Scheduling two-stage hybrid flow shop with availability constraints

Most of the literature on scheduling assumes that machines are always available. However, in real life industry, machines may be subject to some unavailability periods due to maintenance activities such as breakdowns (stochastic case) and preventive maintenance (deterministic case). In this paper we investigate the two-stage hybrid flow shop scheduling problem with only one machine on the first stage and m machines on the second stage to minimize the makespan. We consider that each machine is subject to at most one unavailability period. The start time and the end time of each period are known in advance (deterministic case) and only the non-resumable case is studied. First we discuss the complexity of the problem. Afterwards, we give the Branch and Bound model for this problem. Last, we calculate the worst-case performances of three heuristics: LIST algorithm, LPT algorithm and H-heuristic.