Algorithms and reformulations for lot sizing problems

In this paper we give a "personal" survey of the research on the polyhedral approach to lot-sizing problems developed over the last ten years. Most results concern the formulation and reformulations of single-item problems which can be used to tighten the formulation of practical multi-item and multi-stage problems. The discussion is restricted to exact algorithms, and more specifically to extended linear programming refomulations, cutting planes and separation algorithms. The large body of work on heuristic algorithms is not discussed. The single item lot-sizing subproblems that we discuss in some detail are the uncapacitated lot-sizing problem (ULS), the uncapacitated lot-sizing problem with start-up costs (ULSS), the constant capacity lot-sizing problem (CCLS) and the varying capacity lot-sizing problem (CLS). We give also references to the work done on the reformulations of other single-item, multi-item single stage and multi-item multistage lot-sizing problems.