Stochastic scheduling with optimal customer service

Existing research in stochastic scheduling often ignores the need to achieve high service levels. Optimality is usually defined in terms of minimizing the expected makespan, with the intent to increase the expected utilization of the facility. We argue that this does not address the full ramifications of stochastic variation. Instead, we should minimize our total cost, including losses due to the variation. This, we show, leads to focusing on optimal service level. Furthermore, we show how to compare the mean and the standard deviation of the makespan directly. While this method applies for any distribution, we demonstrate it specifically for the important special case where the makespan distribution is (at least approximately) normal. Finally, we show by simulation (i) that it is very important to take into account that high variation in individual operations causes increases both in the mean and the variance of the final makespan; and (ii) that using the normal distribution results is a good approximation.