Iterative methods for manufacturing systems of two stations in tandem

Abstract

This paper studies the application of Preconditioned Conjugate Gradient (PCG) methods in solving the steady state probability distribution of two-station manufacturing systems under hedging point production policy. The manufacturing system produces one type of product, and its demand is modeled as a Poisson process. Preconditioner is constructed by taking circulant approximation of the generator matrix of the system. We prove that the preconditioned linear system has singular values clustered around one when the number of inventory levels tends to infinity. Hence, conjugate gradient methods will converge very fast when applied to the solution of the preconditioned linear system. Numerical examples are given to verify our claim.