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 12.3. Assume that you now need a diet that supplies at least 150 calories. The RHS section in the input data set 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 set ex5:

data ex5;
   input field1 $ field2 $ field3 $ field4 field5 $ field6;
   datalines;
NAME        .          EX5      .     .         .
ROWS        .          .        .     .         .
 N          diet       .        .     .         .
 G          calories   .        .     .         .
 L          protein    .        .     .         .
 G          fat        .        .     .         .
 G          carbs      .        .     .         .
COLUMNS     .          .        .     .         .
.           br         diet     2     calories  90
.           br         protein  4     fat       1
.           br         carbs    15    .         .
.           mi         diet     3.5   calories  120
.           mi         protein  8     fat       5
.           mi         carbs    11.7  .         .
.           ch         diet     8     calories  106
.           ch         protein  7     fat       9
.           ch         carbs    .4    .         .
.           po         diet     1.5   calories  97
.           po         protein  1.3   fat       .1
.           po         carbs    22.6  .         .
.           fi         diet     11    calories  130
.           fi         protein  8     fat       7
.           fi         carbs    0     .         .
.           yo         diet     1     calories  180
.           yo         protein  9.2   fat       1
.           yo         carbs    17    .         .
RHS         .          .        .     .         .
.           .          calories 150   protein   10
.           .          fat      8     carbs     10
BOUNDS      .          .        .     .         .
UP          .          mi       1     .         .
LO          .          fi       .5    .         .
ENDATA      .          .        .     .         .
;

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

proc optlp data=ex5
   presolver = none
   basis     = warmstart
   primalin  = ex3pout
   dualin    = ex3dout
   algorithm = dual
   primalout = ex5pout
   dualout   = 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=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.