An efficient pseudo-polynomial algorithm for finding a lower bound on the makespan for the Resource Constrained Project Scheduling Problem

Dmitry I. Arkhipov (1) , Alexander A. Lazarev (2, 3, 4) , Olga Battaïa (5)

1 ICS RAS - Trapeznikov Institute of Control Sciences
2 MSU - Lomonosov Moscow State University
3 National Research University Higher School of Economics [St. Petersburg]
4 MIPT - Moscow Institute of Physics and Technology [Moscow]
5 DISC - Département d'Ingénierie des Systèmes Complexes

Several algorithms for finding a lower bound on the makespan for the Resource Constrained Project Scheduling Problem (RCPSP) were proposed in the literature. However, fast computable lower bounds usually do not provide the best estimations and the methods that obtain better bounds are mainly based on the cooperation between linear and constraint programming and therefore are time-consuming. In this paper, a new pseudo-polynomial algorithm is proposed to find a makespan lower bound for RCPSP with time-dependent resource capacities. Its idea is based on a consecutive evaluation of pairs of resources and their cumulated workload. Using the proposed algorithm, several bounds for the PSPLIB benchmark were improved. The results for industrial applications are also presented where the algorithm could provide good bounds even for very large problem instances.

Mots clés: Pseudo-polynomial algorithms; Lower bounds; Project scheduling; Scheduling; RCPSP

Domaines: Recherche opérationnelle [math.OC]

Dmitry I. Arkhipov, Alexander A. Lazarev, Olga Battaïa. An efficient pseudo-polynomial algorithm for finding a lower bound on the makespan for the Resource Constrained Project Scheduling Problem. European Journal of Operational Research, 2019, 275 (1), pp.35-44. ⟨10.1016/j.ejor.2018.11.005⟩. ⟨hal-02002548⟩