IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v283y2020i3p942-953.html
   My bibliography  Save this article

Mean-variance analysis of the newsvendor problem with price-dependent, isoelastic demand

Author

Listed:
  • Rubio-Herrero, Javier
  • Baykal-Gürsoy, Melike

Abstract

We present a mean-variance analysis of the single-product, single-period newsvendor problem with two decision variables, price and stock quantity. The demand is price-dependent, multiplicative, and isoelastic, and the product sold is price-elastic. The main goal of this paper is to completely characterize a framework where most risk sensitivities can be studied and find conditions under which the unimodality of this mean-variance performance measure is guaranteed. We aim at presenting these conditions in terms of a metric that can capture managerial attention. To this end we use the lost sales rate (LSR) elasticity, as it relates directly to the retailer’s level of service. The main contribution of this paper is that, with very few and mild assumptions, we complement currently existing results for the uniqueness of the solution in the presence of price-inelastic products by extending the applicability of the LSR elasticity to the problem with price-elastic goods and assess its unimodality when the decision maker is risk-neutral or risk-sensitive. Finally, we compare the results under this model with others previously obtained for additive demand models, and we emphasize the reasons that make it difficult to attain similar results with an isoelastic demand model.

Suggested Citation

  • Rubio-Herrero, Javier & Baykal-Gürsoy, Melike, 2020. "Mean-variance analysis of the newsvendor problem with price-dependent, isoelastic demand," European Journal of Operational Research, Elsevier, vol. 283(3), pages 942-953.
    • Handle: RePEc:eee:ejores:v:283:y:2020:i:3:p:942-953
    DOI: 10.1016/j.ejor.2019.11.064
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221719309762
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2019.11.064?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. Awi Federgruen & Aliza Heching, 1999. "Combined Pricing and Inventory Control Under Uncertainty," Operations Research, INFORMS, vol. 47(3), pages 454-475, June.
    2. Özler, Aysun & Tan, BarIs & Karaesmen, Fikri, 2009. "Multi-product newsvendor problem with value-at-risk considerations," International Journal of Production Economics, Elsevier, vol. 117(2), pages 244-255, February.
    3. Khouja, Moutaz, 1999. "The single-period (news-vendor) problem: literature review and suggestions for future research," Omega, Elsevier, vol. 27(5), pages 537-553, October.
    4. E. Zabel, 1970. "Monopoly and Uncertainty," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 37(2), pages 205-219.
    5. Fishburn, Peter C, 1977. "Mean-Risk Analysis with Risk Associated with Below-Target Returns," American Economic Review, American Economic Association, vol. 67(2), pages 116-126, March.
    6. George E. Monahan & Nicholas C. Petruzzi & Wen Zhao, 2004. "The Dynamic Pricing Problem from a Newsvendor's Perspective," Manufacturing & Service Operations Management, INFORMS, vol. 6(1), pages 73-91, September.
    7. Youhua (Frank) Chen & Minghui Xu & Zhe George Zhang, 2009. "Technical Note---A Risk-Averse Newsvendor Model Under the CVaR Criterion," Operations Research, INFORMS, vol. 57(4), pages 1040-1044, August.
    8. Choi, Tsan-Ming & Chiu, Chun-Hung, 2012. "Mean-downside-risk and mean-variance newsvendor models: Implications for sustainable fashion retailing," International Journal of Production Economics, Elsevier, vol. 135(2), pages 552-560.
    9. Mokrane Bouakiz & Matthew J. Sobel, 1992. "Inventory Control with an Exponential Utility Criterion," Operations Research, INFORMS, vol. 40(3), pages 603-608, June.
    10. Xinsheng, Xu & Zhiqing, Meng & Rui, Shen & Min, Jiang & Ping, Ji, 2015. "Optimal decisions for the loss-averse newsvendor problem under CVaR," International Journal of Production Economics, Elsevier, vol. 164(C), pages 146-159.
    11. 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.
    12. Li, Tao & Sethi, Suresh P. & Zhang, Jun, 2014. "Supply diversification with isoelastic demand," International Journal of Production Economics, Elsevier, vol. 157(C), pages 2-6.
    13. Qin, Yan & Wang, Ruoxuan & Vakharia, Asoo J. & Chen, Yuwen & Seref, Michelle M.H., 2011. "The newsvendor problem: Review and directions for future research," European Journal of Operational Research, Elsevier, vol. 213(2), pages 361-374, September.
