Production Control and Steady-State Performance Analysis for A Two-stage Manufacturing System with Finite Buffer Sizes

Abstract

A two-station tandem manufacturing system with limited buffer sizes and production capacity is considered. The problem is to examine the stability of the system and to control the service rates to meet an exogenous Poisson demand. A sufficient and necessary condition for the system stability is provided. It is shown that the optimal control policy for this finite buffer capacity problem has the similar structural properties to that of the infinite buffer capacity problem. Three threshold-type control policies are presented and their stability conditions are shown to be the same. The stationary distributions under two threshold policies are obtained, which can then be used to compute steady-state performance measures and find the optimal threshold values. Numerical examples are given to demonstrate the results.