Using the diet problem described in Example 10.3, this example illustrates how to reoptimize an LP problem after modifying the objective function.
Assume that the optimal solution of the diet problem is found and the optimal solutions are stored in the data sets ex3pout and ex3dout.
Suppose the cost of cheese increases from 8 to 10 per unit and the cost of fish decreases from 11 to 7 per serving unit. The COLUMNS section in the input data set ex3 is updated (and the data set is saved as ex4) as follows:
COLUMNS . . . . . ... . ch diet 10 calories 106 ... . fi diet 7 calories 130 ... RHS . . . . . ... ENDATA ;
You can use the following DATA step to create the data set ex4:
data ex4; input field1 $ field2 $ field3$ field4 field5 $ field6 ; datalines; NAME . EX4 . . . 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 10 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 7 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 300 protein 10 . . fat 8 carbs 10 BOUNDS . . . . . UP . mi 1 . . LO . fi .5 . . ENDATA . . . . . ;
You can use the BASIS=WARMSTART option (and the ex3pout and ex3dout data sets from Example 10.3) in the following call to PROC OPTLP to solve the modified problem:
proc optlp data=ex4 presolver = none basis = warmstart primalin = ex3pout dualin = ex3dout solver = primal primalout = ex4pout dualout = ex4dout printfreq = 1; run;
The following iteration log indicates that it takes the primal simplex solver no extra iterations to solve the modified problem by using BASIS=WARMSTART, since the optimal solution to the LP problem in Example 10.3 remains optimal after the objective function is changed.
|NOTE: The problem EX4 has 6 variables (0 free, 0 fixed).|
|NOTE: The problem has 4 constraints (1 LE, 0 EQ, 3 GE, 0 range).|
|NOTE: The problem has 23 constraint coefficients.|
|NOTE: The OPTLP presolver value NONE is applied.|
|NOTE: The PRIMAL SIMPLEX solver is called.|
|NOTE: Objective = 10.9803355.|
|NOTE: The data set WORK.EX4POUT has 6 observations and 10 variables.|
|NOTE: The data set WORK.EX4DOUT has 4 observations and 10 variables.|
Note that the primal simplex solver is preferred because the primal solution to the original LP is still feasible for the modified problem in this case.