A solution approach of production planning problems based on compact formulations for single-item lot-sizing models

Abstract

We survey the main results presented in the author’s PhD Thesis presented in June 2003 at the Universite catholique de Louvain and supervised by Y. Pochet and L.A. Wolsey. The dissertation is written in English and is available from the author. In the first part of the thesis, we investigate the complexity and the polyhedral structure of various extensions of the uncapacitated single-item lot-sizing problem (Barany et al. 1984). In particular, we study models involving fixed charges on stocks, constant capacity and backlogging, and lower bounds on production. We describe algorithms, extended formulations, (facet-defining) valid inequalities and separation algorithms. Emphasis is placed on compact (i.e. of polynomial size) exact extended formulations. In a second part, we show how such extended reformulations for single-item problems can help to improve the solution of much more general production planning problems.