Providing software solutions since 1976
The LP Procedure
The legacy LP procedure solves linear programs, integer programs, and mixed-integer linear programs. It also performs parametric programming and range analysis, reporting on solution sensitivity to changes in the right-hand-side constants and price coefficients. There are no restrictions on the problem size in the LP procedure. The number of constraints and variables in a problem that PROC LP can solve depends on the host platform, the available memory, and the available disk space for utility data sets.
Input Data
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The Model data set can be specified in either a dense or sparse format. The sparse format is more flexible than the mathematical programming system (MPS) format, yet consistent with the MPS input format.
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The Primal data set can be input to warm-start the solution process, using a previous solution.
Output Data
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The Primal data set contains the primal solution, including the basic and nonbasic variable names, their values in the solution, cost coefficients, and reduced costs.
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The Dual data set contains the dual solution, including the values of the constraints and the dual values.
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The Active data set contains a representation of the current state of the branch-and-bound tree for restarting mixed-integer linear problems.
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The macro status variable, which describes the outcome of the optimization process and any solution found, is saved for easier system integration.
Integer Programming Features
- saving and restarting mixed-integer linear problems
- numerous options for controlling the generation and search of the branch-and-bound tree
- program algorithm modification during tree search
Algorithms
- revised simplex algorithm with LU factorization of the basis
- branch-and-bound algorithm for integer variables
- sparse column representation to reduce memory needs and limit arithmetic computation
- crash routine to identify advanced starting basis
- special ordered sets
- scaling the coefficients of both the constraints and objective rows for numerical stability
- numerous pricing algorithms for pivoting
Post-Optimality Analysis
- right-hand-side and price sensitivity analysis
- right-hand-side and price range analysis
- parametric programming
Interactive Features
- interactive and programmed interruption of iterations
- reset of procedure options
- printing intermediate results
- performance of post-optimality analysis
For further details, see the SAS/OR® User's Guide: Mathematical Programming: The LP Procedure.
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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 Problem
- 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
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