ITERATIVE METHODS FOR MANUFACTURING SYSTEMS OF 2 STATIONS IN TANDEM

This paper studies the application of Preconditioned Conjugate Gradien t (PCG) methods in solving the steady state probability distribution o f two-station manufacturing systems under hedging point production pol icy. The manufacturing system produces one type of product, and its de mand 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 cl ustered around one when the number of inventory levels tends to infini ty. Hence, conjugate gradient methods will converge very fast when app lied to the solution of the preconditioned linear system. Numerical ex amples are given to verify our claim.