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Solving a lot-sizing problem by semidefinite programs and cutting planes
Celine Gicquel

26 October 2012, 10h30 - 26 October 2012, 11h30
Salle/Bat : 475/PCRI-N
Contact : celine.gicquel@lri.fr

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Résumé :
We study a combinatorial optimization problem arising in the context of industrial production planning problem, namely the discrete lot-sizing and scheduling problem with sequence-dependent changeover costs. This optimization problem can be formulated as a quadratic binary program. In the present work, we propose to compute a lower bound of the optimal integer solution value by using a semidefinite relaxation of the problem rather than a standard linear relaxation. This is achieved by combining some reformulation techniques previously published in the semidefinite programming literature for general quadratic binary problems with an existing MILP strengthening procedure developped specifically for the problem under study. The results of the computational experiments we carried out on small instances show that the proposed approach consistently provides lower bounds of improved quality as compared with those provided by the best previously published linear relaxations. Moreover it is capable of completely closing the gap between the semidefinite relaxation and the optimal integer solution value for a significant proportion of the studied instances.

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