Optimal due-date determination and sequencing of n jobs on a single machine

Given a set of n jobs with deterministic processing times and the same ready times, the problem is to find the optimal processing-time multiple k* for the T.W.K. due-date assignment method, and the optimal sequence o * to minimize the total amount of missed due-dates. It is found that k* is a constant for a given job set and a* should be in S.P.T. sequence. After the theoretical treatment, a numerical example is given for discussion. The optimal results can readily be extended to situations in which the processing times are random variables with known means and having the same coefficient of variation. From a practical point of view, the main merit of this paper is that it demonstrates how, under certain production environments in which completion times of the jobs can be anticipated, to determine the optimal due-dates and obtain the optimal sequence.