Circulant preconditioners for failure prone manufacturing systems
Ching, Wai Ki (1997) Circulant preconditioners for failure prone manufacturing systems. Linear Algebra and its Applications, 266, 161180. (doi:10.1016/S00243795(97)000013).
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Description/Abstract
This paper studies the application of preconditioned conjugategradient methods in solving for the steadystate probability distribution of manufacturing systems. We consider the optimal hedging policy for a failure prone onemachine system. The machine produces one type of product, and its demand has finite batch arrival. The machine states and the inventory levels are modeled as Markovian processes. We construct the generator matrix for the machineinventory system. The preconditioner is constructed by taking the circulant approximation of the nearToeplitz structure of the generator matrix. We prove that the preconditioned linear system has singular values clustered around one when the number of inventory levels tends to infinity. Hence conjugategradient methods will converge very fast when applied to solving the preconditioned linear system. Numerical examples are given to verify our claim. The average running cost for the system can be written in terms of the steady state probability distribution. The optimal hedging point can then be obtained by varying different values of the hedging point.
Item Type:  Article  

Digital Object Identifier (DOI):  doi:10.1016/S00243795(97)000013  
ISSNs:  00243795 (print) 

Related URLs:  
Subjects:  T Technology > TS Manufactures Q Science > QA Mathematics 

Divisions:  University Structure  Pre August 2011 > School of Mathematics > Operational Research 

ePrint ID:  29739  
Date : 


Date Deposited:  01 May 2007  
Last Modified:  31 Mar 2016 11:55  
URI:  http://eprints.soton.ac.uk/id/eprint/29739 
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