Scheduling jobs of two competing agents on a single machine

This paper studies a single-machine scheduling problem with a two competing agents in which the performance criteria of the first and second agents are to minimize the mean lateness and number of tardy jobs, respectively. Due to the non-deterministic polynomial-time hardness of this problem, we propose an effective and efficient algorithm, denominated as the SPT-M algorithm, to generate the non-dominated solutions of the Pareto set. Computational results conducted on a test problem set reveal that the proposed SPT-M algorithm can generate an efficient Pareto frontier in remarkably short computing time. The contribution of this paper could help practitioners to determine the tradeoffs between the jobs of two agents competing for a single resource.