A two-machine flow-shop scheduling with a deteriorating maintenance activity on the second machine

Simultaneously scheduling jobs and preventive maintenance is a topical subject in the scheduling literature. In this paper, we study a two-machine flow-shop makespan scheduling problem with a deteriorating maintenance period on the second machine, that is, delaying the maintenance increases the time required to perform it. We show that the studied problem is NP-hard and we establish some conditions of the optimal schedule. We also develop a branch and bound (B&B) algorithm to solve this problem. Numerical experiments show that the B&B method can solve large-size instances.