Production Lead Time Problem: Formulation and Solution for Bernoulli Serial Lines

This paper is intended to formulate the so-called production lead time problem as the problem of throughput optimization under a constraint on production lead time. A solution is provided for serial lines with Bernoulli machines and infinite buffers. Specifically, analytical formulas are derived for raw material release rates, which guarantee the desired lead time, while maximizing the throughput. Based on this solution, a method for selecting design parameters of kanban- and CONWIP-controlled systems, which ensure the desired lead time, is provided.