The LP Procedure
- Overview
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Getting Started
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Syntax
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DetailsMissing ValuesDense Data Input FormatSparse Data Input FormatConverting Any PROC LP Format to an MPS-Format SAS Data SetConverting Standard MPS Format to Sparse FormatThe Reduced Costs, Dual Activities, and Current TableauMacro Variable _ORLP_PricingScalingPreprocessingInteger ProgrammingSensitivity AnalysisRange AnalysisParametric ProgrammingInteractive FacilitiesMemory ManagementOutput Data SetsInput Data SetsDisplayed OutputODS Table and Variable NamesMemory Limit
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ExamplesAn Oil Blending ProblemA Sparse View of the Oil Blending ProblemSensitivity Analysis: Changes in Objective CoefficientsAdditional Sensitivity AnalysisPrice Parametric Programming for the Oil Blending ProblemSpecial Ordered Sets and the Oil Blending ProblemGoal-Programming a Product Mix ProblemA Simple Integer ProgramAn Infeasible ProblemRestarting an Integer ProgramAlternative Search of the Branch-and-Bound TreeAn Assignment ProblemA Scheduling ProblemA Multicommodity Transshipment Problem with Fixed ChargesConverting to an MPS-Format SAS Data SetMigration to OPTMODEL: AssignmentMigration to OPTMODEL: Multicommodity Transshipment
- References
An Integer Programming Example
The following is a simple mixed-integer programming problem. Details can be found in Example 4.8 in the section Examples: LP Procedure.
data;
format _row_ $10.;
input _row_ $ choco gumdr ichoco igumdr _type_ $ _rhs_;
datalines;
object .25 .75 -100 -75 max .
cooking 15 40 0 0 le 27000
color 0 56.25 0 0 le 27000
package 18.75 0 0 0 le 27000
condiments 12 50 0 0 le 27000
chocolate 1 0 -10000 0 le 0
gum 0 1 0 -10000 le 0
only_one 0 0 1 1 eq 1
binary . . 1 2 binary .
;
The row with 'binary' type indicates that this problem is a mixed-integer program and all the integer variables are binary.
The integer values of the row set an ordering for PROC LP to pick the branching variable when VARSELECT=PRIOR
is chosen. Smaller values will have higher priorities. The _ROW_ variable here is an alias of the _ID_ variable.
This problem can be solved with the following statements:
proc lp canselect=lifo backtrack=obj varselect=far endpause;
run;
quit;
%put &_orlp_;
The options CANSELECT= , BACKTRACK= , and VARSELECT= specify the rules for picking the next active problem and the rule to choose the branching variable. In this example, the values LIFO, OBJ and FAR serve as the default values, so the three options can be omitted from the PROC LP statement. The following is the output from the %PUT statement:
STATUS=SUCCESSFUL PHASE=3 OBJECTIVE=285 P_FEAS=YES D_FEAS=YES INT_ITER=3
INT_FEAS=2 ACTIVE=0 INT_BEST=285 PHASE1_ITER=0 PHASE2_ITER=5
PHASE3_ITER=5
Preprocessing
Using the PREPROCESS= option, you can apply the preprocessing techniques to pre-solve and then solve the preceding mixed-integer program:
proc lp preprocess=1 endpause;
run;
quit;
%put &_orlp_;
The preprocessing statistics are written to the SAS log file as follows:
NOTE: Preprocessing 1 ... NOTE: 2 upper bounds decreased. NOTE: 2 coefficients reduced. NOTE: Preprocessing 2 ... NOTE: 2 constraints eliminated. NOTE: Preprocessing done.
The new output _ORLP_ is as follows:
STATUS=SUCCESSFUL PHASE=3 OBJECTIVE=285 P_FEAS=YES D_FEAS=YES INT_ITER=0
INT_FEAS=1 ACTIVE=0 INT_BEST=285 PHASE1_ITER=0 PHASE2_ITER=5
PHASE3_ITER=0
In this example, the number of integer iterations (INT_ITER=) is zero, which means that the preprocessing has reduced the gap between the relaxed linear problem and the mixed-integer program to zero.