Common Due-Date Assignment and Scheduling on Single Machine with Exponential Processing Times

This article deals with the problem of common due-date assignment and scheduling on single machine with exponential processing times. The objective is to minimize the expected total cost associated with the due-date and earliness/tardiness of jobs. For large due-date cost, we have derived a closed-form solution, which is applicable to the general processing times as well. In the other case, it is shown that an optimal sequence lies among the V-shaped sequences, and an algorithm is developed for the derivation of optimal solution.