Machine scheduling with deteriorating and resource-dependent maintenance activity

In this paper we investigate scheduling problems with a deteriorating and resource‐dependent maintenance activity on a single machine. The duration of the maintenance is assumed to be dependent both on its starting time and on the resource allocated to it. The objective is determining the job sequence, the position to perform a maintenance activity and the amount of additional resource allocated to it such that the total cost of related measure and resource is minimized. The considered measures are the makespan, flowtime, maximum tardiness and combination of earliness, tardiness and due‐date. Analysis results show that all the considered problems are polynomially solvable.