Total slack transmission graph-based robust scheduling for flexible job shop scheduling under machine breakdowns

In actual manufacturing systems, machine failures happen intermittently due to different types of faults. Therefore, it is important to generate a robust schedule. This paper investigates a flexible job shop scheduling problem under machine breakdowns whereby makespan and the robustness of a schedule have to be considered. The concept of a total slack transmission graph is defined to describe the chain reactions of slack consumption between operations. A total slack transmission algorithm is proposed to update the values of the nodes and edges in the graph. Accordingly, a quality robustness surrogate measure and a solution surrogate measure are derived to introduce the objective of robustness. A two-stage hybrid genetic algorithm is adopted by combining the proposed robustness surrogate measures to generate robust schedules. Six robustness surrogate measures in the existing literature are used for comparisons against the proposed surrogate measures. The experimental results show the superiority of the proposed robustness surrogate measure concerning the deviation of makespan and the completion times of operations between the rescheduled solution and preschedule.