Simultaneously scheduling n jobs and the preventive maintenance on the two-machine flow shop to minimize the makespan

Most of the papers that deal with the two-machine flow shop problem assume that the machines are always available during the scheduling period. However, in most real life industrial settings a machine can be unavailable for many reasons. This paper is concerned with the problem of jointly scheduling n immediately available jobs and the preventive maintenance in a two-machine flow shop with the objective of minimizing the makespan. We consider that one of the two machines must be maintained once during the first T periods of the schedule. Only the non-resumable case is studied. We first focus on the particularity of this problem. After we present some properties of the optimal solution then we show that the problem is NP-hard. We last focus on the optimal solutions under some conditions.