Scheduling step-deteriorating jobs on bounded parallel-batching machines to maximise the total net revenue

This paper addresses a parallel-batching scheduling problem considering processing cost and revenue, with the objective of maximising the total net revenue. Specifically, the actual processing time of a job is assumed to be a step function of its starting time and the common due date. This problem involves assigning jobs to different machines, batching jobs, and sequencing batches on each machine. Some key structural properties are proposed for the scheduling problem, based on which an optimal scheduling scheme is developed for any given machine. Then, an effective hybrid VNS-IRG algorithm which combines Variable Neighborhood Search (VNS) and Iterated Reference Greedy algorithm (IRG) is proposed to solve this problem. Finally, the effectiveness and stability of the proposed VNS-IRG are demonstrated and compared with VNS, IRG, and Particle Swarm Optimization through computational experiments.