Analysis, design, and control of Bernoulli production lines with waiting time constraints

Abstract

Waiting time constraints between two processes are one of common scheduling requirements in many production systems, such as semiconductor, automotive, food, and battery manufacturing. When the time constraints are introduced, quality inspection should be carried out on parts that have exceeded a given time limit and such parts are subject to be re-processed or scrapped, which incurs additional expenses and efforts. Therefore, the foremost goal is to maximize yield, which is defined by the production rate of parts that do not violate the time constraints. In this paper, we present a mathematical model of Bernoulli production lines to evaluate yield and examine its properties with respect to time constraints, buffer capacity, and machine reliability. System properties such as monotonicity and asymptotic characteristics are analyzed. With the analysis results, an efficient algorithm to design an optimal buffer capacity is developed. It is shown that, in contrast to traditional production lines, there is no monotonicity of yield on the reliability of an upstream machine; that is, an upstream machine becoming more reliable does not always contribute to increasing yield. Therefore, optimal control policies are presented to control the upstream machine for maximal yield. Finally, a case study is introduced to illustrate the applicability of the method.