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1、指派问题（assignmentproblem）问题一：今分派个工人去从事项工作.工人从事工作的工作效率为.试求一个分派方案，使每个工人都从事一项工作，每项工作都由一个工人承担，且总工作效率最大.建模：令则可建立如下数学规划模型：算例1利用LINGO软件求解如下指派问题：，.模型求解：Lingo程序：model:sets:Worker/W1..W5/;Job/J1..J5/;links(Worker,Job):c,x;endsetsdata:c=4,8,7,15,12,7,9,17,14,10,6,9,12,8,7,6,7,14,
2、6,10,6,9,12,10,6;enddatamin=@sum(links:c*x);@for(Worker(i):@sum(Job(j):x(i,j))=1);@for(Job(j):@sum(Worker(i):x(i,j))=1);@for(links:@bin(x));end注：程序中并没限制是0-1变量，但由其余约束条件足以保证返回的结果中变量的值为0、1.结果：Globaloptimalsolutionfound.Objectivevalue:34.00000Extendedsolversteps:0Totalso
3、lveriterations:0VariableValueReducedCostC(W1,J1)4.0000000.000000……C(W5,J5)6.0000000.000000X(W1,J1)0.0000004.000000X(W1,J2)0.0000008.000000X(W1,J3)1.0000007.000000X(W1,J4)0.00000015.00000X(W1,J5)0.00000012.00000X(W2,J1)0.0000007.000000X(W2,J2)1.0000009.000000X(W2,J3)0
4、.00000017.00000X(W2,J4)0.00000014.00000X(W2,J5)0.00000010.00000X(W3,J1)1.0000006.000000X(W3,J2)0.0000009.000000X(W3,J3)0.00000012.00000X(W3,J4)0.0000008.000000X(W3,J5)0.0000007.000000X(W4,J1)0.0000006.000000X(W4,J2)0.0000007.000000X(W4,J3)0.00000014.00000X(W4,J4)1.00
5、00006.000000X(W4,J5)0.00000010.00000X(W5,J1)0.0000006.000000X(W5,J2)0.0000009.000000X(W5,J3)0.00000012.00000X(W5,J4)0.00000010.00000X(W5,J5)1.0000006.000000算例2今分派5个工人去从事5项工作.工人从事工作的时间见下表：8610912912711974358958118467511试求一个分派方案，使每个工人都从事一项工作，每项工作都由一个工人承担，且总工作时间最少.建模：令，
6、则可建立如下0-1规划模型：模型求解：Lingo程序如下：model:sets:Worker/W1..W5/;Job/J1..J5/;links(Worker,Job):c,x;endsetsdata:c=8,6,10,9,12,9,12,7,11,9,7,4,3,5,8,9,5,8,11,8,4,6,7,5,11;enddatamin=@sum(links:c*x);@for(Worker(i):@sum(Job(j):x(i,j))=1);@for(Job(j):@sum(Worker(i):x(i,j))=1);@for(
7、links:@bin(x));end结果：Globaloptimalsolutionfound.Objectivevalue:30.00000Extendedsolversteps:0Totalsolveriterations:0VariableValueReducedCostC(W1,J1)8.0000000.000000……C(W5,J5)11.000000.000000X(W1,J1)1.0000008.000000X(W1,J2)0.0000006.000000X(W1,J3)0.00000010.00000X(W1,J
8、4)0.0000009.000000X(W1,J5)0.00000012.00000X(W2,J1)0.0000009.000000X(W2,J2)0.00000012.00000X(W2,J3)0.0000007.000000X(W2,J4)0.0000001
