Targeting problems in manufacturing queueing networks-An iterative scheme and convergence

In order to manage complex manufacturing operations effectively a firm needs to take advantage of the tradeoffs between various performance measures such as work-in-progress, lead time, costs, quality, and investment in capacity. Bitran and Tirupati developed models to describe some of these tradeoffs and to provide the decision maker with a tool to analyze various options. They formulated, for open queueing networks, a targeting problem to study the tradeoff between WIP and capacity for a semiconductor production facility. They showed that the targeting problem can be approximated by a convex program that is easy to solve. They qualitatively argued that the approximation is accurate for large production facilities and demonstrated their claim for specific network examples. In this paper the authors provide a theoretical analysis of such approximation schemes for general networks which, therefore, closes an important loose end of previous analysis. Specifically, they propose an exact iterative algorithm for the targeting problem and present sufficient conditions for its convergence. Moreover, the authors show that, under mild conditions which are easy to verify, the iterative scheme converges for networks of practical interest.