Abstract

We study the polyhedral structure of two primal relaxations of a class of specially structured mixed integer programming problems. This class includes the generalized capacitated plant location problem and a production scheduling problem as special cases. We show that for this class of problems two polyhedra constructed from the constraint sets in two different primal relaxations are identical. The results have the following surprising implications; with linear or nonlinear objective functions, the bounds from two a priori quite different primal relaxations of the capacitated plant location problem are actually equal. In the linear case, this means that a simple Lagrangean substitution yields exactly the same strong bound as the computationally more expensive Lagrangean decomposition introduced in Guignard and Kim (1987) and studied in Cornuejols et al. (1991).

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