Finding robust solutions for resource constrained project scheduling problems involving uncertainties

Abstract

Resource constrained project scheduling problem (RCPSP) is a well known problem in the area of discrete optimization. It involves scheduling a given set of activities such that they are completed within minimum possible time, while satisfying a given set of precedence and resource constraints. RCPSP has a wide applicability in a number of industries, such as engineering, management, software, etc. While the classical RCPSP has been extensively studied, literature is rather scarce when it comes to finding robust solutions to RCPSP involving uncertainties. A robust solution in this context is one whose performance is not likely to vary significantly in presence of uncertainties which are inevitable in real life scenarios, such as delays in a particular activity and/or change in the available resources. Towards addressing this gap, in this paper we formulate a variant of RCPSP with stochastic activity durations and resource availability. Further, we propose a simple population based algorithm which aims to find solutions (activity lists) with minimum average makespan in the presence of uncertainties. The output from the algorithm is compared against a chosen optimal solution for the original RCPSP in terms of robustness. We study the performance of the proposed algorithm on a number of different J30 instances taken from the widely used Project Scheduling Library (PSPLib) in order to demonstrate the utility of the approach.