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

Fouilhoux, Pierre; Mahjoub, Ali Ridha; Quilliot, Alain; Toussaint, Hélène (2017), Branch-and-Cut-and-Price algorithms for the preemptive RCPSP, RAIRO - Operations Research, 52, 2, p. 513–528. 10.1051/ro/2018031

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Type
Article accepté pour publication ou publié
Date
2017
Journal name
RAIRO - Operations Research
Volume
52
Number
2
Pages
513–528
Publication identifier
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Author(s)
Fouilhoux, Pierre
Laboratoire d'Informatique de Paris 6 [LIP6]
Mahjoub, Ali Ridha
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Quilliot, Alain
Laboratoire d'Informatique, de Modélisation et d'optimisation des Systèmes [LIMOS]
Toussaint, Hélène
Laboratoire d'Informatique, de Modélisation et d'optimisation des Systèmes [LIMOS]
Abstract (EN)
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.
Subjects / Keywords
Resource-constrained precedence scheduling problem; Preemptive case; Antichain; Branch-and-Cut-and-Price algorithm