IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v199y2009i2p420-434.html
   My bibliography  Save this article

Single and multi-period optimal inventory control models with risk-averse constraints

Author

Listed:
  • Zhang, Dali
  • Xu, Huifu
  • Wu, Yue

Abstract

This paper presents some convex stochastic programming models for single and multi-period inventory control problems where the market demand is random and order quantities need to be decided before demand is realized. Both models minimize the expected losses subject to risk aversion constraints expressed through Value at Risk (VaR) and Conditional Value at Risk (CVaR) as risk measures. A sample average approximation method is proposed for solving the models and convergence analysis of optimal solutions of the sample average approximation problem is presented. Finally, some numerical examples are given to illustrate the convergence of the algorithm.

Suggested Citation

  • Zhang, Dali & Xu, Huifu & Wu, Yue, 2009. "Single and multi-period optimal inventory control models with risk-averse constraints," European Journal of Operational Research, Elsevier, vol. 199(2), pages 420-434, December.
    • Handle: RePEc:eee:ejores:v:199:y:2009:i:2:p:420-434
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(08)01037-0
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Suresh P. Sethi & Feng Cheng, 1997. "Optimality of ( s , S ) Policies in Inventory Models with Markovian Demand," Operations Research, INFORMS, vol. 45(6), pages 931-939, December.
    2. Stephen M. Robinson, 1996. "Analysis of Sample-Path Optimization," Mathematics of Operations Research, INFORMS, vol. 21(3), pages 513-528, August.
    3. Basak, Suleyman & Shapiro, Alexander, 2001. "Value-at-Risk-Based Risk Management: Optimal Policies and Asset Prices," The Review of Financial Studies, Society for Financial Studies, vol. 14(2), pages 371-405.
    4. Alexander, S. & Coleman, T.F. & Li, Y., 2006. "Minimizing CVaR and VaR for a portfolio of derivatives," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 583-605, February.
    5. Ahmed, Shabbir & Cakmak, Ulas & Shapiro, Alexander, 2007. "Coherent risk measures in inventory problems," European Journal of Operational Research, Elsevier, vol. 182(1), pages 226-238, October.
    6. Tapiero, Charles S., 2005. "Value at risk and inventory control," European Journal of Operational Research, Elsevier, vol. 163(3), pages 769-775, June.
    7. Fangruo Chen & Jing-Sheng Song, 2001. "Optimal Policies for Multiechelon Inventory Problems with Markov-Modulated Demand," Operations Research, INFORMS, vol. 49(2), pages 226-234, April.
    8. Huifu Xu & Fanwen Meng, 2007. "Convergence Analysis of Sample Average Approximation Methods for a Class of Stochastic Mathematical Programs with Equality Constraints," Mathematics of Operations Research, INFORMS, vol. 32(3), pages 648-668, August.
    9. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
    10. Jing-Sheng Song & Paul Zipkin, 1993. "Inventory Control in a Fluctuating Demand Environment," Operations Research, INFORMS, vol. 41(2), pages 351-370, April.
    11. Miguel A. Lejeune & Andrzej Ruszczyński, 2007. "An Efficient Trajectory Method for Probabilistic Production-Inventory-Distribution Problems," Operations Research, INFORMS, vol. 55(2), pages 378-394, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Qiu, Ruozhen & Shang, Jennifer & Huang, Xiaoyuan, 2014. "Robust inventory decision under distribution uncertainty: A CVaR-based optimization approach," International Journal of Production Economics, Elsevier, vol. 153(C), pages 13-23.
    2. Wei Liu & Han Zhao & Shiji Song & Wenxuan He & Xiaochen Li, 2021. "Coping with Loss Aversion and Risk Management in the Supply Chain Coordination," Sustainability, MDPI, vol. 13(8), pages 1-18, April.
    3. Consuelos Salas, Laura & Robles Cárdenas, Manuel & Zhang, Muhong, 2012. "Inventory policies for humanitarian aid during hurricanes," Socio-Economic Planning Sciences, Elsevier, vol. 46(4), pages 272-280.
