Setting due dates in a stochastic single machine environment

A set of n jobs with statistically independent random processing times has to be processed on a single machine without idling between jobs and without preemption. It is required to set due dates and promise them to customers. During the production stage, earliness and tardiness against the promised due dates will be penalized. The goal is to minimize the total expected penalties. We consider two due date setting procedures with optimum customer service level, and an O(nlogn) time complexity. We show that one is asymptotically optimal but the other is not. Both heuristics include safety time and the sequence remains the same regardless of disruptions, so the result is robust. For the normal distribution we provide sufficient optimality conditions, precedence relationships that the optimal sequence must obey, and tight bounds.