IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v214y2011i1p78-84.html
   My bibliography  Save this article

A multi-product risk-averse newsvendor with exponential utility function

Author

Listed:
  • Choi, Sungyong
  • Ruszczynski, Andrzej

Abstract

We consider a multi-product newsvendor using an exponential utility function. We first establish a few basic properties for the newsvendor regarding the convexity of the model and monotonicity of the impact of risk aversion on the solution. When the product demands are independent and the ratio of the degree of risk aversion to the number of products is sufficiently small, we obtain closed-form approximations of the optimal order quantities. The approximations are as easy to compute as the risk-neutral solution. We prove that when this ratio approaches zero, the risk-averse solution converges to the corresponding risk-neutral solution. When the product demands are positively (negatively) correlated, we show that risk aversion leads to lower (higher) optimal order quantities than the solution with independent demands. Using a numerical study, we examine convergence rates of the approximations and thoroughly study the interplay of demand correlation and risk aversion. The numerical study confirms our analytical results and further shows that an increased risk aversion does not always lead to lower order quantities, when demands are strongly negatively correlated.

Suggested Citation

  • Choi, Sungyong & Ruszczynski, Andrzej, 2011. "A multi-product risk-averse newsvendor with exponential utility function," European Journal of Operational Research, Elsevier, vol. 214(1), pages 78-84, October.
  • Handle: RePEc:eee:ejores:v:214:y:2011:i:1:p:78-84
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221711003183
    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. Maurice E. Schweitzer & Gérard P. Cachon, 2000. "Decision Bias in the Newsvendor Problem with a Known Demand Distribution: Experimental Evidence," Management Science, INFORMS, vol. 46(3), pages 404-420, March.
    2. Garrett van Ryzin & Siddharth Mahajan, 1999. "On the Relationship Between Inventory Costs and Variety Benefits in Retail Assortments," Management Science, INFORMS, vol. 45(11), pages 1496-1509, November.
    3. Edward Ignall & Arthur F. Veinott, Jr., 1969. "Optimality of Myopic Inventory Policies for Several Substitute Products," Management Science, INFORMS, vol. 15(5), pages 284-304, January.
    4. Isabelle Huault & V. Perret & S. Charreire-Petit, 2007. "Management," Post-Print halshs-00337676, HAL.
    5. Yossi Aviv & Awi Federgruen, 2001. "Capacitated Multi-Item Inventory Systems with Random and Seasonally Fluctuating Demands: Implications for Postponement Strategies," Management Science, INFORMS, vol. 47(4), pages 512-531, April.
    6. Gregory A. DeCroix & Antonio Arreola-Risa, 1998. "Optimal Production and Inventory Policy for Multiple Products Under Resource Constraints," Management Science, INFORMS, vol. 44(7), pages 950-961, July.
    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. Jiahua Zhang & Shu-Cherng Fang & Yifan Xu, 2018. "Inventory centralization with risk-averse newsvendors," Annals of Operations Research, Springer, vol. 268(1), pages 215-237, September.
    2. Wu, Meng & Zhu, Stuart X. & Teunter, Ruud H., 2014. "A risk-averse competitive newsvendor problem under the CVaR criterion," International Journal of Production Economics, Elsevier, vol. 156(C), pages 13-23.
    3. Chan, Chi Kin & Lee, Y.C.E. & Campbell, J.F., 2013. "Environmental performance—Impacts of vendor–buyer coordination," International Journal of Production Economics, Elsevier, vol. 145(2), pages 683-695.
    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. Zhang, Bin, 2012. "Multi-tier binary solution method for multi-product newsvendor problem with multiple constraints," European Journal of Operational Research, Elsevier, vol. 218(2), pages 426-434.
    6. Mohammad A.M. Abdel-Aal & Mujahid N. Syed & Shokri Z. Selim, 2017. "Multi-product selective newsvendor problem with service level constraints and market selection flexibility," International Journal of Production Research, Taylor & Francis Journals, vol. 55(1), pages 96-117, January.
    7. Menegatti, Mario, 2015. "New results on high-order risk changes," European Journal of Operational Research, Elsevier, vol. 243(2), pages 678-681.
    8. Caliskan Demirag, Ozgun, 2013. "Performance of weather-conditional rebates under different risk preferences," Omega, Elsevier, vol. 41(6), pages 1053-1067.
    9. Avinadav, Tal & Chernonog, Tatyana & Perlman, Yael, 2015. "The effect of risk sensitivity on a supply chain of mobile applications under a consignment contract with revenue sharing and quality investment," International Journal of Production Economics, Elsevier, vol. 168(C), pages 31-40.
    10. Choi, Sungyong & Jeon, Sumin & Kim, Jinmin & Park, Kwangtae, 2019. "A newsvendor analysis of a binomial yield production process," European Journal of Operational Research, Elsevier, vol. 273(3), pages 983-991.
    11. Avinadav, Tal & Chernonog, Tatyana & Ben-Zvi, Tal, 2019. "The effect of information superiority on a supply chain of virtual products," International Journal of Production Economics, Elsevier, vol. 216(C), pages 384-397.
    12. Oh, Sechan & Rhodes, James & Strong, Ray, 2016. "Impact of cost uncertainty on pricing decisions under risk aversion," European Journal of Operational Research, Elsevier, vol. 253(1), pages 144-153.
    13. Avinadav, Tal & Chernonog, Tatyana & Perlman, Yael, 2015. "Consignment contract for mobile apps between a single retailer and competitive developers with different risk attitudes," European Journal of Operational Research, Elsevier, vol. 246(3), pages 949-957.
    14. 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.
    15. Sungyong Choi & KyungBae Park & Sang-Oh Shim, 2018. "Comparing validity of risk measures on newsvendor models in open innovation perspective," Journal of Open Innovation: Technology, Market, and Complexity, MDPI, Open Access Journal, vol. 4(1), pages 1-12, January.
    16. 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.
    17. Mitra, Subrata, 2018. "Newsvendor problem with clearance pricing," European Journal of Operational Research, Elsevier, vol. 268(1), pages 193-202.
    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. Menegatti, Mario, 2014. "New results on the relationship among risk aversion, prudence and temperance," European Journal of Operational Research, Elsevier, vol. 232(3), pages 613-617.
    20. Jianghua Zhang & Felix T. S. Chan & Xinsheng Xu, 0. "The optimal order decisions of a risk-averse newsvendor under backlogging," Annals of Operations Research, Springer, vol. 0, pages 1-23.
    21. Wu, Meng & Zhu, Stuart X. & Teunter, Ruud H., 2013. "The risk-averse newsvendor problem with random capacity," European Journal of Operational Research, Elsevier, vol. 231(2), pages 328-336.
    22. Avinadav, Tal & Chernonog, Tatyana & Perlman, Yael, 2017. "Mergers and acquisitions between risk-averse parties," European Journal of Operational Research, Elsevier, vol. 259(3), pages 926-934.
    23. He, Juan & Ma, Chao & Pan, Kai, 2017. "Capacity investment in supply chain with risk averse supplier under risk diversification contract," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 106(C), pages 255-275.
    24. Pelin Canbolat, 2014. "Optimal halting policies in Markov population decision chains with constant risk posture," Annals of Operations Research, Springer, vol. 222(1), pages 227-237, 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:214:y:2011:i:1:p:78-84. See general information about how to correct material in RePEc.

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

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.