Polynomial algorithms for some scheduling problems with one nonrenewable resource

Abderrahim Sahli (1) , Jacques Carlier (2) , Aziz Moukrim (2)

1 COSYS-GRETTIA - Génie des Réseaux de Transport Terrestres et Informatique Avancée
2 Heudiasyc - Heuristique et Diagnostic des Systèmes Complexes [Compiègne]

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.

Mots clés: Mathematics Subject Classification. 90B35; 05C85 Scheduling problems; nonrenewable resource; decomposition method; series-parallel graph; interval order graph

Domaines: Informatique [cs]

Abderrahim Sahli, Jacques Carlier, Aziz Moukrim. Polynomial algorithms for some scheduling problems with one nonrenewable resource. RAIRO - Operations Research, 2021, 55, pp.3493-3511. ⟨10.1051/ro/2021164⟩. ⟨hal-03521904⟩