The OPTLP Procedure

You can also modify the right-hand side of your problem and use the BASIS=WARMSTART option to obtain an optimal solution more quickly. Since the dual solution to the original LP is still feasible for the modified problem in this case, the dual simplex algorithm is preferred. This case is illustrated by using the same diet problem as in Example 6.3. Assume that you now need a diet that supplies at least 150 calories. The RHS section in the input data table ex3 is updated (and the data set is saved as ex5) as follows:

      ...
   RHS         .          .        .     .         .
   .           .          calories 150   protein   10
   .           .          fat      8     carbs     10
   BOUNDS      .          .        .     .         .
      ...

You can use the following DATA step to create the data table ex5:

data mycas.ex5;
   input _id_ field1 $ field2 $ field3 $ field4 field5 $ field6;
   datalines;
1  NAME        .          EX3      .     .         .
2  ROWS        .          .        .     .         .
3  N           diet       .        .     .         .
4  G           calories   .        .     .         .
5  L           protein    .        .     .         .
6  G           fat        .        .     .         .
7  G           carbs      .        .     .         .
8  COLUMNS     .          .        .     .         .
9  .           br         diet     2     calories  90
10 .           br         protein  4     fat       1
11 .           br         carbs    15    .         .
12 .           mi         diet     3.5   calories  120
13 .           mi         protein  8     fat       5
14 .           mi         carbs    11.7  .         .
15 .           ch         diet     8     calories  106
16 .           ch         protein  7     fat       9
17 .           ch         carbs    .4    .         .
18 .           po         diet     1.5   calories  97
19 .           po         protein  1.3   fat       .1
20 .           po         carbs    22.6  .         .
21 .           fi         diet     11    calories  130
22 .           fi         protein  8     fat       7
23 .           fi         carbs    0     .         .
24 .           yo         diet     1     calories  180
25 .           yo         protein  9.2   fat       1
26 .           yo         carbs    17    .         .
27 RHS         .          .        .     .         .
28 .           .          calories 150   protein   10
29 .           .          fat      8     carbs     10
30 BOUNDS      .          .        .     .         .
31 UP          .          mi       1     .         .
32 LO          .          fi       .5    .         .
33 ENDATA      .          .        .     .         .
;

You can use the BASIS=WARMSTART option in the following call to PROC OPTLP to solve the modified problem:

proc optlp data=mycas.ex5
   presolver = none
   basis     = warmstart
   primalin  = mycas.ex3pout
   dualin    = mycas.ex3dout
   algorithm = dual
   primalout = mycas.ex5pout
   dualout   = mycas.ex5dout
   logfreq   = 1;
run;

Note that the dual simplex algorithm is preferred because the dual solution to the last solved LP is still feasible for the modified problem in this case.

The following iteration log indicates that it takes the dual simplex algorithm just one more phase II iteration to solve the modified problem by using BASIS=WARMSTART.

Compare this with the following call to PROC OPTLP:

proc optlp data=mycas.ex5
   presolver = none
   algorithm = dual
   logfreq   = 1;
run;

This call to PROC OPTLP solves the modified problem "from scratch" (without using the BASIS=WARMSTART option) and produces the following iteration log.

It is clear that using the BASIS=WARMSTART option saves computation time. For larger or more complex examples, the benefits of using this option are more pronounced.