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

Acknowledgments I would like to express my gratitude to my two supervisors, Yves Pochet and Laurence Wolsey. It is difficult to imagine somebody more available for discussion than Yves Pochet. Even when he was crumbling under administrative work, he always had time to spend for discussing my work in progress. Laurence Wolsey have been a continuous source of inspiration and intellectual motivation. By regularly organizing non-scientific activities, he also has been more than a supervisor. Finally, I guess he spent many dozens of hours trying to read my unreadable drafts. If the present text is somewhat readable, it is more his achievement than mine. When I began my PhD in September 1999, I did not know anything about discrete optimization. I simply could not have done this work without them. Thank you. I am also grateful to the LISCOS project for funding. I am in debt to the project, and to my supervisors, as I has been originally hired to develop heuristics for production planning problems. Now, this thesis hardly contains a single paragraph on the subject. People of the LISCOS project, and my supervisors in particular, never complained about this. Thank you. A special thanks to Wim van de Velde from Procter&Gamble for providing the problems Gemini and PG1 of Chapter 7. Some of the work presented here is the outcome of teamwork. The second chapter is partly the result of many years of hard thinking of Francisco Ortega. The fifth chapter is my contribution to a joint work with Andrew Miller and Miguel Constantino. I also want to thank the members of the jury in general for their fruitful comments on ealier versions of the text. CORE is a wonderful place for working, because it is much more than the building where you go every morning. There are wonderful people in there, who I will regret for a long time. I began my research at the same time as Quentin. I wish I could have beaten him more often at tennis. I could also count on the great friendship of Pancho. Pancho, I must thank you for introducing me to the arcane of all softwares related to my research. My soccer and squash skills have also greatly improved thanks to you. My numerous conversations with Christine and Mady have been healthily refreshing in a sometimes arid scientific environment. In order of appearance, I also want to Eloisa for …