The LP Procedure
- Overview
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Getting Started
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Syntax
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Details
Missing Values Dense Data Input Format Sparse Data Input Format Converting Any PROC LP Format to an MPS-Format SAS Data Set Converting Standard MPS Format to Sparse Format The Reduced Costs, Dual Activities, and Current Tableau Macro Variable ORLP Pricing Scaling Preprocessing Integer Programming Sensitivity Analysis Range Analysis Parametric Programming Interactive Facilities Memory Management Output Data Sets Input Data Sets Displayed Output ODS Table and Variable Names Memory Limit
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Examples
An Oil Blending Problem A Sparse View of the Oil Blending Problem Sensitivity Analysis: Changes in Objective Coefficients Additional Sensitivity Analysis Price Parametric Programming for the Oil Blending Problem Special Ordered Sets and the Oil Blending Problem Goal-Programming a Product Mix Problem A Simple Integer Program An Infeasible Problem Restarting an Integer Program Alternative Search of the Branch-and-Bound Tree An Assignment Problem A Scheduling Problem A Multicommodity Transshipment Problem with Fixed Charges Converting to an MPS-Format SAS Data Set Migration to OPTMODEL: Assignment Migration to OPTMODEL: Multicommodity Transshipment
- References
Getting Started: LP Procedure
PROC LP expects the definition of one or more linear, integer, or mixed-integer programs in an input data set. There are two formats, a dense format and a sparse format, for this data set.
In the dense format, a model is expressed in a similar way as it is formulated. Each SAS variable corresponds to a model’s column, and each SAS observation corresponds to a model’s row. A SAS variable in the input data set is one of the following:
a type variable
an id variable
a structural variable
a right-hand-side variable
a right-hand-side sensitivity analysis variable or
a range variable
The type variable tells PROC LP how to interpret the observation as a part of the mathematical programming problem. It identifies and classifies objectives, constraints, and the rows that contain information of variables like types, bounds, and so on. PROC LP recognizes the following keywords as values for the type variable: MIN, MAX, EQ, LE, GE, SOSEQ, SOSLE, UNRSTRT, LOWERBD, UPPERBD, FIXED, INTEGER, BINARY, BASIC, PRICESEN, and FREE. The values of the id variable are the names of the rows in the model. The other variables identify and classify the columns with numerical values.
The sparse format to PROC LP is designed to enable you to specify only the nonzero coefficients in the description of linear programs, integer programs, and mixed-integer programs. The SAS data set that describes the sparse model must contain at least four SAS variables:
a type variable
a column variable
a row variable and
a coefficient variable
Each observation in the data set associates a type with a row or a column, or defines a coefficient or a numerical value in the model, or both. In addition to the keywords in the dense format, PROC LP also recognizes the keywords RHS, RHSSEN, and RANGE as values of the type variable. The values of the row and column variables are the names of the rows and columns in the model. The values of the coefficient variables give the coefficients or other numerical data. The SAS data set can contain multiple pairs of row and coefficient variables. In this way, more information about the model can be specified in each observation in the data set. See the section Sparse Data Input Format for further discussion.
With both the dense and sparse formats for model specification, the observation order is not important. This feature is particularly useful when using the sparse model input.