Minmax common due-window assignment and scheduling on a single machine with two competing agents

We study the classical method of common due-date assignment and focus on minmax objective functions. In due-date assignment problems, the objective is to find the optimal due-date and job sequence that minimize the total earliness, tardiness and due-date-related costs. We extend the single-agent problem to a setting involving two competing agents and to a setting of multi-agent. In the two-agent setting (herein agents A and B), the scheduler needs to minimize the maximum cost of the agent A, subject to an upper bound on the maximal cost of the agent B. In the general model of multi-agent scheduling, the scheduler needs to minimize the cost among all A-type agents, subject to an agent-dependent upper bound on the maximal cost of the B-type agents. We further generalize the problems to the method of common due-window assignment. For all studied problems, we introduce efficient polynomial time solutions.