+Leapms>load
 Current directory is "ROOT".
 .........
        02-01.leap
        02-02.leap
        02-03.leap
        02-39.leap
 .........
please input the filename:02-39
================================================================
1:  //2-39 To improve tax compliance the Texas
2:  //Comptroller’s staff regularly audits at corporate
3:  //home offices the records of out-of-state corporations
4:  //doing business in Texas. Texas is considering
5:  //the opening of a series of small offices near
6:  //these corporate locations to reduce the travel
7:  //costs now associated with such out-of-state audits.
8:  //The following table shows the fixed cost (in
9:  //thousands of dollars) of operating such offices at
10:  //5 sites i, the number of audits required in each
11:  //of 5 states j, and the travel cost (in thousands of
12:  //dollars) per audit performed in each state from a
13:  //base at any of the proposed office sites.
14:  //=======================================================
15:  //TaxSite|FixedCost|Costa
16:  //=======================================================
17:  //           1   2   3   4   5
18:  //     1 160 0   0.4 0.8 0.4 0.8
19:  //     2  49 0.7 0   0.8 0.4 0.4
20:  //     3 246 0.6 0.4 0 0.5 0.4
21:  //     4  86 0.6 0.4 0.9 0 0.4
22:  //     5 100 0.9 0.4 0.7 0.4 0
23:  //Audits     200 100 300 100 200
24:  //=======================================================
25:  //We seek a minimum total cost auditing plan.
26:
27:  min sum{i=1,..m;j=1,..,n}c[i][j]a[j]x[i][j] + -->
28:     sum{i=1,..m}f[i]y[i]
29:  subject to
30:     sum{i=1,..,m}x[i][j]= 1 | j=1,..,n
31:     sum{j=1,..,n}x[i][j] <= M*y[i] |i=1,..,m
32:  where
33:     m,n are integers
34:     M is a number
35:     f[i] is a number|i=1,..,m
36:     a[j] is a number|j=1,..,n
37:     c[i][j] is a number|i=1,..,m;j=1,..,m
38:     y[j] is a variable of binary|j=1,...,n
39:     x[i][j] is a variable of nonnegative number -->
40:             |i=1,..,m;j=1,..,n
41:  data_relation
42:     M=sum{j=1,..,n}a[j]
43:  data
44:     m=5
45:     n=5
46:     f={160 49 246 86 100}
47:     c={
48:         0 0.4 0.8 0.4 0.8
49:       0.7   0 0.8 0.4 0.4
50:       0.6 0.4   0 0.5 0.4
51:       0.6 0.4 0.9 0   0.4
52:       0.9 0.4 0.7 0.4   0
53:     }
54:     a={200 100 300 100 200}
================================================================
>>end of the file.
Parsing model:
1D
2R
3V
4O
5C
6S
7End.
..................................
number of variables=30
number of constraints=10
..................................
+Leapms>mip
relexed_solution=0.712222; number_of_nodes_branched=0; memindex=(2,2)
The Problem is solved to optimal as an MIP.
找到整数规划的最优解.非零变量值和最优目标值如下：
  .........
    x2_2* =1
    x2_4* =1
    x3_1* =1
    x3_3* =1
    x3_5* =1
    y2* =1
    y3* =1
  .........
    Objective*=535
  .........
+Leapms>