(Q; r) model with Cv aRα of costs minimization

In the classical stochastic continuous review, (Q,r) model [18,19], the inventory cost c(Q,r) has an averaging term which is given as an integral of the expected costs over the different inventory positions during the lead time on any given cycle. The main objective of the article is to study risk a...

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Fecha de publicación:
2017
Institución:
Universidad de Medellín
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Repositorio UDEM
Idioma:
eng
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oai:repository.udem.edu.co:11407/3350
Acceso en línea:
http://hdl.handle.net/11407/3350
Palabra clave:
(Q,r) model
CVaR
Risk averse optimization
Risk measure
Inventory models
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restrictedAccess
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http://purl.org/coar/access_right/c_16ec
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repository_id_str
dc.title.none.fl_str_mv (Q; r) model with Cv aRα of costs minimization
dc.title.english.eng.fl_str_mv (Q,r) model with CVaRα of costs minimization
title (Q; r) model with Cv aRα of costs minimization
spellingShingle (Q; r) model with Cv aRα of costs minimization
(Q,r) model
CVaR
Risk averse optimization
Risk measure
Inventory models
title_short (Q; r) model with Cv aRα of costs minimization
title_full (Q; r) model with Cv aRα of costs minimization
title_fullStr (Q; r) model with Cv aRα of costs minimization
title_full_unstemmed (Q; r) model with Cv aRα of costs minimization
title_sort (Q; r) model with Cv aRα of costs minimization
dc.subject.spa.fl_str_mv (Q,r) model
CVaR
Risk averse optimization
Risk measure
Inventory models
topic (Q,r) model
CVaR
Risk averse optimization
Risk measure
Inventory models
description In the classical stochastic continuous review, (Q,r) model [18,19], the inventory cost c(Q,r) has an averaging term which is given as an integral of the expected costs over the different inventory positions during the lead time on any given cycle. The main objective of the article is to study risk averse optimization in the classical (Q,r) model using CVaRα as a coherent risk measure with respect to the probability distribution of the demand D on inventory position costs (the sum of the inventory holding and backorder penality cost), for any given (generic) confidence level α∈[0,1). We show that the objective function is jointly convex in (Q,r). We also compare the risk averse solution and some other solutions in both analytical and computational ways. Additionally, some general and useful results are obtained.
publishDate 2017
dc.date.accessioned.none.fl_str_mv 2017-06-15T21:49:40Z
dc.date.available.none.fl_str_mv 2017-06-15T21:49:40Z
dc.date.created.none.fl_str_mv 2017
dc.type.eng.fl_str_mv Article
dc.type.coar.fl_str_mv http://purl.org/coar/resource_type/c_6501
http://purl.org/coar/resource_type/c_2df8fbb1
dc.type.driver.none.fl_str_mv info:eu-repo/semantics/article
dc.identifier.citation.spa.fl_str_mv Arias Serna, M. A.; Puerta Yepes, M. E.; Escalante Coterio, C. E. & Arango Ospina, G. (2017).(Q; r) Model with CV aR of costs minimization. Journal of industrial and management optimization. Volume 13, number 1, pp. 135-146
dc.identifier.issn.none.fl_str_mv 15475816
dc.identifier.uri.none.fl_str_mv http://hdl.handle.net/11407/3350
dc.identifier.doi.none.fl_str_mv doi:10.3934/jimo.2016008
dc.identifier.eissn.none.fl_str_mv 1553166X
identifier_str_mv Arias Serna, M. A.; Puerta Yepes, M. E.; Escalante Coterio, C. E. & Arango Ospina, G. (2017).(Q; r) Model with CV aR of costs minimization. Journal of industrial and management optimization. Volume 13, number 1, pp. 135-146
15475816
doi:10.3934/jimo.2016008
1553166X
url http://hdl.handle.net/11407/3350
dc.language.iso.none.fl_str_mv eng
language eng
dc.relation.isversionof.spa.fl_str_mv http://aimsciences.org/journals/pdfs.jsp?paperID=12311&mode=full
dc.relation.ispartofes.spa.fl_str_mv Journal of industrial and management optimization. Volume 13, number 1, january 2017 pp. 135-146
dc.relation.references.spa.fl_str_mv S. Ahmed, U. Cakmak and A. Shapiro, Coherent risk measures in inventory problems, European Journal of Operational Research, 1 (2007), 226-238.
P. Artzner, F. Delbaen, J. Eber and D.Heath, Coherent measure of risk, Mathematical Finance, 9 (1999), 203-227.
X. Chen, M. Sim, D. Simchi-Levi and P. Sun, Risk aversion in inventory management, Operations Research, 55 (2007), 828-842.
