The OPTLP Procedure

Example 12.2 Using the Interior Point Algorithm

You can also solve the oil refinery problem described in Example 12.1 by using the interior point algorithm. You can create the input data set from an external MPS-format flat file by using the SAS macro %MPS2SASD or SAS DATA step code, both of which are described in Getting Started: OPTLP Procedure. You can use the following SAS code to solve the problem:

proc optlp data=ex1
  objsense  = max
  algorithm = ip
  primalout = ex1ipout
  dualout   = ex1idout
  logfreq   = 1;
run;

The optimal solution is displayed in Output 12.2.1.

Output 12.2.1: Interior Point Algorithm: Primal Solution Output

Primal Solution

Obs	Objective Function ID	Variable Name	Variable Type	Objective Coefficient	Upper Bound	Variable Value	Variable Status	Reduced Cost
1	profit	a_l	D	-175	110	110.000	U	10.2083
2	profit	a_h	D	-165	165	0.000	L	-22.8125
3	profit	br	D	-205	80	80.000	U	2.8125
4	profit	na_l	N	0	1.7977E308	7.450	B	0.0000
5	profit	na_i	N	0	1.7977E308	21.800	B	0.0000
6	profit	h_o	N	0	1.7977E308	77.300	B	0.0000
7	profit	j_1	N	350	1.7977E308	72.667	B	0.0000
8	profit	j_2	N	350	1.7977E308	33.042	B	-0.0000

The iteration log is displayed in Output 12.2.2.

Output 12.2.2: Log: Solution Progress

NOTE: The OPTLP procedure is executing in single-machine mode.

NOTE: The problem EX1 has 8 variables (0 free, 0 fixed).

NOTE: The problem has 6 constraints (3 LE, 3 EQ, 0 GE, 0 range).

NOTE: The problem has 19 constraint coefficients.

WARNING: The objective sense has been changed to maximization.

NOTE: The LP presolver value AUTOMATIC is applied.

NOTE: The LP presolver removed 3 variables and 3 constraints.

NOTE: The LP presolver removed 6 constraint coefficients.

NOTE: The presolved problem has 5 variables, 3 constraints, and 13 constraint

coefficients.

NOTE: The LP solver is called.

NOTE: The Interior Point algorithm is used.

NOTE: The deterministic parallel mode is enabled.

NOTE: The Interior Point algorithm is using up to 4 threads.

Primal Bound Dual

Iter Complement Duality Gap Infeas Infeas Infeas Time

0 4.0651E+01 2.0527E+00 5.6871E-15 0.0000E+00 2.7019E-01 0

1 6.9884E+00 3.0632E+00 4.7807E-15 0.0000E+00 5.3371E-02 0

2 5.9956E+00 3.5765E-01 1.1439E-14 2.3345E-17 4.8803E-02 0

3 1.3976E+00 1.0163E-01 3.2245E-14 8.6465E-18 1.0468E-02 0

4 1.0306E+00 6.8392E-02 5.5550E-14 3.9055E-17 5.8619E-03 0

5 2.5202E-02 2.9900E-04 3.4399E-14 2.3359E-17 2.0848E-04 0

6 2.5230E-04 3.0238E-06 2.3857E-14 3.1581E-17 2.0848E-06 0

7 6.8270E-04 3.6281E-08 2.1556E-15 3.9670E-17 4.5403E-06 0

8 6.8270E-06 3.6281E-10 3.0346E-15 5.7575E-17 4.5403E-08 0

9 0.0000E+00 5.0568E-16 2.8899E-15 0.0000E+00 6.7382E-15 0

NOTE: The Interior Point solve time is 0.00 seconds.

NOTE: The CROSSOVER option is enabled.

NOTE: The crossover basis contains 0 primal and 0 dual superbasic variables.

Objective

Phase Iteration Value Time

P C 1 0.000000E+00 0

P 2 2 1.347917E+03 0

D 2 3 1.347917E+03 0

NOTE: The Crossover time is 0.00 seconds.

NOTE: Optimal.

NOTE: Objective = 1347.9166667.

NOTE: The data set WORK.EX1IPOUT has 8 observations and 10 variables.

NOTE: The data set WORK.EX1IDOUT has 6 observations and 10 variables.