In practice, it is often convenient to be able to specify the problem in a non-standardized form in which some of the constraints represent "greater than," others represent "less than," and others represent equality.Computer software can translate the problem into a standardized form and solve it.As an example of how to solve a linear programming problem in SAS, let's pose a particular two-variable problem: ) is defined by the two axes and the three linear inequalities.
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Graphical Method: Owing to the importance of linear programming models in various industries, many types of algorithms have been developed over the years to solve them.
This article shows two ways to solve linear programming problems in SAS: You can use the OPTMODEL procedure in SAS/OR software or use the LPSOLVE function in SAS/IML software.
A linear programming problem can always be written in a standard vector form.
In this problem, the feasible polygon has only five vertices, so you could evaluate the objective function at each vertex by hand to find the optimal solution.
For high-dimensional problems, however, you definitely want to use a computer! It provides a natural programming language with which to define and solve all kinds of optimization problems.
The green star indicates the optimal solution, which is x = .
The theory of linear programming says that an optimal solution will always be found at a vertex of the feasible region, which in 2-D is a polygon.
The LPSOLVE subroutine supports many features that are not mentioned here. The LPSOLVE subroutine was introduced in SAS/IML 13.1, which was shipped with SAS 9.4m1.
The LPSOLVE function replaces the older LP subroutine, which is deprecated.