IDEAS home Printed from https://ideas.repec.org/a/bla/popmgt/v29y2020i3p788-796.html
   My bibliography  Save this article

Concavity and Unimodality of Expected Revenue Under Discrete Willingness to Pay Distributions

Author

Listed:
  • Anh Ninh
  • Zuo‐Jun Max Shen
  • Martin A. Lariviere

Abstract

Most pricing and revenue management models have at their core an optimization problem; one needs to determine the optimal price or quantity to maximize a profit or revenue function. To ensure tractability, conditions that assure the objective function has a unique solution are enormously helpful. So far, several technical assumptions have been proposed for the continuous case, but comparatively little attention has been given to the discrete counterpart despite its prevalence in practice. Thus, this study aims to develop new technical assumptions, built upon relevant economic concepts, to guarantee the tractability of revenue management models in discrete settings. In particular, we present two sufficient conditions for the revenue function to be concave, in terms of quantity or price and propose a condition for the revenue function to be unimodal, called discrete increasing generalized failure rate (IGFR). Our definition has an appropriate economic interpretation and offers comparable properties to those of the continuous version. Finally, we show the discrete IGFR property holds for several discrete distributions.

Suggested Citation

  • Anh Ninh & Zuo‐Jun Max Shen & Martin A. Lariviere, 2020. "Concavity and Unimodality of Expected Revenue Under Discrete Willingness to Pay Distributions," Production and Operations Management, Production and Operations Management Society, vol. 29(3), pages 788-796, March.
    • Handle: RePEc:bla:popmgt:v:29:y:2020:i:3:p:788-796
    DOI: 10.1111/poms.13138
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/poms.13138
    Download Restriction: no
    File URL: https://libkey.io/10.1111/poms.13138?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
    ---><---

    References listed on IDEAS

    as
    1. Anh Ninh & Honggang Hu & David Allen, 2019. "Robust newsvendor problems: effect of discrete demands," Annals of Operations Research, Springer, vol. 275(2), pages 607-621, April.
    2. Yingjie Lan & Huina Gao & Michael O. Ball & Itir Karaesmen, 2008. "Revenue Management with Limited Demand Information," Management Science, INFORMS, vol. 54(9), pages 1594-1609, September.
    3. Guillermo Gallego & Garrett van Ryzin, 1994. "Optimal Dynamic Pricing of Inventories with Stochastic Demand over Finite Horizons," Management Science, INFORMS, vol. 40(8), pages 999-1020, August.
    4. Leemis, Lawrence M. & McQueston, Jacquelyn T., 2008. "Univariate Distribution Relationships," The American Statistician, American Statistical Association, vol. 62, pages 45-53, February.
    5. Anand Paul, 2005. "A Note on Closure Properties of Failure Rate Distributions," Operations Research, INFORMS, vol. 53(4), pages 733-734, August.
    6. Panos Kouvelis & Guang Xiao & Nan Yang, 2018. "On the Properties of Yield Distributions in Random Yield Problems: Conditions, Class of Distributions and Relevant Applications," Production and Operations Management, Production and Operations Management Society, vol. 27(7), pages 1291-1302, July.
    7. Martin A. Lariviere, 2006. "A Note on Probability Distributions with Increasing Generalized Failure Rates," Operations Research, INFORMS, vol. 54(3), pages 602-604, June.
    8. Serhan Ziya & Hayriye Ayhan & Robert D. Foley, 2004. "Relationships Among Three Assumptions in Revenue Management," Operations Research, INFORMS, vol. 52(5), pages 804-809, October.
    9. Yao Zhao, 2008. "Evaluation and Optimization of Installation Base-Stock Policies in Supply Chains with Compound Poisson Demand," Operations Research, INFORMS, vol. 56(2), pages 437-452, April.
    10. Mihai Banciu & Prakash Mirchandani, 2013. "Technical Note—New Results Concerning Probability Distributions with Increasing Generalized Failure Rates," Operations Research, INFORMS, vol. 61(4), pages 925-931, August.
    11. Blyth C. Archibald & Edward A. Silver, 1978. "(s, S) Policies Under Continuous Review and Discrete Compound Poisson Demand," Management Science, INFORMS, vol. 24(9), pages 899-909, May.
    12. Stephen A. Smith & Narendra Agrawal, 2000. "Management of Multi-Item Retail Inventory Systems with Demand Substitution," Operations Research, INFORMS, vol. 48(1), pages 50-64, February.
    13. Martin A. Lariviere & Evan L. Porteus, 2001. "Selling to the Newsvendor: An Analysis of Price-Only Contracts," Manufacturing & Service Operations Management, INFORMS, vol. 3(4), pages 293-305, May.
    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. Ninh, Anh & Bao, Yunhong & McGibney, Daniel & Nguyen, Tuan, 2024. "Clinical site selection problems with probabilistic constraints," European Journal of Operational Research, Elsevier, vol. 316(2), pages 779-791.
    2. Yue Yuan & Mary E. Deily & Yuliang Yao, 2022. "Willingness to Pay for Status Signals in Online Luxury Markets," Production and Operations Management, Production and Operations Management Society, vol. 31(2), pages 668-680, February.

