-
Previous Article
An efficient cutting plane algorithm for the smallest enclosing circle problem
- JIMO Home
- This Issue
-
Next Article
Intrinsic impediments to category captainship collaboration
$ (Q,r) $ Model with $ CVaR_α $ of costs minimization
1. | School of Engineering, University of Medellín, Medellín 3300, Colombia |
2. | Basic Sciences Department, EAFIT University, Medellín 3300, Colombia |
3. | Risk Engineering, Empresas Públicas de Medellín, Medellín 3300, Colombia |
In the classical stochastic continuous review, $ (Q,r) $ model [
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.
References:
[1] |
S. Ahmed, U. Cakmak and A. Shapiro,
Coherent risk measures in inventory problems, European Journal of Operational Research, 1 (2007), 226-238.
doi: 10.1016/j.ejor.2006.07.016. |
[2] |
P. Artzner, F. Delbaen, J. Eber and D. Heath,
Coherent measure of risk, Mathematical Finance, 9 (1999), 203-227.
doi: 10.1111/1467-9965.00068. |
[3] |
X. Chen, M. Sim, D. Simchi-Levi and P. Sun,
Risk aversion in inventory management, Operations Research, 55 (2007), 828-842.
doi: 10.1287/opre.1070.0429. |
[4] |
L. Cheng and Z. Wana,
Bilevel newsvendor models considering retailer with CVaR objective, Computers Industrial Engineering, 57 (2009), 310-318.
doi: 10.1016/j.cie.2008.12.002. |
[5] |
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.
doi: 10.1287/opre.40.2.384. |
[6] |
J. Gotoh and Y. Takano,
Newsvendor solutions via conditional value-at-risk minimization, EuropeanJournal of Operational Research, 179 (2007), 80-96.
doi: 10.1016/j.ejor.2006.03.022. |
[7] | G. Hadley and M. Whittin, Analysis of Inventory Systems, 2 edition, Prentice-Hall, New York, 1963. Google Scholar |
[8] | W. J. Hopp and M. L. Spearman, Factory Physics, 2 edition, McGraw-Hill, New York, 2001. Google Scholar |
[9] |
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. Google Scholar |
[10] |
J. G. Murillo, M. A. Arias and L. C. Franco, Riesgo Operativo: Técnicas de modelación cuantitativa, 1st Sello Editorial Universidad de Medellín, Colombia, 2014. Google Scholar |
[11] |
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.
doi: 10.1007/978-1-4757-3150-7_15. |
[12] |
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.
doi: 10.1287/mnsc.43.7.951. |
[13] |
M. E. Puerta, M. A. Arias and J. I. Londoño, Matemáticas Aplicadas: Optimización de Inventarios Aleatorios, 1st Sello Editorial Universidad de Medellín, Colombia, 2011. Google Scholar |
[14] |
R. T. Rockafellar and S. P. Uryasev, Conditional Value-at-Risk for general loss distributions, Journal of Banking and Finance, 23 (2002), 1443-1471. Google Scholar |
[15] |
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.
doi: 10.1016/j.aml.2008.04.017. |
[16] |
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. Google Scholar |
[17] |
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.
doi: 10.1216/RMJ-2010-40-3-1061. |
[18] |
Y. Zheng,
On properties of stochastic inventory systems, Rocky Mountain Journal of Mathematics, 38 (1992), 87-101.
doi: 10.1287/mnsc.38.1.87. |
[19] | P. H. Zipkin, Foundations of Inventory Management, 2 edition, McGraw-Hill, New York, 2000. Google Scholar |
show all references
References:
[1] |
S. Ahmed, U. Cakmak and A. Shapiro,
Coherent risk measures in inventory problems, European Journal of Operational Research, 1 (2007), 226-238.
doi: 10.1016/j.ejor.2006.07.016. |
[2] |
P. Artzner, F. Delbaen, J. Eber and D. Heath,
Coherent measure of risk, Mathematical Finance, 9 (1999), 203-227.
doi: 10.1111/1467-9965.00068. |
[3] |
X. Chen, M. Sim, D. Simchi-Levi and P. Sun,
Risk aversion in inventory management, Operations Research, 55 (2007), 828-842.
