Unrelated parallel machine scheduling with random rework and limited preemption

This study examines the problem of unrelated parallel machine scheduling with random rework and limited preemption. In this setting, new rework jobs are permitted to preempt ongoing jobs, provided that preempted jobs are resumed on the same machine. Due to the inherent complexity of this problem, exact methods based on stochastic dynamic programming are impractical for real-world applications. To address this issue, several efficient approximate methods are proposed to derive suboptimal policies for large-scale problems. First, a mixed integer programming model and several modified metaheuristics, based on aggregate duration estimation, are proposed to solve the decision problem in each state. Subsequently, a two-stage heuristic algorithm is presented. This algorithm first employs a priority rule to sort waiting jobs and then assigns them to machines using a mathematical programming approach. Computational experiments are conducted to evaluate the performance of the proposed methods. The results demonstrate that significant improvements can be achieved by incorporating limited preemption. The modified metaheuristics exhibit superior overall performance in large-scale problems, while the two-stage heuristic algorithm is most effective in a large-scale and very loose due date problem environment. Furthermore, sensitivity analysis on rework intensity reveals an approximately positive linear correlation between the benefits of preemption and rework intensity in large-scale problems.