Partial rescheduling for permutation flow-shop scheduling subject to a machine breakdown

This paper discusses a permutation flow-shop scheduling problem with efficiency and stability as bi-criterion, where an unforeseen breakdown may happen in a machine during the execution of a long initial schedule. We only concern the situation that the breakdown happens at an earlier time of the execution and a large number of jobs are to be processed after repairing the machine. Instead of traditional full rescheduling and right-shift rescheduling, a partial rescheduling procedure is developed for the permutation flow-shop scheduling problem in this paper, where how to identify a partial rescheduling window and model a local rescheduling sub-problem are important and critical steps. A local objective function for the rescheduling sub-problem, which is the combination of the efficiency for the sub-problem and the total delay of unfinished jobs due to breakdown, is established. An extensive experiment was conducted to compare the partial rescheduling procedure and the right-shift rescheduling procedure. Computational results show that the partial rescheduling can provide a reasonable trade-off between solution quality and computational efforts and greatly improve stability of schedules with little sacrifice in efficiency.