Parametric Integer Programming: The Right-Hand-Side-Case

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.Supported in part by the U.S. Army Research Office (Durham) under Contract DAHC04-73-C-0032