On optimal minmax group scheduling with resource allocation and common due-window

This work investigates a single-machine group scheduling problem that integrates convex resource allocation with a common due-window assignment. The objective is of the minmax type, aiming to minimise a total cost function that comprises earliness, tardiness, common due-window assignment, and resource allocation penalties. Under the assumption of group-position-dependent penalties, a set of optimality properties is established. Based on these properties, it is proved that the problem is polynomially solvable in [Formula: see text] time, where [Formula: see text] denotes the total number of jobs.