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

Abstract

Production Lead Time $\mbi (LT)$ is the average time a part spends in the system, being processed or waiting for processing. In systems with unlimited buffers, $\mbi LT$ 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 $\mbi LT$ 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 $\mbi LT$ 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 $\mbi LT$ . 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 $\mbi LT$ 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 $\mbi LT$ is ensured, while the throughput is maximized.