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

¹ Sorbonne Universités, Université Pierre et Marie Curie, Laboratoire LIP6, CNRS UMR 7606, 4 place Jussieu 75005 Paris, France.
² Université Paris-Dauphine, LAMSADE, CNRS UMR 7243, Place du Maréchal de Lattre de Tassigny, 75775 Paris CEDEX 16, France.
³ Université Blaise Pascal Clermont II, Laboratoire LIMOS, CNRS UMR 6158, Complexe Scientifique des Cézeaux, 63117 Aubière Cedex, France.

^* Corresponding author: pierre.fouilhoux@lip6.fr

Received: 30 June 2017
Accepted: 27 April 2018

Abstract

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.