Polynomial algorithms for some scheduling problems with one nonrenewable resource

• Published in: R.A.I.R.O. Recherche opérationnelle Vol. 55; no. 6; pp. 3493 - 3511
• Main Authors: Sahli, Abderrahim, Carlier, Jacques, Moukrim, Aziz
• Format: Journal Article
• Language: English
• Published: Paris EDP Sciences 01.11.2021
• Subjects: Algorithms; Chains; Completion time; Computer Science; Job shops; Nonrenewable resources; Polynomials; Precedence constraints; Resource scheduling; Schedules; Mathematics Subject Classification. 90B35; 05C85 Scheduling problems; decomposition method; series-parallel graph; interval order graph; nonrenewable resource
• ISSN: 0399-0559; 1290-3868
• DOI: 10.1051/ro/2021164

This paper deals with the Extended Resource Constrained Project Scheduling Problem (ERCPSP) which is defined by events, nonrenewable resources and precedence constraints between pairs of events. The availability of a resource is depleted and replenished at the occurrence times of a set of events. The decision problem of ERCPSP consists of determining whether an instance has a feasible schedule or not. When there is only one nonrenewable resource, this problem is equivalent to find a feasible schedule that minimizes the number of resource units initially required. It generalizes the maximum cumulative cost problem and the two-machine maximum completion time flow-shop problem. In this paper, we consider this problem with some specific precedence constraints: parallel chains, series-parallel and interval order precedence constraints. For the first two cases, polynomial algorithms based on a linear decomposition of chains are proposed. For the third case, a polynomial algorithm is introduced to solve it. The priority between events is defined using the properties of interval orders.