A hybrid BA-VNS algorithm for coordinated serial-batching scheduling with deteriorating jobs, financial budget, and resource constraint in multiple manufacturers

We study a coordinated serial-batching scheduling problem that features deteriorating jobs, financial budget, resource constraints, resource-dependent processing times, setup times, and multiple manufacturers simultaneously. A unique feature but also a significant challenge in this problem is the dual constraints on resources, i.e., financial budget and resource quantity. Some key structural properties are first identified for the setting where the jobs and resources are already assigned to each manufacturer, which enables us to develop the optimal resource allocation scheme. Then, a polynomial-time scheduling rule is proposed to search for the optimal solution for each manufacturer in this setting. Then, a hybrid BA-VNS algorithm combining Bat algorithm (BA) and variable neighborhood search (VNS) is proposed to tackle the studied problem, and the optimal scheduling rule is implemented in its encoding procedure. Finally, computational experiments are conducted to test the performance of the proposed algorithm, and the efficiency and improvements are compared with those of BA, VNS, and Particle Swarm Optimization (PSO), with respect to convergence speed as well as computational stability.