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The vast majority of applications found in operations research and industrial engineering involve the use of discrete variables in problem formulation. Over the last two decades great strides have been made in solving ever larger optimization models derived for these applications. The design and analysis of flexible manufacturing systems, airline crew scheduling, sequencing mixed-model assemble lines, and personnel scheduling in the service sector are a few examples that come to mind. Success in these areas can be attributed in part to the development of interior point methods for linear programming. This has led to a greater understanding of how to deal with the underlying linear algebra which, in turn, has enabled code developers to build much improved versions of the simplex method. Commercial systems still rely on the different variations of the simplex method to solve integer programs (IPs).

A second …