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oudu_t(1,6); %长度约束
tx_tebie1=i5*houdu_t(1,5)+i6*houdu_t(1,6);
tx_tebie2=i55*houdu_t(1,5)+i66*houdu_t(1,6); %特别约束
if wx1<=40000&&wx2<=40000&&tx1<=1020&&tx2<=1020&&tx_tebie1<=302.7&&tx_tebie2<=302.7%是否满足约束 tx_max0=tx1+tx2;
if tx_max0==2.039400000000000e+03%以求解出最大空间为max=2.039400000000000e+03 n=n+1;
first_che(n,1)=i1; first_che(n,2)=i2;
first_che(n,3)=i3; %记录满足条件的方案 first_che(n,4)=i4; first_che(n,5)=i5; first_che(n,6)=i6; first_che(n,7)=0; second_che(n,1)=i11; second_che(n,2)=i22; second_che(n,3)=i33; second_che(n,4)=i44; second_che(n,5)=i55; second_che(n,6)=i66; second_che(n,7)=0;
end end end end end end end end
zongzhong1=zeros(5,1); zongzhong2=zeros(5,1); zongzhong=zeros(5,1);
zhongliang_chazhi=zeros(5,1); for i=1:5 for j=1:7
zongzhong1(i,1)=zongzhong1(i,1)+first_che(i,j)*zhongliang_w(1,j); zongzhong2(i,1)=zongzhong2(i,1)+second_che(i,j)*zhongliang_w(1,j); end
zongzhong(i,1)=zongzhong2(i,1)+zongzhong1(i,1);
zhongliang_chazhi(i,1)=abs(zongzhong1(i,1)-zongzhong2(i,1)); end
zongkongjian1=zeros(5,1); zongkongjian2=zeros(5,1);
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zongkongjian=zeros(5,1);
zongkongjian_chazhi=zeros(5,1); for i=1:5 for j=1:7
zongkongjian1(i,1)=zongkongjian1(i,1)+first_che(i,j)*houdu_t(1,j); zongkongjian2(i,1)=zongkongjian2(i,1)+second_che(i,j)*houdu_t(1,j); end
zongkongjian(i,1)=zongkongjian2(i,1)+zongkongjian1(i,1);
zongkongjian_chazhi(i,1)=abs(zongkongjian1(i,1)-zongkongjian2(i,1)); end
得出最优解和最优值为
x?{6,2,6,0,0,0,4} y?{0,5,2,5,2,1,2} z?2040
即总使用空间为2040厘米，没有浪费空间。
习 题7
7.1 用分枝定界法解：
max z?x1?x2
951?x?x??114214?1?s..t??2x1?x2?.
3??x1,x2?0,x1,x2整数??7.2 试将下述非线性的0?1规划问题转换成线性的0?1规划问题
maxz?x1?x1x2?x3
???2x1?3x2?x3?3s..t?.
x?0或1，(j?1,2,3)??j7.3 某钻井队要从以下10个可供选择的井位中确定5个钻井探油，使总的钻探费用为最小。若10个井位的代号为s1,s2,?,s10，相应的钻探费用为c1,c2,?,c10，并且井位选择上要满足下列限制条件：
(1)或选择s1和s7，或选择钻探s9；
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(2)选择了s3或s4就不能选s5，或反过来也一样；
(3)在s5,s6,s7,s8中最多只能选两个；试建立这个问题的整数规划模型.
目录
第7章 整数规划 .......................................................................................................................... 134
7.1 整数规划模型................................................................................................................. 134
7.1.1 整数规划的定义 ................................................................................................. 134 7.1.2 整数规划的分类 ................................................................................................. 134 7.1.3 整数规划的模型 ................................................................................................. 135 7.1.4 整数规划求解思想和方法分类 ......................................................................... 135 7.2 分枝定界法..................................................................................................................... 136 7.3 0-1整数规划.................................................................................................................. 139
7.3.1 0-1变量在建立数学模型中的作用 .................................................................. 139 7.3.2 0-1整数规划的应用 .......................................................................................... 143 7.4 指派问题 ...................................................................................................................... 147 7.5 应用MATLAB解整数规划问题 ....................................................................................... 149
7.5.1 整数规划枚举法 ................................................................................................... 149 7.5.2 用MATLAB求解一般混合整数规划问题 ........................................................... 151 7.5.3 用MATLAB求解0-1规划问题 ........................................................................... 158 7.6 建模实例:两辆平板车的装载问题 ............................................................................... 166
习 题7 ............................................................................................................................. 170