运筹学兼职值班员问题.docx
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运筹学兼职值班员问题.docx
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运筹学兼职值班员问题
运筹学兼职值班员问题
3.兼职值班员问题
某部队后勤值班室准备聘请4名兼职值班员(代号为1,2,3,4)和2名兼职带班员(代号5,6)值班,已知每人从周一到周日每天最多可以安排的值班时间及每人每小时值班的报酬如下表。
每人每天可值班的时间和报酬
值班员
代号
报酬
(元/h)
每天最多可安排的值班时间/h
周一周二周三周四周五周六周日
+9*(a41*x41+a42*x42+a43*x43+a45*x45+a47*x47)
+15*(a51*x51+a53*x53+a54*x54+a56*x56)
+16*(a62*x62+a64*x64+a65*x65+a67*x67);
a11*x11+a13*x13+a15*x15+a16*x16>=10;
a22*x22+a24*x24+a27*x27>=10;
a31*x31+a32*x32+a33*x33+a35*x35+a36*x36+a37*x37>=10;
a41*x41+a42*x42+a43*x43+a45*x45+a47*x47>=10;
a51*x51+a53*x53+a54*x54+a56*x56>=8;
a62*x62+a64*x64+a65*x65+a67*x67>=8;
x11+x12+x13+x14+x15+x16+x17<=4;
x21+x22+x23+x24+x25+x26+x27<=4;
x31+x32+x33+x34+x35+x36+x37<=4;
x41+x42+x43+x44+x45+x46+x47<=4;
x51+x52+x53+x54+x55+x56+x57<=4;
x61+x62+x63+x64+x65+x66+x67<=4;
x11+x21+x31+x41+x51+x61<=3;
x12+x22+x32+x42+x52+x62<=3;
x13+x23+x33+x43+x53+x63<=3;
x14+x24+x34+x44+x54+x64<=3;
x15+x25+x35+x45+x55+x65<=3;
x16+x26+x36+x46+x56+x66<=3;
x17+x27+x37+x47+x57+x67<=3;
x51+x61>0;
x52+x62>0;
x53+x63>0;
x54+x64>0;
x55+x65>0;
x56+x66>0;
x57+x67>0;
a11*x11+a31*x31+a41*x41+a51*x51>=14;
a22*x22+a32*x32+a42*x42+a62*x62>=14;
a13*x13+a33*x33+a43*x43+a53*x53>=14;
a24*x24+a54*x54+a64*x64>=14;
a15*x15+a35*x35+a45*x45+a65*x65>=14;
a16*x16+a36*x36+a56*x56>=14;
a27*x27+a37*x37+a47*x47+a67*x67>=14;
@bin(x11);@bin(x12);@bin(x13);@bin(x14);@bin(x15);@bin(x16);@bin(x17);
@bin(x21);@bin(x22);@bin(x23);@bin(x24);@bin(x25);@bin(x26);@bin(x27);
@bin(x31);@bin(x32);@bin(x33);@bin(x34);@bin(x35);@bin(x36);@bin(x37);
@bin(x41);@bin(x42);@bin(x43);@bin(x44);@bin(x45);@bin(x46);@bin(x47);
@bin(x51);@bin(x52);@bin(x53);@bin(x54);@bin(x55);@bin(x56);@bin(x57);
@bin(x61);@bin(x62);@bin(x63);@bin(x64);@bin(x65);@bin(x66);@bin(x67);
a11<=6;a11>=2;
a13<=6;a13>=2;
a15<=7;a15>=2;
a16<=12;a16>=2;
a22<=6;a22>=2;
a24<=6;a24>=2;
a27<=12;a27>=2;
a31<=4;a31>=2;
a32<=8;a32>=2;
a33<=3;a33>=2;
a35<=5;a35>=2;
a36<=12;a36>=2;
a37<=12;a37>=2;
a41<=5;a41>=2;
a42<=5;a42>=2;
a43<=6;a42>=2;
a45<=4;a45>=2;
a47<=12;a47>=2;
a51<=3;a51>=2;
a53<=4;a53>=2;
a54<=8;a54>=2;
a56<=12;a56>=2;
a62<=6;a62>=2;
a64<=6;a64>=2;
a65<=3;a65>=2;
a67<=12;a67>=2;
@gin(a11);@gin(a12);@gin(a13);@gin(a14);@gin(a15);@gin(a16);@gin(a17);
@gin(a21);@gin(a22);@gin(a23);@gin(a24);@gin(a25);@gin(a26);@gin(a27);
@gin(a31);@gin(a32);@gin(a33);@gin(a34);@gin(a35);@gin(a36);@gin(a37);
@gin(a41);@gin(a42);@gin(a43);@gin(a44);@gin(a45);@gin(a46);@gin(a47);
@gin(a51);@gin(a52);@gin(a53);@gin(a54);@gin(a55);@gin(a56);@gin(a57);
@gin(a61);@gin(a62);@gin(a63);@gin(a64);@gin(a65);@gin(a66);@gin(a67);
Lingo运行结果:
Localoptimalsolutionfound.
Objectivevalue:
1012.000
Objectivebound:
1012.000
Infeasibilities:
0.000000
Extendedsolversteps:
258
Totalsolveriterations:
10940
VariableValue
A115.000000
X111.000000
A134.000000
X131.000000
A157.000000
X151.000000
A162.000000
X160.000000
A222.000000
X221.000000
A246.000000
X241.000000
A272.000000
X271.000000
A314.000000
X311.000000
A327.000000
X321.000000
A333.000000
X330.000000
A355.000000
X351.000000
A3612.00000
X361.000000
A3712.00000
X370.000000
A415.000000
X411.000000
A425.000000
X421.000000
A436.000000
X431.000000
A454.000000
X450.000000
A4712.00000
X471.000000
A513.000000
X510.000000
A534.000000
X531.000000
A542.000000
X541.000000
A562.000000
X561.000000
A622.000000
X620.000000
A646.000000
X641.000000
A652.000000
X651.000000
A6712.00000
X670.000000
X120.000000
X140.000000
X170.000000
X210.000000
X230.000000
X250.000000
X260.000000
X340.000000
X440.000000
X460.000000
X520.000000
X550.000000
X570.000000
X610.000000
X630.000000
X660.000000
A120.000000
A140.000000
A170.000000
A210.000000
A230.000000
A250.000000
A260.000000
A340.000000
A440.000000
A460.000000
A520.000000
A550.000000
A570.000000
A610.000000
A630.000000
A660.000000
每人每天可值班的时间
值班员
代号
每天安排的值班时间/h
周一周二周三周四周五周六周日
1
2
3
4
5
6
5040700
0206002
47005120
55600012
0042020
0006200
值班人员表
周一
周二
周三
周四
周五
周六
周日
1
8:
00-13:
00
8:
00-12:
00
8:
00-15:
00
2
8:
00-10:
00
8:
00-14:
00
8:
00-10:
00
3
10:
00-17:
00
15:
00-20:
00
8:
00-20:
00
4
13:
00-17:
00
17:
00-22:
00
12:
00-18:
00
10:
00-22:
00
5
17:
00-22:
00
18:
00-22:
00
14:
00-16:
00
20:
00-22:
00
6
16:
00-22:
00
20:
00-22:
00
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