Optimal assignment of slack due-dates and sequencing of jobs with random processing times on a single machine

This paper considers the problem of due-date assignment and sequencing of n stochastically independent jobs with random processing times on a single machine. The objective is to find the optimal due-dates, under the slack due-date assignment method, and the optimal job sequence that jointly minimize the expected total cost. This cost is a function of the length of the assigned due-dates and the deviations of job completion times from the due-dates. It is shown that the optimal due-dates can be analytically determined. An efficient algorithm of the order O(n log n) is developed to find the optimal job sequence under mild conditions. It is also shown that, with further suitable and reasonable assumptions, the job sequence in the shortest expected processing time order is optimal.