Tabu search for proactive project scheduling problem with flexible resources

Abstract

In this paper, we address a proactive resource-constrained project scheduling problem where resources have several skills and can switch the selected skill at discrete time instants. The objective of this paper is to simultaneously determine the starting times of activities and select the skills of resources to maximize the schedule robustness, while satisfying constraints of precedence, renewable resources and a project deadline. After defining the problem, an integer linear programming model is constructed and the studied problem is proven to be NP-hard. Considering the NP-hardness of the problem, we develop a tabu search embedded with two special algorithms to solve the problem. Based on the characteristics of the problem, a resource allocation algorithm for determining the skill for resources is proposed. The two special algorithms are regarded as two improvement measures to combine with the basic tabu search, leading to three versions of the tabu search, i.e., TS, TS-IM1, and TS-IM12. A commercial mathematical programming solver, which can optimally solve the model, is used as a benchmark for comparing the developed algorithm. Through a computational experiment performed on a randomly generated dataset, the effectiveness of the designed algorithms and the two improvement measures is verified, and the results for single-skilled resources as well as the skill switching of flexible resources are discussed. In addition, the effects of the key parameters on the objective function are also analysed. From the computational results, we can draw several conclusions. First, among the three developed algorithms, TS-IM12, which is the tabu search embedded with two improvement measures, performs best, and compared with the commercial software, TS-IM12 shows a higher efficiency in solving the studied problem. Second, the increase in the resource flexibility should be moderate. Third, the robustness of the baseline schedule increases with an increase of the resource flexibility, the resource availability and the project deadline. Finally, the improvement of the schedule robustness brought by the increase of the resource flexibility or the resource availability will be further magnified as the project deadline extends, while the improvement of the schedule robustness caused by the increase of the resource flexibility will be reduced as the resource availability augments.