The LP Procedure

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.

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An Introductory Example

An Integer Programming Example

An MPS Format to Sparse Format Conversion Example