Single-machine scheduling with two competing agents and learning consideration

Scheduling with learning effects has been receiving increasing attention in recent years. However, most researchers assumed that there is a common goal of minimization for all the jobs. In many applications and methodological fields, it is known that multiple agents pursuing different objectives compete for the usage of a common processing resource. In this paper, we studied a single-machine problem with learning effects, where the objective is to minimize the total weighted completion time of jobs from the first agent, given that the number of tardy jobs of the second agent is zero. We proposed a branch-and-bound algorithm and four heuristic algorithms to search for the optimal solution and near-optimal solutions, respectively.