doi: 10.1287/opre.1070.0429. |
[4] |
L. Cheng and Z. Wana,
Bilevel newsvendor models considering retailer with CVaR objective, Computers Industrial Engineering, 57 (2009), 310-318.
doi: 10.1016/j.cie.2008.12.002. |
[5] |
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.
doi: 10.1287/opre.40.2.384. |
[6] |
J. Gotoh and Y. Takano,
Newsvendor solutions via conditional value-at-risk minimization, EuropeanJournal of Operational Research, 179 (2007), 80-96.
doi: 10.1016/j.ejor.2006.03.022. |
[7] | G. Hadley and M. Whittin, Analysis of Inventory Systems, 2 edition, Prentice-Hall, New York, 1963. Google Scholar |
[8] | W. J. Hopp and M. L. Spearman, Factory Physics, 2 edition, McGraw-Hill, New York, 2001. Google Scholar |
[9] |
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. Google Scholar |
[10] |
J. G. Murillo, M. A. Arias and L. C. Franco, Riesgo Operativo: Técnicas de modelación cuantitativa, 1st Sello Editorial Universidad de Medellín, Colombia, 2014. Google Scholar |
[11] |
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.
doi: 10.1007/978-1-4757-3150-7_15. |
[12] |
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.
doi: 10.1287/mnsc.43.7.951. |
[13] |
M. E. Puerta, M. A. Arias and J. I. Londoño, Matemáticas Aplicadas: Optimización de Inventarios Aleatorios, 1st Sello Editorial Universidad de Medellín, Colombia, 2011. Google Scholar |
[14] |
R. T. Rockafellar and S. P. Uryasev, Conditional Value-at-Risk for general loss distributions, Journal of Banking and Finance, 23 (2002), 1443-1471. Google Scholar |
[15] |
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.
doi: 10.1016/j.aml.2008.04.017. |
[16] |
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. Google Scholar |
[17] |
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.
doi: 10.1216/RMJ-2010-40-3-1061. |
[18] |
Y. Zheng,
On properties of stochastic inventory systems, Rocky Mountain Journal of Mathematics, 38 (1992), 87-101.
doi: 10.1287/mnsc.38.1.87. |
[19] | P. H. Zipkin, Foundations of Inventory Management, 2 edition, McGraw-Hill, New York, 2000. Google Scholar |
[1] |
W. Cary Huffman. On the theory of $\mathbb{F}_q$-linear $\mathbb{F}_{q^t}$-codes. Advances in Mathematics of Communications, 2013, 7 (3) : 349-378. doi: 10.3934/amc.2013.7.349 |
[2] |
Charlene Kalle, Niels Langeveld, Marta Maggioni, Sara Munday. Matching for a family of infinite measure continued fraction transformations. Discrete & Continuous Dynamical Systems - A, 2020, 40 (11) : 6309-6330. doi: 10.3934/dcds.2020281 |
[3] |
Tuvi Etzion, Alexander Vardy. On $q$-analogs of Steiner systems and covering designs. Advances in Mathematics of Communications, 2011, 5 (2) : 161-176. doi: 10.3934/amc.2011.5.161 |
[4] |
Carlos Gutierrez, Nguyen Van Chau. A remark on an eigenvalue condition for the global injectivity of differentiable maps of $R^2$. Discrete & Continuous Dynamical Systems - A, 2007, 17 (2) : 397-402. doi: 10.3934/dcds.2007.17.397 |
[5] |
Ardeshir Ahmadi, Hamed Davari-Ardakani. A multistage stochastic programming framework for cardinality constrained portfolio optimization. Numerical Algebra, Control & Optimization, 2017, 7 (3) : 359-377. doi: 10.3934/naco.2017023 |
[6] |
Luke Finlay, Vladimir Gaitsgory, Ivan Lebedev. Linear programming solutions of periodic optimization problems: approximation of the optimal control. Journal of Industrial & Management Optimization, 2007, 3 (2) : 399-413. doi: 10.3934/jimo.2007.3.399 |
