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Constraint-Propagation-Based Cutting Planes: An Application to the Resource-Constrained Project Scheduling Problem

Laboratoire d'Informatique d'Avignon, 339, Chemin des Meinajariés, Agroparc, BP 1228, 84911 Avignon Cedex 9, France
Laboratoire d'Informatique d'Avignon, 339, Chemin des Meinajariés, Agroparc, BP 1228, 84911 Avignon Cedex 9, France
Laboratoire d'Informatique d'Avignon, 339, Chemin des Meinajariés, Agroparc, BP 1228, 84911 Avignon Cedex 9, France
sophie.demassey{at}lia.univ-avignon.fr
christian.artigues{at}lia.univ-avignon.fr
philippe.michelon{at}lia.univ-avignon.fr

We propose a cooperation method between constraint programming and integer programming to compute lower bounds for the resource-constrained project scheduling problem (RCPSP). The lower bounds are evaluated through linear-programming (LP) relaxations of two different integer linear formulations. Efficient resource-constraint propagation algorithms serve as a preprocessing technique for these relaxations. The originality of our approach is to use additionally some deductions performed by constraint propagation, and particularly by the shaving technique, to derive new cutting planes that strengthen the linear programs. Such new valid linear inequalities are given in this paper, as well as a computational analysis of our approach. Through this analysis, we also compare the two considered linear formulations for the RCPSP and confirm the efficiency of lower bounds computed in a destructive way.

Key words: resource-constrained project scheduling problem; cutting plane; constraint propagation; shaving
History: received February 2001; revised December 2001; revised December 2002; revised March 2003; accepted May 2003.