An approximate model for base-stock-controlled assembly systems

Abstract

This study is on continuously reviewed base-stock-controlled assembly systems with Poisson demand arrivals and exponential single-server facilities used for manufacturing and assembly operations. A partially aggregated but exact queueing model is developed and approximated assuming that the state-dependent transition rates arising as a result of the partial aggregation are constant. It is shown that the steady-state probability distribution of this approximate model is a product-form distribution for the simplest case with two components making up an assembly. Based on this analytical observation, similar product-form distributions are proposed for more complex assembly systems. Comparisons with simulation and matrix-geometric solutions show that the proposed product-form steady-state distributions accurately approximate relevant performance measures with a considerable advantage in terms of the required computational effort. A greedy heuristic is devised to use approximate steady-state probabilities for optimizing design parameters like base-stock levels. [Supplementary materials are available for this article. Go to the publisher's online edition of IIE Transactions for the following free supplemental resources: appendix for the proofs, additional remarks, and figures and tables for the numerical results.]