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Article: Circulant preconditioners for failure prone manufacturing systems

TitleCirculant preconditioners for failure prone manufacturing systems
Authors
Issue Date1997
PublisherElsevier Inc. The Journal's web site is located at http://www.elsevier.com/locate/laa
Citation
Linear Algebra And Its Applications, 1997, v. 266 n. 1-3, p. 161-180 How to Cite?
AbstractThis paper studies the application of preconditioned conjugate-gradient methods in solving for the steady-state probability distribution of manufacturing systems. We consider the optimal hedging policy for a failure prone one-machine 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 machine-inventory system. The preconditioner is constructed by taking the circulant approximation of the near-Toeplitz 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 conjugate-gradient 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. © 1997 Elsevier Science Inc.
Persistent Identifierhttp://hdl.handle.net/10722/156138
ISSN
2015 Impact Factor: 0.965
2015 SCImago Journal Rankings: 0.837
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorChing, WKen_US
dc.date.accessioned2012-08-08T08:40:33Z-
dc.date.available2012-08-08T08:40:33Z-
dc.date.issued1997en_US
dc.identifier.citationLinear Algebra And Its Applications, 1997, v. 266 n. 1-3, p. 161-180en_US
dc.identifier.issn0024-3795en_US
dc.identifier.urihttp://hdl.handle.net/10722/156138-
dc.description.abstractThis paper studies the application of preconditioned conjugate-gradient methods in solving for the steady-state probability distribution of manufacturing systems. We consider the optimal hedging policy for a failure prone one-machine 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 machine-inventory system. The preconditioner is constructed by taking the circulant approximation of the near-Toeplitz 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 conjugate-gradient 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. © 1997 Elsevier Science Inc.en_US
dc.languageengen_US
dc.publisherElsevier Inc. The Journal's web site is located at http://www.elsevier.com/locate/laaen_US
dc.relation.ispartofLinear Algebra and Its Applicationsen_US
dc.titleCirculant preconditioners for failure prone manufacturing systemsen_US
dc.typeArticleen_US
dc.identifier.emailChing, WK:wching@hku.hken_US
dc.identifier.authorityChing, WK=rp00679en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.doi10.1016/S0024-3795(97)00001-3-
dc.identifier.scopuseid_2-s2.0-21944446582en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-21944446582&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume266en_US
dc.identifier.issue1-3en_US
dc.identifier.spage161en_US
dc.identifier.epage180en_US
dc.identifier.isiWOS:A1997YA27900010-
dc.publisher.placeUnited Statesen_US
dc.identifier.scopusauthoridChing, WK=13310265500en_US

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