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

We study 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. CORE, Université Catholique de Louvain, Belgium CORE and INMA, Université Catholique de Louvain, Belgium This paper presents research results of the Belgian Program on Interuniversity Poles of Attraction initiated by the Belgian State, Prime Minister’s Office, Science Policy Programming. The scientific responsibility is assumed by the authors. This research was also supported by the European Commission GROWTH Programme, Research Project LISCOS, Large Scale Integrated Supply Chain Optimization Software Based on Branch–and–Cut and Constraint Programming Methods, Contract No. GRDI–1999–10056.