Optimal common due-date with limited completion time deviation

Given a set of n jobs with deterministic processing times and the same ready times, the problem is to find the optimal common flow allowance k* for the common due-date assignment method, and the optimal job sequence σ* to minimize a penalty function of missing due-dates. It is assumed that penalty will not occur if the deviation of job completion from the due-date is sufficiently small. Three lemmas are presented and a numerical example is provided to illustrate the use of the results to determine the optimal solution to the due-date determination and sequencing problem.