Production lead time in exponential serial lines: Analysis and control

Production lead time (LT) is the average time a part spends in the system, being processed and waiting for processing. Some recent work provided methods for analysis of LT in systems with machines obeying the Bernoulli reliability model. Since this reliability model is hardly applicable to machining and other operations with a relatively long downtime, the current paper addresses serial lines with exponential machines and infinite buffers. Specifically, analytical formulas for LT as a function of machine parameters are derived, and qualitative and quantitative properties of LT are investigated. Using these formulas, the so-called lead time control problem is solved, whereby the raw material release rate is selected so that LT takes the desired value, while the throughput is maximized. Both open- and closed-loop solutions of this problem are provided.