Parallel machine scheduling problems with common flow-allowance

In due-date assignment problems with a common flow-allowance, the job-dependent due-dates are determined as linear functions of the job processing times. This paper studies due-date and due-window assignment problems based on flow-allowance with a minmax objective function. We consider a setting of parallel identical machines. The problems are proved to be NP-hard, and efficient heuristic procedures and simple lower bounds are introduced. Worst case analysis is provided in both cases. Our numerical tests indicate that the heuristics produce extremely close-to-optimal schedules. Our procedures (heuristics and bounds) are extended to parallel uniform machines, and based on our numerical tests, the average optimality gaps remain very small.