Production Lead Time in Serial Lines: Evaluation, Analysis, and Control

Production Lead Time (LT) is the average time a part spends in the system, being processed or waiting for processing. In systems with unlimited buffers, LT may be orders of magnitude larger than the total processing time, leading to serious economic and quality problems. At present, no systematic analytical methods for evaluation, analysis, and control of LT in systems with machines having up- and downtime characterized by continuous random variables are available. This paper is intended to develop such methods. Specifically, we address synchronous serial lines with exponential machines and derive formulas for LT as a function of machine parameters and raw material release rate. Using these formulas, we develop methods for open- and closed-loop raw material release, which result in the desired LT. For asynchronous exponential lines, we provide an upper bound on LT. For non-exponential lines (e.g., Weibull, gamma, and log-normal), we offer an empirical formula for LT as an affine function of the coefficient of variation. The results reported in this paper enable a new paradigm for production systems management, namely: manage a production system so that the desired LT is ensured, while the throughput is maximized. This paper analyzes production lead time in manufacturing systems with hardware-unlimited buffers. The main practical insights obtained are as follows. . The lead time as a function of the raw material release rate has a “knee-type” behavior. . Releasing raw material beyond the knee results in no noticeable increase of the throughput, but in unlimited increase of the lead time. . To maintain the lead time close to the knee (and, thus, maximize the throughput), a simple control law may be used: release raw material on, say, hourly or shift-type basis, if the total work-in-process is below a certain threshold (provided in the paper) and do not release otherwise.