数学建模算法与应用——整数规划

2_3

某公司新购置了某种设备6台，欲分配给下属的4个企业，已知各企业获得这种设备后年创立润如图2所示，单位为千万元。问应该如何分配这些设备能使年创利润最大，最大利润是多少。

 %非常规指派问题
clc,clear,close all
prob = optimproblem(ObjectiveSense,max);
x = optimvar(x,6,4,TYPE,integer,LowerBound,0,UpperBound,1);
c = [4 2 3 4;6 4 5 5;7 6 7 6;7 8 8 6;7 9 8 6;7 10 8 6];
M=c.*x;
prob.Objective = sum(sum(M));
prob.Constraints.con2 =sum(x)>=1;%每列求和，结果大于等于1
prob.Constraints.con1 =sum(x,2)==1;%每行求和，结果等于1
[sol,flav,flag] = solve(prob);
xx = sol.x
sum(sum(c.*xx))

本题最后可有多种情况，原因是设备3在甲企业和丙企业收益相同，设备4在乙丙企业收益相同。

2_6

clc,clear,close all
prob = optimproblem;
x = optimvar(x,5,TYPE,integer,LowerBound,0);
prob.Objective = 20*x(1)+90*x(2)+80*x(3)+70*x(4)+30*x(5);
prob.Constraints.con1 = x(1)+x(2)+x(5)>=30;
prob.Constraints.con2 = x(3)+x(4)>=30;
prob.Constraints.con3 = 3*x(1)+2*x(3)<=120;
prob.Constraints.con4 = 3*x(2)+2*x(4)+x(5)<=48;
[sol,flav,flag] = solve(prob);
sol.x

2_8

指派矩阵

clc,clear,close all
prob = optimproblem;
x = optimvar(x,6,6,TYPE,integer,LowerBound,0,UpperBound,1);
c = [6 7 5 8 9 10
     6 3 7 9 3 8
     8 11 12 6 7 9
     9 7 5 4 7 6
     5 8 9 6 10 7
     9 8 7 6 5 9];
M=c.*x;
prob.Objective = sum(M(:));
prob.Constraints.con1 = sum(x) == 1;
prob.Constraints.con2 = sum(x,2) ==1;
[sol,flav,flag] = solve(prob);
sol.x