Optimal lead time policies

This paper examines two due-date setting problems first studied by Wein. The first problem seeks to minimize the average due-date lead time (due-date minus arrival date) of jobs subject to a constraint on the fraction of tardy jobs (Problem I) while the second uses the same objective subject to a constraint on average job tardiness (Problem II). We show that under very general conditions, Problem I leads to unethical practice (i.e., quote lead times for which there is no hope to achieve when the system is highly congested) while Problem II results in policies that quote lead times that are monotonically increasing with the congestion level. Furthermore, we prove that Problem II is equivalent to a policy that is widely used and is easy to compute. This policy quotes lead times that guarantee the same serviceability level (the fraction of tardy jobs) to all jobs.