Adjustments of Release and Due Dates for Cumulative Scheduling Problems

This paper presents a set of satisfiability tests and time-bound adjustments that can be applied to cumulative scheduling problems. We introduce the Cumulative Scheduling Problem (CuSP), an extension of the m-machine problem in which activities, having both release and due dates, can require more than one unit of the resource. Given a CuSP instance, we present two necessary conditions for the existence of solutions. They are obtained by polynomial relaxations of the CuSP: the Fully Elastic relaxation and the Partially Elastic Relaxation. These necessary conditions are related to well-known lower bounds of the m-machine problem. Moreover, we present two constraint propagation algorithms, based on the previously mentioned necessary conditions, to adjust release and due dates of activities. These algorithms extend the edge-finding techniques developed for the one-machine problem. Thanks to their “low” complexity, these algorithms have been incorporated in a branch and bound procedure to solve the Resource-Constrained Project Scheduling Problem. Computational results are reported.