# 储蓄所服务员问题

1212345min 1001004040404040z m m n n n n n =++++++

s.t.

1211212121234

3

4m m n m m n n m m n n n ++≥+++≥++++≥

212346m n n n n ++++≥

1m 23455n n n n ++++≥

12m m + 3456n n n +++≥

12m m + 458n n ++≥

12m m + 58n +≥

123453n n n n n ++++≤

2312145,,,,,,0m m n n n n n ≥且为整数

1212345121234512123453,4,0,0,2,0,1,820.m 5,6,0,0,0,0,0,1100-=m 0,0,4,0,0,2,8,560m m n n n n n m n n n n n m n n n n n =====================最小费用为元如果不能雇佣半时服务员，则最优解为最小费用为元，即每天至少增加的费用为1100820280元.

《数学模型（第三版）》 作者：姜启源 谢金星 叶俊

Global optimal solution found.

Objective value: 820.0000 Extended solver steps: 1 Total solver iterations: 23

Variable Value Reduced Cost M1 2.000000 100.0000 M2 5.000000 100.0000 N1 0.000000 40.00000 N2 2.000000 40.00000 N3 0.000000 40.00000 N4 0.000000 40.00000 N5 1.000000 40.00000

Row Slack or Surplus Dual Price

2 3.000000 0.000000

3 6.000000 0.000000

4 5.000000 0.000000

5 1.000000 0.000000

6 0.000000 0.000000

7 2.000000 0.000000

8 0.000000 0.000000

9 0.000000 0.000000

10 0.000000 0.000000

（2）

Global optimal solution found.

Objective value: 1100.000

Extended solver steps: 0

Total solver iterations: 0

Variable Value Reduced Cost M1 5.000000 100.0000 M2 6.000000 100.0000 N1 0.000000 0.000000 N2 0.000000 0.000000 N3 0.000000 0.000000 N4 0.000000 0.000000 N5 0.000000 0.000000

Row Slack or Surplus Dual Price

1 1100.000 -1.000000

2 7.000000 0.000000

3 8.000000 0.000000

4 7.000000 0.000000

5 0.000000 0.000000

6 0.000000 0.000000

7 5.000000 0.000000

8 3.000000 0.000000

9 3.000000 0.000000

10 0.000000 -40.00000

11 0.000000 -40.00000

12 0.000000 -40.00000

14 0.000000 -40.00000

（3）Global optimal solution found.

Objective value: 560.0000

Extended solver steps: 0

Total solver iterations: 5

Variable Value Reduced Cost M1 0.000000 100.0000 M2 0.000000 100.0000 N1 4.000000 40.00000 N2 2.000000 40.00000 N3 0.000000 40.00000 N4 0.000000 40.00000 N5 8.000000 40.00000

Row Slack or Surplus Dual Price

1 560.0000 -1.000000

2 0.000000 0.000000

3 3.000000 0.000000

4 2.000000 0.000000

5 0.000000 0.000000

6 5.000000 0.000000

7 2.000000 0.000000

8 0.000000 0.000000

9 0.000000 0.000000