Iterative methods for manufacturing systems of two stations in tandem
Iterative methods for manufacturing systems of two stations in tandem
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.
manufacturing system, steady state distribution, preconditioner conjugate gradient method
7-12
Ching, Wai Ki
cfee9d26-97e3-42ce-a4e9-b91e6d8aeef7
1998
Ching, Wai Ki
cfee9d26-97e3-42ce-a4e9-b91e6d8aeef7
Ching, Wai Ki
(1998)
Iterative methods for manufacturing systems of two stations in tandem.
Applied Mathematics Letters, 11 (1), .
(doi:10.1016/S0893-9659(97)00124-9).
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.
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Published date: 1998
Keywords:
manufacturing system, steady state distribution, preconditioner conjugate gradient method
Organisations:
Operational Research
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Local EPrints ID: 29742
URI: http://eprints.soton.ac.uk/id/eprint/29742
ISSN: 0893-9659
PURE UUID: f8dadc1e-1f15-4915-8e59-2a403523783e
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Date deposited: 01 May 2007
Last modified: 15 Mar 2024 07:34
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Author:
Wai Ki Ching
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