Due-date assignment to multi-job customer orders

The paper addresses deterministic, nonpreemptive scheduling of jobs that are immediately available for processing on a single machine. The jobs are partitioned into several multi-job customer orders. The problem is to determine a due-date for each customer order and to schedule all the jobs such that a total penalty function is minimized. The total penalty function is the sum of penalties for job earliness, penalties for job tardiness, and penalties associated with the lead times of customer orders. The main result is that there is an optimal solution in which the jobs within each customer order are processed contiguously. This is an appealing feature in terms of implementation. Efficient algorithms are presented for solving special cases of this problem.