A scheduling problem with three competing agents

Scheduling with multiple agents has become a popular topic in recent years. However, most of the research focused on problems with two competing agents. In this article, we consider a single-machine scheduling problem with three agents. The objective is to minimize the total weighted completion time of jobs from the first agent given that the maximum completion time of jobs from the second agent does not exceed an upper bound and the maintenance activity from the third agent must be performed within a specified period of time. A lower bound based on job division and several propositions are developed for the branch-and-bound algorithm, and a genetic algorithm with a local search is constructed to obtain near-optimal solutions. In addition, computational experiments are conducted to test the performance of the algorithms.