Noncooperative game theory as a unified framework for single machine scheduling

Since most production scheduling problems are NP-hard and very complex, we try to decompose the original problem according to jobs. We model the scheduling problem as the competition of machine resources among a group of selfish jobs, which have independent performance objectives. Focusing on the single machine, multi-jobs and non-preemptive scheduling (SMMNS) problem, a noncooperative game model is established. Based on the model, the existence of Nash equilibrium schedule is proved and the worst-case performance ratio of Nash equilibrium set for the single machine total completion time (SMTCT) problem is discussed.