An effective branch-and-price algorithm for the Preemptive Resource Constrained Project Scheduling Problem based on minimal Interval Order Enumeration

Aziz Moukrim (1, 2) , Alain Quilliot (3) , Hélène Toussaint (3)

1 Labex MS2T - Laboratoire d'Excellence "Maîtrise des Systèmes de Systèmes Technologiques"
2 Heudiasyc - Heuristique et Diagnostic des Systèmes Complexes [Compiègne]
3 LIMOS - Laboratoire d'Informatique, de Modélisation et d'optimisation des Systèmes

In this paper we address the Preemptive Resource Constrained Project Scheduling Problem (PRCPSP). PRCPSP requires a partially ordered set of activities to be scheduled using limited renewable resources such that any activity can be interrupted and later resumed without penalty. The objective is to minimize the project duration. This paper proposes an effective branch-and-price algorithm for solving PRCPSP based upon minimal Interval Order Enumeration involving column generation as well as constraint propagation. Experiments conducted on various types of instances have given very satisfactory results. Our algorithm is able to solve to optimality the entire set of J30, BL and Pack instances while satisfying the preemptive requirement. Furthermore, this algorithm provides improved best-known lower bounds for some of the J60, J90 and J120 instances in the non-preemptive case (RCPSP).

Mots clés: Project scheduling; Interval order; Column generation; Constraint propagation; Antichain

Domaines: Recherche opérationnelle [math.OC]; Mathématique discrète [cs.DM]

Aziz Moukrim, Alain Quilliot, Hélène Toussaint. An effective branch-and-price algorithm for the Preemptive Resource Constrained Project Scheduling Problem based on minimal Interval Order Enumeration. European Journal of Operational Research, 2015, 244 (2), pp.360-368. ⟨10.1016/j.ejor.2014.12.037⟩. ⟨hal-01306519⟩