Discrete Lot–Sizing and Convex Integer Programming

We study the polyhedral structure of variants of the discrete lot–sizing problem viewed as special cases of convex integer programs. Our approach in studying convex integer programs is to develop results for simple mixed integer sets that can be used to model integer convex objective functions. These results allow 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. Our 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.