A rule-based genetic algorithm with an improvement heuristic for unrelated parallel machine scheduling problem with time-dependent deterioration and multiple rate-modifying activities

- An unrelated parallel machine scheduling with time-deterioration and multiple rate-modifying activities is considered.
- The deterioration is a linear function of a gap between starting time of job and the ending time of the previous RMA.
- A mixed integer programming model for the problem is developed to find the optimal solution.
- A novel rule-based genetic algorithm with improvement heuristic is robust for the problem.

In this article, we consider an unrelated parallel machine scheduling (UPMS) problem with time-dependent deterioration and multiple rate-modifying activities (RMAs). The actual processing time of a job is defined by a linear function of a gap between starting time of the job and ending time of the recent RMA. The starting rate of the actual processing time of jobs is restored to the original processing time through the application of RMAs. In the UPMS problem, we simultaneously determine the schedule of jobs and the number and positions of RMAs to minimize the makespan. To solve the problem, a mixed integer linear programming (MILP) model for the problem is developed to find the optimal solution. Then, we propose a novel rule-based genetic algorithm (GA) with a chromosome representing job assigning sequence to one of the machines and the schedule of jobs and the number and positions of RMAs in each machine are determined by a completion time rule-based dispatching heuristic during the decoding process of the chromosome. To enhance the solution effectiveness, an improvement heuristic is implemented to the GA. Extensive computational experiments are conducted through randomly generated examples to evaluate the performance of the proposed algorithms.