L. Cheng and Z. Wana, Bilevel newsvendor models considering retailer with CVaR objective, Computers Industrial Engineering, 57 (2009), 310-318.
A. Federgruen and Y. S. Zheng, A simple and efficient algorithm for computing optimal (r, Q) Policies in continuous-review stochastic inventory systems, Operations Research, 40 (1992), 808-813.
J. Gotoh and Y. Takano, Newsvendor solutions via conditional value-at-risk minimization, EuropeanJournal of Operational Research, 179 (2007), 80-96.
G. Hadley and M. Whittin, Analysis of Inventory Systems, edition, Prentice-Hall, New York, 1963.
W. J. Hopp and M. L. Spearman, Factory Physics, edition, McGraw-Hill, New York, 2001.
S. Moosa, A. Mohammed and S. S. Yadavalli, A note on evaluating the risk in continuous review inventory systems, International Journal of Production Research, 47 (2009), 5543-5558.
J. G. Murillo, M. A. Arias and L. C. Franco, Riesgo Operativo: Técnicas de modelación cuantitativa, Sello Editorial Universidad de Medellín, Colombia, 2014.
G. Pflug, Some remarks on the value-at-risk and the conditional value-at-risk, in Probabilistic Constrained Optimization, Nonconvex Optim. Appl., 49, Kluwer Acad. Publ., Dordrecht, 2000, 272-281.
D. E. Platt, L. W. Robinson and R. B. Freund, Tractable (Q, R) heuristic models for constrained service levels, Management Science, 43 (1997), 951-965.
M. E. Puerta, M. A. Arias and J. I. Londoño, Matemáticas Aplicadas: Optimización de Inventarios Aleatorios, Sello Editorial Universidad de Medellín, Colombia, 2011.
R. T. Rockafellar and S. P. Uryasev, Conditional Value-at-Risk for general loss distributions, Journal of Banking and Finance, 23 (2002), 1443-1471.
H. N. Shi, D. Li and Ch. Gu, The Schur-convexity of the mean of a convex function, Applied Mathematics Letters, 22 (2009), 932-937.
R. Vinod, S. Amitabh and J. B. Raturi, On incorporating business risk into continuous review inventory models, European Journal of Operational Research, 75 (1994), 136-150.
X. M. Zhang and Y. M. Chu, Convexity of the integral arithmetic mean of a convex function, Rocky Mountain Journal of Mathematics, 40 (2010), 1061-1068.
Y. Zheng, On properties of stochastic inventory systems, Rocky Mountain Journal of Mathematics, 38 (1992), 87-101.
P. H. Zipkin, Foundations of Inventory Management, edition, McGraw-Hill, New York, 2000.
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_16ec
dc.rights.accessrights.none.fl_str_mv info:eu-repo/semantics/restrictedAccess
eu_rights_str_mv restrictedAccess
rights_invalid_str_mv http://purl.org/coar/access_right/c_16ec
dc.publisher.spa.fl_str_mv AIMS - American Institute of Mathematical Sciences
dc.publisher.program.spa.fl_str_mv Ingeniería Financiera
dc.publisher.faculty.spa.fl_str_mv Facultad de Ingenierías
dc.source.spa.fl_str_mv Journal of industrial and management optimization
institution Universidad de Medellín
bitstream.url.fl_str_mv http://repository.udem.edu.co/bitstream/11407/3350/1/Articulo.html
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repository.name.fl_str_mv Repositorio Institucional Universidad de Medellin
repository.mail.fl_str_mv repositorio@udem.edu.co
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spelling 2017-06-15T21:49:40Z2017-06-15T21:49:40Z2017Arias Serna, M. A.; Puerta Yepes, M. E.; Escalante Coterio, C. E. & Arango Ospina, G. (2017).(Q; r) Model with CV aR of costs minimization. Journal of industrial and management optimization. Volume 13, number 1, pp. 135-14615475816http://hdl.handle.net/11407/3350doi:10.3934/jimo.20160081553166XIn the classical stochastic continuous review, (Q,r) model [18,19], the inventory cost c(Q,r) has an averaging term which is given as an integral of the expected costs over the different inventory positions during the lead time on any given cycle. The main objective of the article is to study risk averse optimization in the classical (Q,r) model using CVaRα as a coherent risk measure with respect to the probability distribution of the demand D on inventory position costs (the sum of the inventory holding and backorder penality cost), for any given (generic) confidence level α∈[0,1). We show that the