An evaluation of semidefinite programming based approaches for discrete lot-sizing problems

Céline Gicquel (1) , Abdel Lisser (1) , Michel Minoux (2)

1 LRI - Laboratoire de Recherche en Informatique
2 DECISION

The present work is intended as a first step towards applying semidefinite programming models and tools to discrete lot-sizing problems including sequence-dependent changeover costs and times. Such problems can be formulated as quadratically constrained quadratic binary programs. We investigate several semidefinite relaxations by combining known reformulation techniques recently proposed for generic quadratic binary problems with problem-specific strengthening procedures developped for lot-sizing problems. Our computational results show that the semidefinite relaxations consistently provide lower bounds of significantly improved quality as compared with those provided by the best previously published linear relaxations. In particular, the gap between the semidefinite relaxation and the optimal integer solution value can be closed for a significant proportion of the small-size instances, thus avoiding to resort to a tree search procedure. The reported computation times are significant. However improvements in SDP technology can still be expected in the future, making SDP based approaches to discrete lot-sizing more competitive.

Mots clés: sequence-dependent changeover costs and times; discrete lot-sizing and scheduling problem; quadratically constrained quadratic binary programming; manufacturing; cutting planes; semidefinite relaxation

Domaines: Recherche opérationnelle [math.OC]

Céline Gicquel, Abdel Lisser, Michel Minoux. An evaluation of semidefinite programming based approaches for discrete lot-sizing problems. European Journal of Operational Research, 2014, 237 (2), pp.498-507. ⟨10.1016/j.ejor.2014.02.027⟩. ⟨hal-01120234⟩