A Genetic Algorithm for the Proactive Resource-Constrained Project Scheduling Problem With Activity Splitting

Proactive scheduling aims at the generation of robust baseline schedules, which has been studied for many years with the assumption that activity splitting is not allowed. In this paper, we focus on the proactive resource-constrained project scheduling problem in which each activity can be split at discrete time instants under the constraints of a maximum number of splitting and a minimum period of continuous execution. In this problem, setup times are also considered. A mathematical model is established and analyzed, of which two properties and one lemma are proposed. As the problem is proved to be ${\text{NP}}$-hard in the strong sense, for solving the model, we develop a genetic algorithm (GA) in which the two proposed properties and the lemma are applied as local search operators. After linearizing the proposed model, we use a commercial mathematical programming solver as a benchmark to solve the problem. From the computational results, we find that the developed GA is effective and efficient in solving the defined problem, and activity splitting improves robustness. With the growth of the maximum number of splitting, the decline in the minimum execution time, the decrease in the setup times, and the extension of the project due date, robustness increases.