e Spreadsheet Formulation B C F G Unit Cost Destination (Warehouse) Sacramento Salt Lake City Rapid CityAlbuquerque 513 6(Cannery Eugene 416 5791 Albert Lea 5995 5388 10 Shipment Quantity Destination (Warehouse) 11(Truckloads) I Sacramento Salt Lake City Rapid City Albuquerque Total Shipped ource Bellingham 75 13(Cannery) 0 0 25=125 14 Bert Lea 0 70 30 100 100 Total Received Total Cost Demand 152535 Copyright2007@深圳大学管理学院运筹学21
Copyright 2007 © 深圳大学管理学院 运筹学 21 Spreadsheet Formulation
e Network Representation Supplies Demands Destinations Sout D180(Sacr amento) 464 (Bellingham) 75( S1 4 D265(Salt Lake City (Eugene)125(S 690 91 3)70(Rapid City 388 (Albert Leayoo(S3 D4)85(Albuquerque) Copyright2007@深圳大学管理学院运筹学22
Copyright 2007 © 深圳大学管理学院 运筹学 22 Network Representation
e间题的网络表逊 ●忽略出发地和目的地在地理上的 布局 ●左边一列为出发地(),旁边的数 字代表供应量 ●右边一列为目的地①D),旁边的 数字代表需求量 ●箭头表示可能的运输途径,其上 面的数字代表单位运输成本 Copyright2007c深圳大学管理学院运筹学23
Copyright 2007 © 深圳大学管理学院 运筹学 23 运输问题的网络表述 忽略出发地和目的地在地理上的 布局 左边一列为出发地(S)，旁边的数 字代表供应量 右边一列为目的地(D)，旁边的 数字代表需求量 箭头表示可能的运输途径，其上 面的数字代表单位运输成本
&e The Transportation Problem is an LP Let x= the number of truckloads to ship from cannery i to warehouse j ( 设x;是从第罐头加工厂运送到第述个 仓库的车数)(=1,2,3;j=1,2,3,4) Minimize cost=$464xu +s513xu t s654x13+s867x14+$352x21+$416x2 +$690x23+$791x24+$995x31+ s682xx2+$388x3+$685x34 Copyright2007@深圳大学管理学院运筹学24
Copyright 2007 © 深圳大学管理学院 运筹学 24 The Transportation Problem is an LP Let xij = the number of truckloads to ship from cannery i to warehouse j (假 设xij是从第i个罐头加工厂运送到第j个 仓库的车数) (i = 1, 2, 3; j = 1, 2, 3, 4) Minimize Cost = $464x11 + $513x12 + $654x13 + $867x14 + $352x21 + $416x22 + $690x23 + $791x24 + $995x31 + $682x32 + $388x33 + $685x34
&e The Transportation Problem is an LP subject to(约束 Cannery 1 x1+x1+x13+x14 75 Cannery 2: x21 +x2+x2+x,4=125 Cannery3:x31+x32+x33+x34=100 Warehouse 1: xu +x21+x31=80 Warehouse 2: x12+x22+x32=65 Warehouse 3: x13+x23+x33=70 Warehouse 4: xu ttx=85 andx;≥0(i=1,2,3;j=1,2,3,4) Copyright2007c深圳大学管理学院运筹学25
Copyright 2007 © 深圳大学管理学院 运筹学 25 The Transportation Problem is an LP subject to (约束) Cannery 1: x11 + x12 + x13 + x14 = 75 Cannery 2: x21 + x22 + x23 + x24 = 125 Cannery 3: x31 + x32 + x33 + x34 = 100 Warehouse 1: x11 + x21 + x31 = 80 Warehouse 2: x12 + x22 + x32 = 65 Warehouse 3: x13 + x23 + x33 = 70 Warehouse 4: x14 + x24 + x34 = 85 and xij ≥ 0 (i = 1, 2, 3; j = 1, 2, 3, 4)