    14. Xu, Minghui & Chen, Youhua (Frank) & Xu, Xiaolin, 2010. "The effect of demand uncertainty in a price-setting newsvendor model," European Journal of Operational Research, Elsevier, vol. 207(2), pages 946-957, December.
    15. Christensen, Finn, 2017. "A necessary and sufficient condition for a unique maximum with an application to potential games," Economics Letters, Elsevier, vol. 161(C), pages 120-123.
    16. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    17. Nicholas C. Petruzzi & Maqbool Dada, 1999. "Pricing and the Newsvendor Problem: A Review with Extensions," Operations Research, INFORMS, vol. 47(2), pages 183-194, April.
    18. Edwin S. Mills, 1959. "Uncertainty and Price Theory," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 73(1), pages 116-130.
    19. Britz, Wolfgang & Heckelei, Thomas, 2008. "Recent Developments In Eu Policies – Challenges For Partial Equilibrium Models," 107th Seminar, January 30-February 1, 2008, Sevilla, Spain 6315, European Association of Agricultural Economists.
    20. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    21. Werner Jammernegg & Peter Kischka, 2007. "Risk-averse and risk-taking newsvendors: a conditional expected value approach," Review of Managerial Science, Springer, vol. 1(1), pages 93-110, April.
    22. Kavallari, Aikaterini & Borresch, Rene & Schmitz, P. Michael, 2006. "Modelling agricultural policy reforms in the Mediterranean basin - Adjustments of AGRISIM," 98th Seminar, June 29-July 2, 2006, Chania, Crete, Greece 10074, European Association of Agricultural Economists.
    23. Louis Eeckhoudt & Christian Gollier & Harris Schlesinger, 1995. "The Risk-Averse (and Prudent) Newsboy," Management Science, INFORMS, vol. 41(5), pages 786-794, May.
    24. Duan Li & Wan‐Lung Ng, 2000. "Optimal Dynamic Portfolio Selection: Multiperiod Mean‐Variance Formulation," Mathematical Finance, Wiley Blackwell, vol. 10(3), pages 387-406, July.
    25. Xu, Xiaolin & Cai, Xiaoqiang & Chen, Youhua, 2011. "Unimodality of price-setting newsvendor's objective function with multiplicative demand and its applications," International Journal of Production Economics, Elsevier, vol. 133(2), pages 653-661, October.
    26. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    27. Yunzeng Wang & Li Jiang & Zuo-Jun Shen, 2004. "Channel Performance Under Consignment Contract with Revenue Sharing," Management Science, INFORMS, vol. 50(1), pages 34-47, January.
    28. Grootveld, Henk & Hallerbach, Winfried, 1999. "Variance vs downside risk: Is there really that much difference?," European Journal of Operational Research, Elsevier, vol. 114(2), pages 304-319, April.
    29. 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.
    30. Rubio-Herrero, Javier & Baykal-Gürsoy, Melike, 2018. "On the unimodality of the price-setting newsvendor problem with additive demand under risk considerations," European Journal of Operational Research, Elsevier, vol. 265(3), pages 962-974.
    31. Ayşe Kocabıyıkoğlu & Ioana Popescu, 2011. "An Elasticity Approach to the Newsvendor with Price-Sensitive Demand," Operations Research, INFORMS, vol. 59(2), pages 301-312, April.
    32. Vipul Agrawal & Sridhar Seshadri, 2000. "Impact of Uncertainty and Risk Aversion on Price and Order Quantity in the Newsvendor Problem," Manufacturing & Service Operations Management, INFORMS, vol. 2(4), pages 410-423, July.
    33. Chunming (Victor) Shi & Lan Guo, 2012. "Profit Target Setting for Multiple Divisions: A Newsvendor Perspective," International Series in Operations Research & Management Science, in: Tsan-Ming Choi (ed.), Handbook of Newsvendor Problems, edition 127, chapter 0, pages 341-359, Springer.
    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. Kumar, Uday M & Bhat, Sanjay P. & Kavitha, Veeraruna & Hemachandra, Nandyala, 2023. "Approximate solutions to constrained risk-sensitive Markov decision processes," European Journal of Operational Research, Elsevier, vol. 310(1), pages 249-267.
    2. Zhang, Qiao & Chen, Jing & Lin, Jun, 2022. "Market targeting with social influences and risk aversion in a co-branding alliance," European Journal of Operational Research, Elsevier, vol. 297(1), pages 301-318.
    3. Andrea C. Hupman & Jay Simon, 2023. "The Legacy of Peter Fishburn: Foundational Work and Lasting Impact," Decision Analysis, INFORMS, vol. 20(1), pages 1-15, March.

