IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1912.09552.html
   My bibliography  Save this paper

Robust Product-line Pricing under Generalized Extreme Value Models

Author

Listed:
  • Tien Mai
  • Patrick Jaillet

Abstract

We study robust versions of pricing problems where customers choose products according to a generalized extreme value (GEV) choice model, and the choice parameters are not known exactly but lie in an uncertainty set. We show that, when the robust problem is unconstrained and the price sensitivity parameters are homogeneous, the robust optimal prices have a constant markup over products, and we provide formulas that allow to compute this constant markup by bisection. We further show that, in the case that the price sensitivity parameters are only homogeneous in each partition of the products, under the assumption that the choice probability generating function and the uncertainty set are partition-wise separable, a robust solution will have a constant markup in each subset, and this constant-markup vector can be found efficiently by convex optimization. We provide numerical results to illustrate the advantages of our robust approach in protecting from bad scenarios. Our results hold for convex and bounded uncertainty sets,} and for any arbitrary GEV model, including the multinomial logit, nested or cross-nested logit.

Suggested Citation

  • Tien Mai & Patrick Jaillet, 2019. "Robust Product-line Pricing under Generalized Extreme Value Models," Papers 1912.09552, arXiv.org, revised Oct 2021.
  • Handle: RePEc:arx:papers:1912.09552
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1912.09552
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Bhat, Chandra R., 1998. "Accommodating variations in responsiveness to level-of-service measures in travel mode choice modeling," Transportation Research Part A: Policy and Practice, Elsevier, vol. 32(7), pages 495-507, September.
    2. Small, Kenneth A, 1987. "A Discrete Choice Model for Ordered Alternatives," Econometrica, Econometric Society, vol. 55(2), pages 409-424, March.
    3. Woonghee Tim Huh & Hongmin Li, 2015. "Technical Note—Pricing Under the Nested Attraction Model with a Multistage Choice Structure," Operations Research, INFORMS, vol. 63(4), pages 840-850, August.
    4. Hongmin Li & Woonghee Tim Huh, 2011. "Pricing Multiple Products with the Multinomial Logit and Nested Logit Models: Concavity and Implications," Manufacturing & Service Operations Management, INFORMS, vol. 13(4), pages 549-563, October.
    5. Guillermo Gallego & Garrett van Ryzin, 1997. "A Multiproduct Dynamic Pricing Problem and Its Applications to Network Yield Management," Operations Research, INFORMS, vol. 45(1), pages 24-41, February.
    6. Fosgerau, Mogens & McFadden, Daniel & Bierlaire, Michel, 2010. "Choice probability generating functions," MPRA Paper 24214, University Library of Munich, Germany.
    7. Wallace J. Hopp & Xiaowei Xu, 2005. "Product Line Selection and Pricing with Modularity in Design," Manufacturing & Service Operations Management, INFORMS, vol. 7(3), pages 172-187, August.
    8. Koppelman, Frank S. & Wen, Chieh-Hua, 2000. "The paired combinatorial logit model: properties, estimation and application," Transportation Research Part B: Methodological, Elsevier, vol. 34(2), pages 75-89, February.
    9. McFadden, Daniel, 1980. "Econometric Models for Probabilistic Choice among Products," The Journal of Business, University of Chicago Press, vol. 53(3), pages 13-29, July.
    10. ,, 2000. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 16(2), pages 287-299, April.
    11. Paat Rusmevichientong & Huseyin Topaloglu, 2012. "Robust Assortment Optimization in Revenue Management Under the Multinomial Logit Choice Model," Operations Research, INFORMS, vol. 60(4), pages 865-882, August.
    12. Daly, Andrew & Bierlaire, Michel, 2006. "A general and operational representation of Generalised Extreme Value models," Transportation Research Part B: Methodological, Elsevier, vol. 40(4), pages 285-305, May.
    13. Kalyan Talluri & Garrett van Ryzin, 2004. "Revenue Management Under a General Discrete Choice Model of Consumer Behavior," Management Science, INFORMS, vol. 50(1), pages 15-33, January.
    14. Wen, Chieh-Hua & Koppelman, Frank S., 2001. "The generalized nested logit model," Transportation Research Part B: Methodological, Elsevier, vol. 35(7), pages 627-641, August.
    15. Guillermo Gallego & Ruxian Wang, 2014. "Multiproduct Price Optimization and Competition Under the Nested Logit Model with Product-Differentiated Price Sensitivities," Operations Research, INFORMS, vol. 62(2), pages 450-461, April.
    16. Lingxiu Dong & Panos Kouvelis & Zhongjun Tian, 2009. "Dynamic Pricing and Inventory Control of Substitute Products," Manufacturing & Service Operations Management, INFORMS, vol. 11(2), pages 317-339, December.
    17. Guillermo Gallego & Ming Hu, 2014. "Dynamic Pricing of Perishable Assets Under Competition," Management Science, INFORMS, vol. 60(5), pages 1241-1259, May.
    18. Mai, Tien & Frejinger, Emma & Fosgerau, Mogens & Bastin, Fabian, 2017. "A dynamic programming approach for quickly estimating large network-based MEV models," Transportation Research Part B: Methodological, Elsevier, vol. 98(C), pages 179-197.
    19. A. Ben-Tal & A. Nemirovski, 1998. "Robust Convex Optimization," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 769-805, November.
    20. Daniel McFadden & Kenneth Train, 2000. "Mixed MNL models for discrete response," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(5), pages 447-470.
    Full references (including those not matched with items on IDEAS)

