Multi-objective optimization is an alternative to a cost-benefit analysis that allows us to analyze decisions that have multiple, conflicting objectives without conversion to a common currency.

Linear programming (LP) is a special form of multi-objective optimization, where the objectives and constraints that describe a decision are represented by linear equations, which are then used to find the best (optimal) solutions.

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.

The color in the interior of the region indicates the value of the objective function within the feasible region.

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.

In addition to companies that license SAS/IML software, SAS/IML is part of the free SAS University Edition, which has been downloaded almost one million times by students, teachers, researchers, and self-learners.

Whereas the syntax in PROC OPTMODEL closely reflects the mathematical formulation, the SAS/IML language uses matrices and vectors to specify the problem.

For an introduction to using the OPTMODEL procedure to solve linear programming problems, see the 2011 paper by Rob Pratt and Ed Hughes.

Not every SAS customer has a license for SAS/OR software, but hundreds of thousands of people have access to the SAS/IML matrix language.

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