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.
Highlights
In the literature, the Resource Constrained Project Scheduling Problem (RCPSP) plays a fundamental role in scheduling theory
The decision problem of Extended Resource Constrained Project Scheduling Problem (ERCPSP) consists of determining whether an instance has a feasible schedule or not
This paper deals with the Extended Resource Constrained Project Scheduling Problem (ERCPSP)
Summary
The Resource Constrained Project Scheduling Problem (RCPSP) plays a fundamental role in scheduling theory. Neumann and Schwindt formalized the project scheduling problem with inventory constraints where the availability of each resource is at any time upper and lower bounded To solve this problem, they introduced a branch-and-bound algorithm with a filtered beam search heuristic. Other authors worked on the Two-Machine Maximum Flow Time Problem with Series-Parallel Precedence Constraints. A feasible schedule can be constructed by using the Johnson’s algorithm An adaptation of this algorithm is presented for the series-parallel case and for scheduling problem with cumulative continuous resources.
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