Single‐machine scheduling problems simultaneously with deterioration and learning effects under deteriorating multi‐maintenance activities consideration

Maintenance is important to manufacturing process as it helps improve the efficiency of production. Although different models of joint deterioration and learning effects have been studied extensively in various areas, it has rarely been studied in the context of scheduling with maintenance activities. This paper considers scheduling with jointly the deterioration and learning effects and multi‐maintenance activities on a single‐machine setting. We assume that the machine may have several maintenance activities to improve its production efficiency during the scheduling horizon, and the duration of each maintenance activity depends on the running time of the machine. The objectives are to determine the optimal maintenance frequencies, the optimal maintenance locations, and the optimal job schedule such that the makespan and the total completion time are minimized, respectively, when the upper bound of the maintenance frequencies on the machine is known in advance. We show that all the problems studied can be solved by polynomial time algorithms.