Minimizing the weighted completion time on an integrated single machine scheduling problem with maintenance activities

In this paper we consider an integrated single machine scheduling problem that involves the scheduling of jobs and planning of maintenance activities. Each job has a release time, a processing time, and a weight. The maintenance activity has to be performed after the machine continuously works for a maximum tolerance time. The maintenance time and the maximum tolerance time are known in advance. For the problem, we construct a mixed integer programming model to obtain optimal solutions for small-size problems. The problem is also NP-hard because the problem without considering maintenance activities is NP-hard. Three heuristic algorithms including FF, WSPT-based, and Greedy heuristics are developed for efficiently obtaining good-enough solutions. Through conducting the computational experiments, the results showed that Greedy algorithm could obtain more optimal solutions among them for the small problems, but also have good solution-quality for all problems. Overall, Greedy algorithm is significantly better than the first two algorithms.