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The 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,
UNRSTRCT, 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

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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