    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. Schweizer, Nikolaus & Szech, Nora, 2015. "A quantitative version of Myerson regularity," Working Paper Series in Economics 76, Karlsruhe Institute of Technology (KIT), Department of Economics and Management.
    2. Chaves, Isaías N. & Ichihashi, Shota, 2024. "Auction timing and market thickness," Games and Economic Behavior, Elsevier, vol. 143(C), pages 161-178.
    3. Schweizer, Nikolaus & Szech, Nora, 2015. "The quantitative view of Myerson regularity," Discussion Papers, Research Unit: Economics of Change SP II 2015-307, WZB Berlin Social Science Center.
    4. Stefanos Leonardos & Costis Melolidakis & Constandina Koki, 2022. "Monopoly pricing in vertical markets with demand uncertainty," Annals of Operations Research, Springer, vol. 315(2), pages 1291-1318, August.
    5. Brusset, Xavier & Cattan-Jallet, Roxane, 2009. "Estimating the buyer's willingness to pay using Bayesian belief distribution with IFR," MPRA Paper 22638, University Library of Munich, Germany, revised 10 May 2010.
    6. Colombo, Luca & Labrecciosa, Paola, 2012. "A note on pricing with risk aversion," European Journal of Operational Research, Elsevier, vol. 216(1), pages 252-254.
    7. Mihai Banciu & Prakash Mirchandani, 2013. "Technical Note—New Results Concerning Probability Distributions with Increasing Generalized Failure Rates," Operations Research, INFORMS, vol. 61(4), pages 925-931, August.
    8. Gökgür, Burak & Karabatı, Selçuk, 2019. "Dynamic and targeted bundle pricing of two independently valued products," European Journal of Operational Research, Elsevier, vol. 279(1), pages 184-198.
    9. Gómez-Déniz, Emilio & Sordo, Miguel A. & Calderín-Ojeda, Enrique, 2014. "The Log–Lindley distribution as an alternative to the beta regression model with applications in insurance," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 49-57.
    10. Xiaowei Xu & Wallace J. Hopp, 2009. "Technical Note---Price Trends in a Dynamic Pricing Model with Heterogeneous Customers: A Martingale Perspective," Operations Research, INFORMS, vol. 57(5), pages 1298-1302, October.
    11. Ye, Yu-Sen & Ma, Zu-Jun & Dai, Ying, 2016. "The price of anarchy in competitive reverse supply chains with quality-dependent price-only contracts," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 89(C), pages 86-107.
    12. Paulo Oliveira & Nuria Torrado, 2015. "On proportional reversed failure rate class," Statistical Papers, Springer, vol. 56(4), pages 999-1013, November.
    13. Schur, Rouven & Gönsch, Jochen & Hassler, Michael, 2019. "Time-consistent, risk-averse dynamic pricing," European Journal of Operational Research, Elsevier, vol. 277(2), pages 587-603.
    14. Georgia Perakis & Guillaume Roels, 2007. "The Price of Anarchy in Supply Chains: Quantifying the Efficiency of Price-Only Contracts," Management Science, INFORMS, vol. 53(8), pages 1249-1268, August.
    15. Liu, Tian-Liang & Chen, Jian & Huang, Hai-Jun, 2011. "Existence and efficiency of oligopoly equilibrium under toll and capacity competition," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 47(6), pages 908-919.
    16. 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.
    17. Shovan Chowdhury & Amarjit Kundu, 2016. "Stochastic Comparison of Parallel Systems with Finite Range Distributed Components," Working papers 201, Indian Institute of Management Kozhikode.
    18. Ioannis Stamatopoulos & Naveed Chehrazi & Achal Bassamboo, 2019. "Welfare Implications of Inventory-Driven Dynamic Pricing," Management Science, INFORMS, vol. 65(12), pages 5741-5765, December.
    19. 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.
    20. Xiaoming Yan & Yong Wang & Zhaofu Hong, 2016. "Comparison of Bertrand and Cournot competitions under random yield," International Journal of Production Research, Taylor & Francis Journals, vol. 54(11), pages 3256-3276, June.

    More about this item

    Statistics

    Access and download statistics

    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:bla:popmgt:v:29:y:2020:i:3:p:788-796. 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: Wiley Content Delivery (email available below). General contact details of provider: http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1937-5956 .

    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.