Polynomial algorithms for some scheduling problems with one nonrenewable resource

¹ COSYS/GRETTIA, Univ Gustave Eiffel, CNRS, ESIEE Paris, F-77454 Marne-la-Vallée, France
² Sorbonne universités, Université de Technologie de Compiègne, CNRS, laboratoire Heudiasyc UMR 7253, CS 60 319, 60 203 Compiègne Cedex, France

^* Corresponding author: abderrahim.sahli@esiee.fr

Received: 7 February 2021
Accepted: 26 October 2021

Abstract

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.