objective function is jointly convex in (Q,r). We also compare the risk averse solution and some other solutions in both analytical and computational ways. Additionally, some general and useful results are obtained.engAIMS - American Institute of Mathematical SciencesIngeniería FinancieraFacultad de Ingenieríashttp://aimsciences.org/journals/pdfs.jsp?paperID=12311&mode=fullJournal of industrial and management optimization. Volume 13, number 1, january 2017 pp. 135-146S. Ahmed, U. Cakmak and A. Shapiro, Coherent risk measures in inventory problems, European Journal of Operational Research, 1 (2007), 226-238.P. Artzner, F. Delbaen, J. Eber and D.Heath, Coherent measure of risk, Mathematical Finance, 9 (1999), 203-227.X. Chen, M. Sim, D. Simchi-Levi and P. Sun, Risk aversion in inventory management, Operations Research, 55 (2007), 828-842.L. Cheng and Z. Wana, Bilevel newsvendor models considering retailer with CVaR objective, Computers Industrial Engineering, 57 (2009), 310-318.A. Federgruen and Y. S. Zheng, A simple and efficient algorithm for computing optimal (r, Q) Policies in continuous-review stochastic inventory systems, Operations Research, 40 (1992), 808-813.J. Gotoh and Y. Takano, Newsvendor solutions via conditional value-at-risk minimization, EuropeanJournal of Operational Research, 179 (2007), 80-96.G. Hadley and M. Whittin, Analysis of Inventory Systems, edition, Prentice-Hall, New York, 1963.W. J. Hopp and M. L. Spearman, Factory Physics, edition, McGraw-Hill, New York, 2001.S. Moosa, A. Mohammed and S. S. Yadavalli, A note on evaluating the risk in continuous review inventory systems, International Journal of Production Research, 47 (2009), 5543-5558.J. G. Murillo, M. A. Arias and L. C. Franco, Riesgo Operativo: Técnicas de modelación cuantitativa, Sello Editorial Universidad de Medellín, Colombia, 2014.G. Pflug, Some remarks on the value-at-risk and the conditional value-at-risk, in Probabilistic Constrained Optimization, Nonconvex Optim. Appl., 49, Kluwer Acad. Publ., Dordrecht, 2000, 272-281.D. E. Platt, L. W. Robinson and R. B. Freund, Tractable (Q, R) heuristic models for constrained service levels, Management Science, 43 (1997), 951-965.M. E. Puerta, M. A. Arias and J. I. Londoño, Matemáticas Aplicadas: Optimización de Inventarios Aleatorios, Sello Editorial Universidad de Medellín, Colombia, 2011.R. T. Rockafellar and S. P. Uryasev, Conditional Value-at-Risk for general loss distributions, Journal of Banking and Finance, 23 (2002), 1443-1471.H. N. Shi, D. Li and Ch. Gu, The Schur-convexity of the mean of a convex function, Applied Mathematics Letters, 22 (2009), 932-937.R. Vinod, S. Amitabh and J. B. Raturi, On incorporating business risk into continuous review inventory models, European Journal of Operational Research, 75 (1994), 136-150.X. M. Zhang and Y. M. Chu, Convexity of the integral arithmetic mean of a convex function, Rocky Mountain Journal of Mathematics, 40 (2010), 1061-1068.Y. Zheng, On properties of stochastic inventory systems, Rocky Mountain Journal of Mathematics, 38 (1992), 87-101.P. H. Zipkin, Foundations of Inventory Management, edition, McGraw-Hill, New York, 2000.Journal of industrial and management optimization(Q,r) modelCVaRRisk averse optimizationRisk measureInventory models(Q; r) model with Cv aRα of costs minimization(Q,r) model with CVaRα of costs minimizationArticleinfo:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1info:eu-repo/semantics/restrictedAccesshttp://purl.org/coar/access_right/c_16ecArias Serna, María AndreaPuerta Yepes, María EugeniaEscalante Coterio, César EdinsonArango Ospina, GerardoArias Serna, María Andrea; Universidad de MedellínPuerta Yepes, María Eugenia; Universidad EAFITEscalante Coterio, César Edinson; Empresas Públicas de MedellínArango Ospina, Gerardo; Universidad EAFITORIGINALArticulo.htmltext/html491http://repository.udem.edu.co/bitstream/11407/3350/1/Articulo.html9928f43e86877113723540e989aa88fdMD5111407/3350oai:repository.udem.edu.co:11407/33502021-02-03 15:12:56.235Repositorio Institucional Universidad de Medellinrepositorio@udem.edu.co

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