用matlab求解整数规划的例子

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有四个人，要指派他们分别完成四项工作，每人做各项工作所消耗的时间如表所示：

c=[15,18,21,24,19,23,22,18,26,17,16,19,19,21,23,17];

a=[15,18,21,24,zeros(1,12);

zeros(1,4),19,23,22,18,zeros(1,8);

zeros(1,8),26,17,16,19,zeros(1,4);

zeros(1,12),19,21,23,17;

15,zeros(1,3),19,zeros(1,3),26,zeros(1,3),19,zeros(1,3);

zeros(1,1),18,zeros(1,3),23,zeros(1,3),17,zeros(1,3),21,zeros(1,2);

zeros(1,2),21,zeros(1,3),22,zeros(1,3),16,zeros(1,3),23,0;

zeros(1,3),24,zeros(1,3),18,zeros(1,3),19,zeros(1,3),17];

b=[24;23;26;23;26;23;23;24];

A=[ones(1,4),zeros(1,12);

zeros(1,4),ones(1,4),zeros(1,8);

zeros(1,8),ones(1,4),zeros(1,4);

zeros(1,12),ones(1,4);

1,zeros(1,3),1,zeros(1,3),1,zeros(1,3),1,zeros(1,3);

0,1,zeros(1,3),1,zeros(1,3),1,zeros(1,3),1,zeros(1,2);

0,0,1,zeros(1,3),1,zeros(1,3),1,zeros(1,3),1,0;

zeros(1,3),1,zeros(1,3),1,zeros(1,3),1,zeros(1,3),1];

B=ones(1,8);

m=zeros(1,16);

[Q,W]=bintprog(c,a,b,A,B,m)

c=[15,18,21,24,19,23,22,18,26,17,16,19,19,21,23,17];

a=[15,18,21,24,zeros(1,12);zeros(1,4),19,23,22,18,zeros(1,8);zeros(1, 8),26,17,16,19,zeros(1,4);zeros(1,12),19,21,23,17;15,zeros(1,3),19,ze ros(1,3),26,zeros(1,3),19,zeros(1,3);zeros(1,1),18,zeros(1,3),23,zero s(1,3),17,zeros(1,3),21,zeros(1,2);zeros(1,2),21,zeros(1,3),22,zeros( 1,3),16,zeros(1,3),23,0;zeros(1,3),24,zeros(1,3),18,zeros(1,3),19,zer os(1,3),17];

b=[24;23;26;23;26;23;23;24];

A=[ones(1,4),zeros(1,12);zeros(1,4),ones(1,4),zeros(1,8);zeros(1,8),o nes(1,4),zeros(1,4);zeros(1,12),ones(1,4);1,zeros(1,3),1,zeros(1,3),1 ,zeros(1,3),1,zeros(1,3);0,1,zeros(1,3),1,zeros(1,3),1,zeros(1,3),1,z eros(1,2);0,0,1,zeros(1,3),1,zeros(1,3),1,zeros(1,3),1,0;zeros(1,3),1 ,zeros(1,3),1,zeros(1,3),1,zeros(1,3),1];

B=ones(1,8);

m=zeros(1,16);

[Q,W]=bintprog(c,a,b,A,B,m)

Warning: The given starting point x0 is not binary integer feasible; it will be ignored.

> In bintprog at 291

Optimization terminated.

Q =

(2,1) 1

(5,1) 1

(11,1) 1

(16,1) 1

W =

即甲B,乙A,丙C,丁D

最小总耗时，w=70