Finite production run-based serial lines with Bernoulli machines: Performance analysis, bottleneck, and case study

In manufacturing systems with large variety of products, small- to medium-size production runs are typically carried out according to the customers' orders. When the volume of a production run is small, the production system operates partially (or entirely) in the transient regime and the traditional steady-state analysis may become inapplicable. In this paper, under the framework of serial production lines with finite buffers and with machines having the Bernoulli reliability model, we study the problems of performance evaluation, system-theoretic properties, and bottleneck of such systems. Specifically, we study the mathematical model for the one- and two-machine cases and derive analytical formulas to evaluate the performance measures of such systems. Then, for longer lines, a computationally efficient algorithm based on aggregation is developed to approximate the system performance measures with high accuracy. In addition, the monotonicity and reversibility properties and completion time bottleneck are discussed. Finally, a case study in a lighting equipment assembly plant is described to illustrate the theoretical results obtained.