME(WH4,V3)0.0000004.000000VOLUME(WH4,V4)5.0000000.000000VOLUME(WH4,V5)0.0000007.000000VOLUME(WH4,V6)0.0000000.000000VOLUME(WH4,V7)0.0000002.000000VOLUME(WH4,V8)38.000000.000000VOLUME(WH5,V1)35.000000.000000VOLUME(WH5,V2)0.0000001.000000VOLUME(WH5,V3)0.0000006.000000VOLUME(WH5,V4)0.0000002.000000VOLUME(WH5,V5)0.0000003.000000VOLUME(WH5,V6)6.0000000.000000VOLUME(WH5,V7)0.0000001.000000VOLUME(WH5,V8)0.0000004.000000VOLUME(WH6,V1)0.0000004.000000VOLUME(WH6,V2)0.0000004.000000VOLUME(WH6,V3)11.000000.000000VOLUME(WH6,V4)13.000000.000000VOLUME(WH6,V5)0.0000005.000000VOLUME(WH6,V6)28.000000.000000VOLUME(WH6,V7)0.0000000.000000VOLUME(WH6,V8)0.0000003.000000RowSlackorSurplusDualPrice1638.0000-1.00000020.000000-2.00000030.000000-2.00000040.000000-3.00000050.000000-3.00000060.000000-4.00000070.000000-2.00000080.000000-5.00000090.000000-1.000000100.0000000.0000001141.000000.000000120.0000002.000000130.0000000.000000140.0000000.000000150.0000001.0000003、用lingo解整数规划问题min=5*x1+x2+3*x3+7*x4+x5+x6+3*x7;6*x1+3*x2+2*x3+x4+x5>=50;x2+2*x4+x5+5*x6>=35;x3+x5+3*x7>=10;在lingo窗口输入以下代码，min=5*x1+x2+3*x3+7*x4+x5+x6+3*x7;6*x1+3*x2+2*x3+x4+x5>=50;x2+2*x4+x5+5*x6>=35;x3+x5+3*x7>=10;@gin(x1);@gin(x2);@gin(x3);@gin(x4);@gin(x3);@gin(x6);@gin(x7);END运行结果为：G