Minimizing Makespan in Semiresumable Case of Single-Machine Scheduling with an Availability Constraint

A single-machine scheduling problem with an unavailable period to minimize makespan is discussed in this article. The disrupted job is assumed to be semiresumable. It is shown that the relative worst-case error bound of the longest processing time (LPT) algorithm is α/2, where α is reprocess-ratio. Furthermore, an example is provided to show the tightness of this bound, and then a LPT-based heuristic is proposed. Computational results show that this heuristic is quite effective in finding an optimal or near-optimal solution. Effects of different parameters on this algorithm are also analyzed.