Parametric Integer Programming the Right Hand Side Case

Roy A. Marsten and Thomas Morin

No 106, NBER Working Papers from National Bureau of Economic Research, Inc

Abstract: A family of integer programs is considered whose right-hand-sides lie on a given line segment L. This family is called a parametric integer program (PIP). Solving a (PIP) means finding an optimal solution for every program in the family. It is shown how a simple generalization of the conventional branch-and-bound approach to integer programming makes it possible to solve such a (PIP). The usual bounding test is extended from a comparison of two point values to a comparison of two functions defined on the line segment L. The method is illustrated on a small example and computational results for some larger problems are reported.

Date: 1975-10
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Published as Hammer, P. L., E.L. Johnson, B.H. Korte and G.L. Nemhauer (eds.) Studies in integer programming, Volume 1 (Annals of Discrete Mathematics). Amstendam, New York, and Oxford: Elsevier, 1977.

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