Iterative methods for manufacturing systems of two stations in tandem

Ching, Wai Ki (1998) Iterative methods for manufacturing systems of two stations in tandem. Applied Mathematics Letters, 11, (1), 7-12. (doi:10.1016/S0893-9659(97)00124-9).


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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.

Item Type: Article
Digital Object Identifier (DOI): doi:10.1016/S0893-9659(97)00124-9
ISSNs: 0893-9659 (print)
Related URLs:
Keywords: manufacturing system, steady state distribution, preconditioner conjugate gradient method
Subjects: T Technology > TS Manufactures
Q Science > QA Mathematics
Divisions : University Structure - Pre August 2011 > School of Mathematics > Operational Research
ePrint ID: 29742
Accepted Date and Publication Date:
Date Deposited: 01 May 2007
Last Modified: 31 Mar 2016 11:55

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