Branch-and-Cut-and-Price algorithms for the preemptive RCPSP

Pierre Fouilhoux (1) , A.Ridha Mahjoub (2) , Alain Quilliot (3) , Hélène Toussaint (3)

1 RO - Recherche Opérationnelle
2 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision
3 LIMOS - Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes

In this article, we address the preemptive Resource-Constrained Precedence Scheduling Problem. We propose two mixed integer formulations containing an exponential number of variables and inequalities. An antichain is a set of pairwise incomparable elements with respect to the precedence constraints. In the first formulation, the integer variables are associated with the antichains. For the second, the integer variables are limited to a particular subset of antichains. We propose two Branch-and-Cut-and-Price algorithms for each of these formulations. We introduce some valid inequalities in order to reinforce the second formulation. Finally, we give some computational results on instances of the PSPLIB and compare the formulations.

Mots clés: Resource-constrained precedence scheduling problem; Preemptive case; Antichain; Branch-and-Cut-and-Price algorithm

Domaines: Mathématiques [math]

Pierre Fouilhoux, A.Ridha Mahjoub, Alain Quilliot, Hélène Toussaint. Branch-and-Cut-and-Price algorithms for the preemptive RCPSP. RAIRO - Operations Research, 2018, 52 (2), pp.513-528. ⟨10.1051/ro/2018031⟩. ⟨hal-02024839⟩