A two-stage approach with softmax scoring mechanism for a multi-project scheduling problem sharing multi-skilled staff

Abstract

This paper studies a multi-project scheduling problem sharing multi-skilled staff (MSMPSP). In a distributed decision-making environment, each project is independently scheduled by its project managers, while multiple projects compete for limited staff with multiple skills. A two-stage decomposition model, including an initial local scheduling stage and a global coordination stage, is established to describe this problem. Then, a two-stage approach with softmax scoring mechanism (TSA-SSM) is proposed to solve the local schedule of minimizing the single-project makespan and the global coordination decision of minimizing the total tardiness cost (TTC). According to the local scheduling plan obtained by the forward–backward scheduling genetic algorithm (FBSGA), the softmax scoring mechanism uses a greedy assignment strategy to solve the resource conflicts in the global decision stage, which is combined with the characteristics of multi-skilled staff. Based on the collection of multi-project instances, some numerical experiments are carried out. The results show that our TSA-SSM gets better solutions to large-size and strong conflict instances than some distributed and centralized methods, which proves that our method can effectively coordinate the allocation of multi-skilled staff among multiple projects. In addition, further experiments show that our method is also suitable for solving de-coupled problems, and satisfactory results are obtained.