The OPTMILP Procedure

This example illustrates a model in an MPS-format data table. This data table is passed to PROC OPTMILP, and a solution is found.

Consider a scenario where you have a container with a set of limiting attributes (volume V and weight W) and a set I of items that you want to pack. Each item type i has a certain value , a volume , and a weight . You must choose at most four items of each type so that the total value is maximized and all the chosen items fit into the container. Let be the number of items of type i to be included in the container. This model can be formulated as the following integer linear program:

Constraint (volume_con) enforces the volume capacity limit, while constraint (weight_con) enforces the weight capacity limit. An instance of this problem can be saved in an MPS-format data table by using the following code:

data mylib.ex1data;
   input _id_ field1 $ field2 $ field3 $ field4 field5 $ field6;
   datalines;
1  NAME       .             ex1data           .     .                 .
2  ROWS       .             .                 .     .                 .
3  MAX        z             .                 .     .                 .
4  L          volume_con    .                 .     .                 .
5  L          weight_con    .                 .     .                 .
6  COLUMNS    .             .                 .     .                 .
7  .          .MRK0         'MARKER'          .     'INTORG'          .
8  .          x[1]          z                 1     volume_con       10
9  .          x[1]          weight_con       12     .                 .
10 .          x[2]          z                 2     volume_con      300
11 .          x[2]          weight_con       15     .                 .
12 .          x[3]          z                 3     volume_con      250
13 .          x[3]          weight_con       72     .                 .
14 .          x[4]          z                 4     volume_con      610
15 .          x[4]          weight_con      100     .                 .
16 .          x[5]          z                 5     volume_con      500
17 .          x[5]          weight_con      223     .                 .
18 .          x[6]          z                 6     volume_con      120
19 .          x[6]          weight_con       16     .                 .
20 .          x[7]          z                 7     volume_con       45
21 .          x[7]          weight_con       73     .                 .
22 .          x[8]          z                 8     volume_con      100
23 .          x[8]          weight_con       12     .                 .
24 .          x[9]          z                 9     volume_con      200
25 .          x[9]          weight_con      200     .                 .
26 .          x[10]         z                10     volume_con       61
27 .          x[10]         weight_con      110     .                 .
28 .          .MRK1         'MARKER'          .     'INTEND'          .
29 RHS        .             .                 .     .                 .
30 .          .RHS.         volume_con     1000     .                 .
31 .          .RHS.         weight_con      500     .                 .
32 BOUNDS     .             .                 .     .                 .
33 UP         .BOUNDS.      x[1]              4     .                 .
34 UP         .BOUNDS.      x[2]              4     .                 .
35 UP         .BOUNDS.      x[3]              4     .                 .
36 UP         .BOUNDS.      x[4]              4     .                 .
37 UP         .BOUNDS.      x[5]              4     .                 .
38 UP         .BOUNDS.      x[6]              4     .                 .
39 UP         .BOUNDS.      x[7]              4     .                 .
40 UP         .BOUNDS.      x[8]              4     .                 .
41 UP         .BOUNDS.      x[9]              4     .                 .
42 UP         .BOUNDS.      x[10]             4     .                 .
43 ENDATA     .             .                 .     .                 .
;

In the COLUMNS section of this data table, the name of the objective is z, and the objective coefficients appear in field4. The coefficients of (volume_con) appear in field6. The coefficients of (weight_con) appear in field4. In the RHS section, the bounds V and W appear in field4. The _id_ column ensures that the data can be read in the right order even if the table is stored on separate machines in CAS. This problem can be solved by using the following statements to call the OPTMILP procedure:

proc optmilp data=mylib.ex1data primalout=mylib.ex1soln;
run;

The progress of the solver is shown in Output 6.1.1.

The data table ex1soln is shown in Output 6.1.2.

The optimal solution is , and , with a total value of 87. From this solution, you can compute the total volume used, which is 988 (); the total weight used is 499 (). The problem summary and solution summary are shown in Output 6.1.3.