Preemptive Parallel Processor Scheduling with Distinct Due Windows and Min-Max Criterion

Problem of scheduling n preemptive jobs on m identical parallel processors is studied, in which for each job a distinct due window is given in advance and an integer release date is specified. If a job is completed within its due window, then it incurs no penalty. Otherwise, it incurs a job-dependent earliness or tardiness cost. The objective is to find a job schedule such that a maximum of job-dependent costs associated with earliness, tardiness and a time a job is in process is minimized. It is proved that optimal solutions to this problem can be found by a solving a polynomial number of instances of classical maximum flow problem.