Parametric Integer Programming

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Abstract
A parametric integer linear program (PILP) may be defined as a family of closely related integer linear programs (ILP). Within this definition the author incorporates not only continuous scalar parameterizations but also finite parameterizations. These may include an ILP with a finite number of objective functions or right hand sides or constraint matrices or any combination of these. A general framework for PILP is presented. It begins by outlining the need for PILP algorithms. Basic solution methodologies are explained and two rudimentary approaches for the PILP are stated. Theoretical properties for special parameterizations are proved, and techniques for improving algorithmic efficiency are discussed. The framework concludes with an examination of underlying factors which intimately relate to the scheduling of solution priorities in a PILP algorithm.

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