Single-machine scheduling with maintenance and repair rate-modifying activities

Most papers in the scheduling field are based on the assumption that machines are always available at constant speed. However, in industry applications, it is very common for a machine to be in subnormal condition after running for a certain period of time. Motivated by a problem commonly found in the surface-mount technology of electronic assembly lines, this paper deals with scheduling problems involving repair and maintenance rate-modifying activities. When a machine is running at less than an efficient speed, a production planner can decide to stop the machine and maintain it or wait and maintain it later. If the choice is made to continue running the machine without fixing it, it is possible that the machine will break down and repair will be required immediately. Both maintenance and repair activities can change the machine speed from a sub-normal production rate to a normal one. Hence, we call them rate-modifying activities. Our purpose here is to simultaneously sequence jobs and schedule maintenance activity to optimize regular performance measures. In this paper, we assume that processing time is deterministic, while machine breakdown is a random process following certain distributions. We consider two types of processing cases: resumable and nonresumable. We study problems with objective functions such as expected makespan, total expected completion time, maximum expected lateness, and expected maximum lateness, respectively. Several interesting results are obtained, especially for the nonresumable case.