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

• Published in: European journal of operational research Vol. 275; no. 1; pp. 35 - 44
• Main Authors: Arkhipov, Dmitry, Battaïa, Olga, Lazarev, Alexander
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 16.05.2019; Elsevier
• Subjects: Computer Science; Lower bounds; Operations Research; Project scheduling; Pseudo-polynomial algorithms; RCPSP; Scheduling; Lower bounds; Project scheduling; Scheduling; Pseudo-polynomial algorithms; RCPSP
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2018.11.005

•New task domain adjustment techniques for project scheduling problem are presented.•A pseudo-polynomial algorithm is developed for a lower bound on project duration.•The efficiency of the algorithms is shown on benchmark and industrial instances. 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.