Resource Allocation and Minmax Scheduling Under Group Technology and Different Due-Window Assignments

This article investigates single-machine group scheduling integrated with resource allocation under different due-window (DIFDW) assignment. Three distinct scenarios are examined: one with constant processing times, one with a linear resource consumption function, and one with a convex resource consumption function. The objective is to minimize the total cost comprising the maximum earliness/tardiness penalties, the due-window starting time cost, the due-window size cost, and the resource consumption cost. For each problem variant, we analyze the structural properties of optimal solutions and develop corresponding solution algorithms: a polynomial-time optimal algorithm for the case with constant processing times, heuristic algorithms for problems involving linear and convex resource allocation, and the branch-and-bound algorithm for obtaining exact solutions. Numerical experiments are conducted to evaluate the performance of the proposed algorithms.