A Robust Optimization Approach for the Resource-Constrained Project Scheduling Problem with Uncertain Activity Release Times

Abstract

This paper studies the resource-constrained project scheduling problem with uncertain activity release times, a practical problem rarely addressed in the literature. The activity release times are assumed to be in a polyhedral uncertainty set, in order to model that the actual release times of all activities will not be all much larger than their predicted release times. A robust optimization model is proposed, where the objective function is to minimize the worst-case makespan. The model allows the robustness level to be controlled by a protective factor related to the risk aversion of the decision maker. A specialized decomposition algorithm is proposed to solve the robust counterpart of the problem. Extensive computational experiments on instances from the PSPLIB and on an instance of a real case generated from aircraft manufacturing, are carried out to assess the performance of the proposed algorithm. A comparison of our model with the resource-constrained project scheduling problem with uncertain activity processing times is also presented, confirming the superiority of our modeling technique..

Keywords: project scheduling, Resource constraints, Uncertain release times, Robust optimization, benders decomposition