    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. Rubio-Herrero, Javier & Baykal-Gürsoy, Melike, 2018. "On the unimodality of the price-setting newsvendor problem with additive demand under risk considerations," European Journal of Operational Research, Elsevier, vol. 265(3), pages 962-974.
    2. Jammernegg, Werner & Kischka, Peter, 2013. "The price-setting newsvendor with service and loss constraints," Omega, Elsevier, vol. 41(2), pages 326-335.
    3. Li, Xiang & Qi, Xiangtong & Li, Yongjian, 2021. "On sales effort and pricing decisions under alternative risk criteria," European Journal of Operational Research, Elsevier, vol. 293(2), pages 603-614.
    4. Bai, Tian & Wu, Meng & Zhu, Stuart X., 2019. "Pricing and ordering by a loss averse newsvendor with reference dependence," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 131(C), pages 343-365.
    5. Qin, Yan & Wang, Ruoxuan & Vakharia, Asoo J. & Chen, Yuwen & Seref, Michelle M.H., 2011. "The newsvendor problem: Review and directions for future research," European Journal of Operational Research, Elsevier, vol. 213(2), pages 361-374, September.
    6. 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.
    7. Mandal, Prasenjit & Kaul, Rupali & Jain, Tarun, 2018. "Stocking and pricing decisions under endogenous demand and reference point effects," European Journal of Operational Research, Elsevier, vol. 264(1), pages 181-199.
    8. Xu, Minghui & Lu, Ye, 2013. "The effect of supply uncertainty in price-setting newsvendor models," European Journal of Operational Research, Elsevier, vol. 227(3), pages 423-433.
    9. Mitra, Subrata, 2018. "Newsvendor problem with clearance pricing," European Journal of Operational Research, Elsevier, vol. 268(1), pages 193-202.
    10. Wang, Ruopeng & Wang, Jinting, 2018. "Procurement strategies with quantity-oriented reference point and loss aversion," Omega, Elsevier, vol. 80(C), pages 1-11.
    11. Gholami, Reza Azad & Sandal, Leif Kristoffer & Ubøe, Jan, 2021. "A solution algorithm for multi-period bi-level channel optimization with dynamic price-dependent stochastic demand," Omega, Elsevier, vol. 102(C).
    12. 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).
    13. Serel, Doğan A., 2017. "A single-period stocking and pricing problem involving stochastic emergency supply," International Journal of Production Economics, Elsevier, vol. 185(C), pages 180-195.
    14. Arcelus, F.J. & Kumar, Satyendra & Srinivasan, G., 2012. "Risk tolerance and a retailer's pricing and ordering policies within a newsvendor framework," Omega, Elsevier, vol. 40(2), pages 188-198, April.
    15. Doran Wood & Sıla Çetinkaya, 2024. "A comparative analysis of how to handle stockout scenarios: the impact of newsvendor’s risk attitude," Annals of Operations Research, Springer, vol. 338(2), pages 1187-1218, July.
    16. Boutselis, Petros & McNaught, Ken, 2014. "Finite-Time Horizon Logistics Decision Making Problems: Consideration of a Wider Set of Factors," Chapters from the Proceedings of the Hamburg International Conference of Logistics (HICL), in: Blecker, Thorsten & Kersten, Wolfgang & Ringle, Christian M. (ed.), Innovative Methods in Logistics and Supply Chain Management: Current Issues and Emerging Practices. Proceedings of the Hamburg International Conferenc, volume 19, pages 249-274, Hamburg University of Technology (TUHH), Institute of Business Logistics and General Management.
    17. Eskandarzadeh, Saman & Eshghi, Kourosh & Bahramgiri, Mohsen, 2016. "Risk shaping in production planning problem with pricing under random yield," European Journal of Operational Research, Elsevier, vol. 253(1), pages 108-120.
    18. Arıkan, Emel & Fichtinger, Johannes, 2017. "The risk-averse newsvendor problem under spectral risk measures: A classification with extensions," European Journal of Operational Research, Elsevier, vol. 256(1), pages 116-125.
    19. Kyparisis, George J. & Koulamas, Christos, 2018. "Optimal pricing and seat allocation for a two-cabin airline revenue management problem," International Journal of Production Economics, Elsevier, vol. 201(C), pages 18-25.
    20. Azad Gholami, Reza & Sandal, Leif K. & Ubøe, Jan, 2016. "Channel Coordination in a Multi-period Newsvendor Model with Dynamic, Price-dependent Stochastic Demand," Discussion Papers 2016/6, Norwegian School of Economics, Department of Business and Management Science.

    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:283:y:2020:i:3:p:942-953. 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.