Tight lower bounds by semidefinite relaxations for the discrete lot-sizing and scheduling problem with sequence-dependent changeover costs [chapter]

Celine Gicquel, Abdel Lisser
2012 Operations Research Proceedings  
To cite this version: Céline Gicquel, Abdel Lisser, Michel Minoux. Tight lower bounds by semidefinite relaxation for the discrete lot-sizing and scheduling problem with sequence-dependent changeover costs. 9th International ABSTRACT: We study a production planning problem known as the discrete lot-sizing and scheduling problem with sequence-dependent changeover costs. This optimization problem can be formulated as a quadratic integer program. In the present paper, we propose to compute a tight
more » ... ower bound of the optimal solution value by using a semidefinite relaxation of the problem rather than a standard linear relaxation. This is achieved in particular by using reformulation techniques previously proposed in the semidefinite programming literature for the quadratic knapsack problem. The results of the preliminary computational experiments we carried out on small instances show that the proposed approach provides lower bounds of overall improved quality as compared with other possible LP relaxations. KEYWORDS: discrete lot-sizing and scheduling problem, sequence-dependent changerover costs, quadratic integer programming, semidefinite relaxation
doi:10.1007/978-3-642-29210-1_67 dblp:conf/or/GicquelL11 fatcat:l4u3qofn3jea5h6xduuebswlvq