    4. Tsan-Ming Choi, 2016. "Multi-period risk minimization purchasing models for fashion products with interest rate, budget, and profit target considerations," Annals of Operations Research, Springer, vol. 237(1), pages 77-98, February.
    5. Niu, Baozhuang & Chen, Lei & Liu, Yaoqi & Jin, Yong, 2019. "Joint price and quality decisions considering Chinese customers' variety seeking behavior," International Journal of Production Economics, Elsevier, vol. 213(C), pages 97-107.
    6. Henry Inegbedion* & Sunday Eze & Abiola Asaleye & Adedoyin Lawal, 2019. "Inventory Management and Organisational Efficiency," The Journal of Social Sciences Research, Academic Research Publishing Group, vol. 5(3), pages 756-763, 03-2019.
    7. Weiwei Zhang & Zhongfei Li & Ke Fu & Fan Wang, 2017. "Effect of the Return Policy in a Continuous-Time Newsvendor Problem," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 34(06), pages 1-28, December.
    8. Jammernegg, Werner & Kischka, Peter, 2013. "Risk preferences of a newsvendor with service and loss constraints," International Journal of Production Economics, Elsevier, vol. 143(2), pages 410-415.
    9. Liu, Yongchao & Xu, Huifu & Yang, Shu-Jung Sunny & Zhang, Jin, 2018. "Distributionally robust equilibrium for continuous games: Nash and Stackelberg models," European Journal of Operational Research, Elsevier, vol. 265(2), pages 631-643.
    10. Chung‐Yee Lee & Xi Li & Mingzhu Yu, 2015. "The loss‐averse newsvendor problem with supply options," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(1), pages 46-59, February.
    11. Qiu, Ruozhen & Sun, Minghe & Lim, Yun Fong, 2017. "Optimizing (s, S) policies for multi-period inventory models with demand distribution uncertainty: Robust dynamic programing approaches," European Journal of Operational Research, Elsevier, vol. 261(3), pages 880-892.
    12. Tsan-Ming Choi, 2016. "Multi-period risk minimization purchasing models for fashion products with interest rate, budget, and profit target considerations," Annals of Operations Research, Springer, vol. 237(1), pages 77-98, February.
    13. Salahi, Niloofar & Jafari, Mohsen A., 2016. "Energy-Performance as a driver for optimal production planning," Applied Energy, Elsevier, vol. 174(C), pages 88-100.
    14. Wang, Daao & Dimitrov, Stanko & Jian, Lirong, 2020. "Optimal inventory decisions for a risk-averse retailer when offering layaway," European Journal of Operational Research, Elsevier, vol. 284(1), pages 108-120.
    15. Wen Chen & Burcu Tan, 2022. "Dynamic procurement from multiple suppliers with random capacities," Annals of Operations Research, Springer, vol. 317(2), pages 509-536, October.
    16. Rui Hou & Zibin Cui & You Zhao, 2022. "Pricing leadership decisions of competing firms with consumer learning," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 43(6), pages 2326-2346, September.
    17. Wang, Yulan & Wallace, Stein W. & Shen, Bin & Choi, Tsan-Ming, 2015. "Service supply chain management: A review of operational models," European Journal of Operational Research, Elsevier, vol. 247(3), pages 685-698.
    18. Chun-Hung Chiu & Tsan-Ming Choi, 2016. "Supply chain risk analysis with mean-variance models: a technical review," Annals of Operations Research, Springer, vol. 240(2), pages 489-507, May.
    19. Dai, B. & Chen, H.X. & Li, Y.A. & Zhang, Y.D. & Wang, X.Q. & Deng, Y.M., 2021. "Inventory replenishment planning of a distribution system with storage capacity constraints and multi-channel order fulfilment," Omega, Elsevier, vol. 102(C).
    20. Poormoaied, Saeed & Atan, Zümbül, 2020. "A multi-attribute utility theory approach to ordering policy for perishable items," International Journal of Production Economics, Elsevier, vol. 225(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. E J Lodree Jr & S Taskin, 2008. "An insurance risk management framework for disaster relief and supply chain disruption inventory planning," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(5), pages 674-684, May.
    2. Qiu, Ruozhen & Sun, Minghe & Lim, Yun Fong, 2017. "Optimizing (s, S) policies for multi-period inventory models with demand distribution uncertainty: Robust dynamic programing approaches," European Journal of Operational Research, Elsevier, vol. 261(3), pages 880-892.
