CIRCULANT PRECONDITIONERS FOR FAILURE PRONE MANUFACTURING SYSTEMS

This paper studies the application of preconditioned conjugate-gradien t methods in solving for the steady-state probability distribution of manufacturing systems. We consider the optimal hedging policy for a fa ilure prone one-machine system. The machine produces one type of produ ct, and its demand has finite batch arrival. The machine states and th e inventory levels are modeled as Markovian processes. We construct th e generator matrix for the machine-inventory system. The preconditione r is constructed by taking the circulant approximation of the near-Toe plitz structure of the generator matrix. We prove that the preconditio ned linear system has singular values clustered around one when the nu mber of inventory levels tends to infinity. Hence conjugate-gradient m ethods will converge very fast when applied to solving the preconditio ned linear system. Numerical examples are given to verify our claim. T he average running cost for the system can be written in terms of the steady state probability distribution. The optimal hedging point can t hen be obtained by varying different values of the hedging point. (C) 1997 Elsevier Science Inc.