Recently, several successful applications of strong cutting plane methods to combinatorial optimization problems have renewed interest in cutting plane methods, and polyhedral characterizations, of integer programming problems. In this paper, we investigate the polyhedral structure of the capacitated plant location problem. Our purpose is to identify facets and valid inequalities for a wide range of capacitated fixed charge problems that contain this prototype problem as a substructure. The first part of the paper introduces a family of facets for a version of the capacitated plant location problem with constant capacity K for all plants. These facet inequalities depend on K and thus differ fundamentally from the valid inequalities for the uncapacitated version of the problem. We also introduce a second formulation for a model with indivisible cus-tomer demand and show that it is equivalent to a vertex packing problem on a derived graph. We identify facets and valid inequalities for this version of the problem by applying known results for the vertex packing polytope.

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doi 10.1287/opre.1070.0392

pillars for the management of industries that procure and distribute consumer products. The former is concerned with the management of the demand processes and the development of methodologies and systems required to support this management function. The area of Supply Chain Management is concerned with the the design of a supply process to match a given demand pattern as efficiently as possible. It may therefore be viewed as the complement of the Revenue Management area. Operations management papers have demonstrated that the operational environment and associated cost structures may have a fundamental impact on the equilibrium behavior in the industry, in general, and the resulting price levels in particular. Little remains known, however, about how prices should be set in a competitive environment, in the simultaneous presence of two other major complications: (i) time dependent demand functions and cost parameters, and (ii) scale economies in the operational costs Conversely, traditional inventory and procurement planning models assume that the demand processes for the finished goods are exogenously given, when, in reality,

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