Robustifying the resource-constrained project scheduling against uncertain durations

Abstract

This paper studies the resource-constrained project scheduling problem where uncertain durations are caused by various disruptions with unknown probabilistic functions. To achieve a balance between risk control and computational efficiency, we employ distributionally robust optimization minimizing the worst-case Conditional Value-at-Risk when the upper bounds of durations are not explicitly stipulated. We build a path-based two-stage model over a moment-based ambiguity set. The first stage explicitly generates paths satisfying precedence and resource constraints without any information of uncertainties, while the second stage determines the critical paths over the ambiguity set. Thus, we employ an enhanced Benders decomposition to solve this model where a weighted Benders cut may discriminatingly remove arcs on the critical paths. To ease the computation burden, we develop priority constraints for resource flow and a path elimination method to handle the paths generated by the first stage. A numerical experiment shows that this Benders cut together with the path elimination method can solve more complicated instances efficiently. The result further indicates that this model performs better than the classical model of robust optimization when providing upper bounds for durations. We extract some managerial insights that suggest important guidelines for controlling risk in project scheduling.