    3. Dan A. Iancu & Marek Petrik & Dharmashankar Subramanian, 2015. "Tight Approximations of Dynamic Risk Measures," Mathematics of Operations Research, INFORMS, vol. 40(3), pages 655-682, March.
    4. Li Chen & Jing-Sheng Song & Yue Zhang, 2017. "Serial Inventory Systems with Markov-Modulated Demand: Derivative Bounds, Asymptotic Analysis, and Insights," Operations Research, INFORMS, vol. 65(5), pages 1231-1249, October.
    5. Tan, Tarkan & Gullu, Refik & Erkip, Nesim, 2007. "Modelling imperfect advance demand information and analysis of optimal inventory policies," European Journal of Operational Research, Elsevier, vol. 177(2), pages 897-923, March.
    6. Walid W. Nasr, 2022. "Inventory systems with stochastic and batch demand: computational approaches," Annals of Operations Research, Springer, vol. 309(1), pages 163-187, February.
    7. Lu Huang & Jing-Sheng Song & Jordan Tong, 2016. "Supply Chain Planning for Random Demand Surges: Reactive Capacity and Safety Stock," Manufacturing & Service Operations Management, INFORMS, vol. 18(4), pages 509-524, October.
    8. Long Gao & Susan H. Xu & Michael O. Ball, 2012. "Managing an Available-to-Promise Assembly System with Dynamic Short-Term Pseudo-Order Forecast," Management Science, INFORMS, vol. 58(4), pages 770-790, April.
    9. Manafzadeh Dizbin, Nima & Tan, Barış, 2020. "Optimal control of production-inventory systems with correlated demand inter-arrival and processing times," International Journal of Production Economics, Elsevier, vol. 228(C).
    10. Jinhui Han & Suresh P. Sethi & Chi Chung Siu & Sheung Chi Phillip Yam, 2023. "Co‐op advertising in randomly fluctuating markets," Production and Operations Management, Production and Operations Management Society, vol. 32(6), pages 1617-1635, June.
    11. Alp Muharremoglu & John N. Tsitsiklis, 2008. "A Single-Unit Decomposition Approach to Multiechelon Inventory Systems," Operations Research, INFORMS, vol. 56(5), pages 1089-1103, October.
    12. Scheller-Wolf, Alan & Tayur, Sridhar, 2009. "Risk sharing in supply chains using order bands--Analytical results and managerial insights," International Journal of Production Economics, Elsevier, vol. 121(2), pages 715-727, October.
    13. Arnoud den Boer & Ohad Perry & Bert Zwart, 2018. "Dynamic pricing policies for an inventory model with random windows of opportunities," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(8), pages 660-675, December.
    14. Pesenti, Silvana M. & Millossovich, Pietro & Tsanakas, Andreas, 2019. "Reverse sensitivity testing: What does it take to break the model?," European Journal of Operational Research, Elsevier, vol. 274(2), pages 654-670.
    15. Guillermo Gallego & Özalp Özer, 2003. "Optimal Replenishment Policies for Multiechelon Inventory Problems Under Advance Demand Information," Manufacturing & Service Operations Management, INFORMS, vol. 5(2), pages 157-175, February.
    16. Garud Iyengar & Alfred Ma, 2013. "Fast gradient descent method for Mean-CVaR optimization," Annals of Operations Research, Springer, vol. 205(1), pages 203-212, May.
    17. Jianqiang Hu & Cheng Zhang & Chenbo Zhu, 2016. "( s , S ) Inventory Systems with Correlated Demands," INFORMS Journal on Computing, INFORMS, vol. 28(4), pages 603-611, November.
    18. Poormoaied, Saeed & Atan, Zümbül, 2020. "A multi-attribute utility theory approach to ordering policy for perishable items," International Journal of Production Economics, Elsevier, vol. 225(C).
    19. Cui, Xueting & Zhu, Shushang & Sun, Xiaoling & Li, Duan, 2013. "Nonlinear portfolio selection using approximate parametric Value-at-Risk," Journal of Banking & Finance, Elsevier, vol. 37(6), pages 2124-2139.
    20. Yongchao Liu & Huifu Xu & Jane J. Ye, 2011. "Penalized Sample Average Approximation Methods for Stochastic Mathematical Programs with Complementarity Constraints," Mathematics of Operations Research, INFORMS, vol. 36(4), pages 670-694, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:199:y:2009:i:2:p:420-434. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.