    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. Hongmin Li & Scott Webster, 2017. "Optimal Pricing of Correlated Product Options Under the Paired Combinatorial Logit Model," Operations Research, INFORMS, vol. 65(5), pages 1215-1230, October.
    2. Hongmin Li & Scott Webster & Gwangjae Yu, 2020. "Product Design Under Multinomial Logit Choices: Optimization of Quality and Prices in an Evolving Product Line," Manufacturing & Service Operations Management, INFORMS, vol. 22(5), pages 1011-1025, September.
    3. Hongmin Li & Scott Webster & Nicholas Mason & Karl Kempf, 2019. "Product-Line Pricing Under Discrete Mixed Multinomial Logit Demand," Service Science, INFORMS, vol. 21(1), pages 14-28, January.
    4. Dam, Tien Thanh & Ta, Thuy Anh & Mai, Tien, 2022. "Submodularity and local search approaches for maximum capture problems under generalized extreme value models," European Journal of Operational Research, Elsevier, vol. 300(3), pages 953-965.
    5. Ruxian Wang & Zizhuo Wang, 2017. "Consumer Choice Models with Endogenous Network Effects," Management Science, INFORMS, vol. 63(11), pages 3944-3960, November.
    6. Rui Chen & Hai Jiang, 2020. "Capacitated assortment and price optimization under the nested logit model," Journal of Global Optimization, Springer, vol. 77(4), pages 895-918, August.
    7. Tinessa, Fiore & Marzano, Vittorio & Papola, Andrea, 2020. "Mixing distributions of tastes with a Combination of Nested Logit (CoNL) kernel: Formulation and performance analysis," Transportation Research Part B: Methodological, Elsevier, vol. 141(C), pages 1-23.
    8. Ruxian Wang, 2018. "When Prospect Theory Meets Consumer Choice Models: Assortment and Pricing Management with Reference Prices," Manufacturing & Service Operations Management, INFORMS, vol. 20(3), pages 583-600, July.
    9. Dam, Tien Thanh & Ta, Thuy Anh & Mai, Tien, 2023. "Robust maximum capture facility location under random utility maximization models," European Journal of Operational Research, Elsevier, vol. 310(3), pages 1128-1150.
    10. Strauss, Arne K. & Klein, Robert & Steinhardt, Claudius, 2018. "A review of choice-based revenue management: Theory and methods," European Journal of Operational Research, Elsevier, vol. 271(2), pages 375-387.
    11. Guillermo Gallego & Huseyin Topaloglu, 2014. "Constrained Assortment Optimization for the Nested Logit Model," Management Science, INFORMS, vol. 60(10), pages 2583-2601, October.
    12. Paleti, Rajesh, 2018. "Generalized multinomial probit Model: Accommodating constrained random parameters," Transportation Research Part B: Methodological, Elsevier, vol. 118(C), pages 248-262.
    13. Guang Li & Paat Rusmevichientong & Huseyin Topaloglu, 2015. "The d -Level Nested Logit Model: Assortment and Price Optimization Problems," Operations Research, INFORMS, vol. 63(2), pages 325-342, April.
    14. Zhenzhen Yan & Karthik Natarajan & Chung Piaw Teo & Cong Cheng, 2022. "A Representative Consumer Model in Data-Driven Multiproduct Pricing Optimization," Management Science, INFORMS, vol. 68(8), pages 5798-5827, August.
    15. W. Zachary Rayfield & Paat Rusmevichientong & Huseyin Topaloglu, 2015. "Approximation Methods for Pricing Problems Under the Nested Logit Model with Price Bounds," INFORMS Journal on Computing, INFORMS, vol. 27(2), pages 335-357, May.
    16. James M. Davis & Guillermo Gallego & Huseyin Topaloglu, 2014. "Assortment Optimization Under Variants of the Nested Logit Model," Operations Research, INFORMS, vol. 62(2), pages 250-273, April.
    17. Schlicher, Loe & Lurkin, Virginie, 2022. "Stable allocations for choice-based collaborative price setting," European Journal of Operational Research, Elsevier, vol. 302(3), pages 1242-1254.
    18. Tinessa, Fiore, 2021. "Closed-form random utility models with mixture distributions of random utilities: Exploring finite mixtures of qGEV models," Transportation Research Part B: Methodological, Elsevier, vol. 146(C), pages 262-288.
    19. Yalç{i}n Akçay & Harihara Prasad Natarajan & Susan H. Xu, 2010. "Joint Dynamic Pricing of Multiple Perishable Products Under Consumer Choice," Management Science, INFORMS, vol. 56(8), pages 1345-1361, August.
    20. Hai Jiang & Rui Chen & He Sun, 2017. "Multiproduct price optimization under the multilevel nested logit model," Annals of Operations Research, Springer, vol. 254(1), pages 131-164, July.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:arx:papers:1912.09552. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.