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Tight Mip Formulation for Multi-Item Discrete Lot-Sizing Problems

Department of Industrial Engineering, University of Wisconsin at Madison, Madison, Wisconsin 53706
CORE and INMA, Université Catholique de Louvain, 1348 Louvain-la-Neuve, Belgium
amiller{at}ie.engr.wisc.edu
wolsey{at}core.ucl.ac.be

This paper discusses mixed-integer programming formulations of variants of the discrete lot-sizing problem. Our approach is to identify simple mixed-integer sets within these models and to apply tight formulations for these sets. This allows us to define integral linear programming formulations for the discrete lot-sizing problem in which backlogging and/or safety stocks are present, and to give extended formulations for other cases. The results help significantly to solve test cases arising from an industrial application motivating this research.

Subject classifications: Inventory/production: scale-diseconomies/lot-sizing, discrete lot-sizing; Production/scheduling: planning; Integer programming: convex integer programming, facets, extended formulations.
History: Received February 2001; revision received November 2001; accepted April 2002.

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