Study on Controllable Processing Time and Minmax Group Scheduling with Common Due-Window Assignment

We considerthe single-machine group scheduling problem with controllable processing times (i.e., resource allocation) under a common due-window (condw) assignment. The objective is to minimize a total cost composed of earliness, tardiness, due-window-related penalties, and resource consumption. Motivated by realistic production settings such as aerospace component machining and electronics batch assembly, the study addresses the joint optimization of group sequence, job sequence, due-window placement, and resource allocation. For linear and convex resource models, we propose a branch-and-bound (BaB^) algorithm and efficient heuristics. Numerical experiments show that the BaB^ algorithm can solve instances with up to 250 jobs and 16 groups. The heuristics (UB^), including a simulated annealing (SA^) algorithm, obtain near-optimal solutions with an average error below 0.05% much faster, demonstrating their practical usefulness for real-time scheduling.