[7] |
Cicely K. Macnamara, Mark A. J. Chaplain. Spatio-temporal models of synthetic genetic oscillators. Mathematical Biosciences & Engineering, 2017, 14 (1) : 249-262. doi: 10.3934/mbe.2017016 |
[8] |
Fernando P. da Costa, João T. Pinto, Rafael Sasportes. On the convergence to critical scaling profiles in submonolayer deposition models. Kinetic & Related Models, 2018, 11 (6) : 1359-1376. doi: 10.3934/krm.2018053 |
[9] |
Jian Yang, Bendong Lou. Traveling wave solutions of competitive models with free boundaries. Discrete & Continuous Dynamical Systems - B, 2014, 19 (3) : 817-826. doi: 10.3934/dcdsb.2014.19.817 |
[10] |
Hong Seng Sim, Wah June Leong, Chuei Yee Chen, Siti Nur Iqmal Ibrahim. Multi-step spectral gradient methods with modified weak secant relation for large scale unconstrained optimization. Numerical Algebra, Control & Optimization, 2018, 8 (3) : 377-387. doi: 10.3934/naco.2018024 |
[11] |
Shanshan Chen, Junping Shi, Guohong Zhang. Spatial pattern formation in activator-inhibitor models with nonlocal dispersal. Discrete & Continuous Dynamical Systems - B, 2021, 26 (4) : 1843-1866. doi: 10.3934/dcdsb.2020042 |
[12] |
Alina Chertock, Alexander Kurganov, Mária Lukáčová-Medvi${\rm{\check{d}}}$ová, Șeyma Nur Özcan. An asymptotic preserving scheme for kinetic chemotaxis models in two space dimensions. Kinetic & Related Models, 2019, 12 (1) : 195-216. doi: 10.3934/krm.2019009 |
[13] |
Lei Liu, Li Wu. Multiplicity of closed characteristics on $ P $-symmetric compact convex hypersurfaces in $ \mathbb{R}^{2n} $. Discrete & Continuous Dynamical Systems - A, 2020 doi: 10.3934/dcds.2020378 |
[14] |
Jan Prüss, Laurent Pujo-Menjouet, G.F. Webb, Rico Zacher. Analysis of a model for the dynamics of prions. Discrete & Continuous Dynamical Systems - B, 2006, 6 (1) : 225-235. doi: 10.3934/dcdsb.2006.6.225 |
[15] |
Johannes Kellendonk, Lorenzo Sadun. Conjugacies of model sets. Discrete & Continuous Dynamical Systems - A, 2017, 37 (7) : 3805-3830. doi: 10.3934/dcds.2017161 |
[16] |
Mats Gyllenberg, Jifa Jiang, Lei Niu, Ping Yan. On the classification of generalized competitive Atkinson-Allen models via the dynamics on the boundary of the carrying simplex. Discrete & Continuous Dynamical Systems - A, 2018, 38 (2) : 615-650. doi: 10.3934/dcds.2018027 |
[17] |
Nhu N. Nguyen, George Yin. Stochastic partial differential equation models for spatially dependent predator-prey equations. Discrete & Continuous Dynamical Systems - B, 2020, 25 (1) : 117-139. doi: 10.3934/dcdsb.2019175 |
[18] |
Didier Bresch, Thierry Colin, Emmanuel Grenier, Benjamin Ribba, Olivier Saut. A viscoelastic model for avascular tumor growth. Conference Publications, 2009, 2009 (Special) : 101-108. doi: 10.3934/proc.2009.2009.101 |
[19] |
Ondrej Budáč, Michael Herrmann, Barbara Niethammer, Andrej Spielmann. On a model for mass aggregation with maximal size. Kinetic & Related Models, 2011, 4 (2) : 427-439. doi: 10.3934/krm.2011.4.427 |
[20] |
Luigi C. Berselli, Jishan Fan. Logarithmic and improved regularity criteria for the 3D nematic liquid crystals models, Boussinesq system, and MHD equations in a bounded domain. Communications on Pure & Applied Analysis, 2015, 14 (2) : 637-655. doi: 10.3934/cpaa.2015.14.637 |
2019 Impact Factor: 1.366
Tools
Metrics
Other articles
by authors
[Back to Top]