Scheduling rules for two-stage flexible flow shop scheduling problem subject to tail group constraint

This paper considers a two-stage flexible flow shop scheduling problem with task tail group constraint, where the two stages are made up of unrelated parallel machines. The objective is to find a schedule to minimize the total tardiness of jobs. For this problem, a mathematical model is formulated. Through analyzing this kind of problem, it is proved to be NP-hard and an advantage scheduling rule is proposed. According to the advantage scheduling rule, a new heuristic method called EL algorithm, is designed to solve this problem. From the theoretical analysis of EL algorithm, we provide EL algorithm with the time complexity and worst-case analysis. To test the performance of EL algorithm, a computational experiment is designed. In the computational experiment, both the twelve dispatching rules based on the literatures and EL algorithm are applied to the benchmark instances. Simulation results indicate that LPT-CDS, SPT-Pal, SPT-CDS and EL algorithms are effective and EL algorithm outperforms the other twelve dispatching rules with respect to the two-stage flexible flow shop scheduling problem proposed in this paper.