The following example illustrates how you can use the OPTMODEL procedure to solve linear programs. Suppose you want to solve the following problem:
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You can use the following statements to call the OPTMODEL procedure for solving linear programs:
proc optmodel; var x{i in 1..3} >= 0; max f = x[1] + x[2] + x[3]; con c1: 3*x[1] + 2*x[2] - x[3] <= 1; con c2: -2*x[1] - 3*x[2] + 2*x[3] <= 1; solve with lp / algorithm = ps presolver = none logfreq = 1; print x; quit;
The optimal solution and the optimal objective value are displayed in Figure 6.1.
Figure 6.1: Solution Summary
Problem Summary | |
---|---|
Objective Sense | Maximization |
Objective Function | f |
Objective Type | Linear |
Number of Variables | 3 |
Bounded Above | 0 |
Bounded Below | 3 |
Bounded Below and Above | 0 |
Free | 0 |
Fixed | 0 |
Number of Constraints | 2 |
Linear LE (<=) | 2 |
Linear EQ (=) | 0 |
Linear GE (>=) | 0 |
Linear Range | 0 |
Constraint Coefficients | 6 |
Performance Information | |
---|---|
Execution Mode | On Client |
Number of Threads | 1 |
Solution Summary | |
---|---|
Solver | LP |
Algorithm | Primal Simplex |
Objective Function | f |
Solution Status | Optimal |
Objective Value | 8 |
Iterations | 5 |
Primal Infeasibility | 0 |
Dual Infeasibility | 0 |
Bound Infeasibility | 0 |
[1] | x |
---|---|
1 | 0 |
2 | 3 |
3 | 5 |
The iteration log displaying problem statistics, progress of the solution, and the optimal objective value is shown in Figure 6.2.
Figure 6.2: Log
NOTE: Problem generation will use 4 threads. |
NOTE: The problem has 3 variables (0 free, 0 fixed). |
NOTE: The problem has 2 linear constraints (2 LE, 0 EQ, 0 GE, 0 range). |
NOTE: The problem has 6 linear constraint coefficients. |
NOTE: The problem has 0 nonlinear constraints (0 LE, 0 EQ, 0 GE, 0 range). |
NOTE: The LP presolver value NONE is applied. |
NOTE: The LP solver is called. |
NOTE: The Primal Simplex algorithm is used. |
Objective Entering Leaving |
Phase Iteration Value Time Variable Variable |
P 1 1 0.000000e+00 0 |
P 2 2 0.000000e+00 0 x[3] c2 (S) |
P 2 3 5.000000e-01 0 x[2] c1 (S) |
P 2 4 8.000000e+00 0 |
P 2 5 8.000000e+00 0 |
NOTE: Optimal. |
NOTE: Objective = 8. |
NOTE: The Primal Simplex solve time is 0.02 seconds. |