Unrelated parallel-machine scheduling problems with multiple rate-modifying activities

In this article we investigate scheduling problems with multiple rate-modifying activities on an unrelated parallel-machine setting. We assume that each machine may have multiple rate-modifying activities. The goal is to determine jointly the optimal rate-modifying activity frequencies, the optimal rate-modifying activity positions, and the optimal schedule to minimize the total completion time and the total machine load, respectively. If the number of machines is fixed, we propose two efficient polynomial time algorithms for solving both problems no matter what the processing time of a job scheduled after a rate-modifying activity is greater or less than its processing time scheduled before the rate-modifying activity.