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A Nonparametric Approach to Multiproduct Pricing

Author

Listed:
  • Paat Rusmevichientong

    (School of Operations Research and Industrial Engineering, 221 Rhodes Hall, Cornell University, Ithaca, New York 14853)

  • Benjamin Van Roy

    (Department of Management Science and Engineering, Stanford University, Stanford, California 94305)

  • Peter W. Glynn

    (Department of Management Science and Engineering, Stanford University, Stanford, California 94305)

Abstract

Developed by General Motors (GM), the Auto Choice Advisor website ( http://www.autochoiceadvisor.com ) recommends vehicles to consumers based on their requirements and budget constraints. Through the website, GM has access to large quantities of data that reflect consumer preferences. Motivated by the availability of such data, we formulate a nonparametric approach to multiproduct pricing.We consider a class of models of consumer purchasing behavior, each of which relates observed data on a consumer’s requirements and budget constraint to subsequent purchasing tendencies. To price products, we aim at optimizing prices with respect to a sample of consumer data. We offer a bound on the sample size required for the resulting prices to be near-optimal with respect to the true distribution of consumers. The bound exhibits a dependence of O(n log n) on the number n of products being priced, showing that---in terms of sample complexity---the approach is scalable to large numbers of products.With regards to computational complexity, we establish that computing optimal prices with respect to a sample of consumer data is NP-complete in the strong sense. However, when prices are constrained by a price ladder---an ordering of prices defined prior to price determination---the problem becomes one of maximizing a supermodular function with real-valued variables. It is not yet known whether this problem is NP-hard. We provide a heuristic for our price-ladder-constrained problem, together with encouraging computational results.Finally, we apply our approach to a data set from the Auto Choice Advisor website. Our analysis provides insights into the current pricing policy at GM and suggests enhancements that may lead to a more effective pricing strategy.

Suggested Citation

  • Paat Rusmevichientong & Benjamin Van Roy & Peter W. Glynn, 2006. "A Nonparametric Approach to Multiproduct Pricing," Operations Research, INFORMS, vol. 54(1), pages 82-98, February.
  • Handle: RePEc:inm:oropre:v:54:y:2006:i:1:p:82-98
    DOI: 10.1287/opre.1050.0252
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    References listed on IDEAS

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    3. James M. Davis & Huseyin Topaloglu & David P. Williamson, 2017. "Pricing Problems Under the Nested Logit Model with a Quality Consistency Constraint," INFORMS Journal on Computing, INFORMS, vol. 29(1), pages 54-76, February.
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    5. Yuqing Zhang & Neil Walton, 2019. "Adaptive Pricing in Insurance: Generalized Linear Models and Gaussian Process Regression Approaches," Papers 1907.05381, arXiv.org.
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    7. Juliana M. Nascimento & Warren B. Powell, 2009. "An Optimal Approximate Dynamic Programming Algorithm for the Lagged Asset Acquisition Problem," Mathematics of Operations Research, INFORMS, vol. 34(1), pages 210-237, February.
    8. Mika Sumida & Guillermo Gallego & Paat Rusmevichientong & Huseyin Topaloglu & James Davis, 2021. "Revenue-Utility Tradeoff in Assortment Optimization Under the Multinomial Logit Model with Totally Unimodular Constraints," Management Science, INFORMS, vol. 67(5), pages 2845-2869, May.
    9. Ibrahim, Michael Nawar & Atiya, Amir F., 2016. "Analytical solutions to the dynamic pricing problem for time-normalized revenue," European Journal of Operational Research, Elsevier, vol. 254(2), pages 632-643.
    10. Srikanth Jagabathula & Paat Rusmevichientong, 2017. "Nonparametric Joint Assortment and Price Choice Model," Management Science, INFORMS, vol. 63(9), pages 3128-3145, September.
    11. Domínguez, Concepción & Labbé, Martine & Marín, Alfredo, 2021. "The rank pricing problem with ties," European Journal of Operational Research, Elsevier, vol. 294(2), pages 492-506.
    12. Guillermo Gallego & Gerardo Berbeglia, 2024. "Bounds and Heuristics for Multiproduct Pricing," Management Science, INFORMS, vol. 70(6), pages 4132-4144, June.
    13. Vivek F. Farias & Srikanth Jagabathula & Devavrat Shah, 2013. "A Nonparametric Approach to Modeling Choice with Limited Data," Management Science, INFORMS, vol. 59(2), pages 305-322, December.
    14. Guillermo Gallego & Gerardo Berbeglia, 2021. "Bounds and Heuristics for Multi-Product Personalized Pricing," Papers 2102.03038, arXiv.org, revised Feb 2021.
    15. Omar Besbes & Assaf Zeevi, 2012. "Blind Network Revenue Management," Operations Research, INFORMS, vol. 60(6), pages 1537-1550, December.
    16. Alice Paul & Jacob Feldman & James Mario Davis, 2018. "Assortment Optimization and Pricing Under a Nonparametric Tree Choice Model," Manufacturing & Service Operations Management, INFORMS, vol. 20(3), pages 550-565, July.
    17. Jianqing Fan & Yongyi Guo & Mengxin Yu, 2021. "Policy Optimization Using Semi-parametric Models for Dynamic Pricing," Papers 2109.06368, arXiv.org, revised May 2022.
    18. Cungen Zhu & Zhong Yao, 2018. "Comparison between the agency and wholesale model under the e-book duopoly market," Electronic Commerce Research, Springer, vol. 18(2), pages 313-337, June.
    19. Garrett van Ryzin & Gustavo Vulcano, 2015. "A Market Discovery Algorithm to Estimate a General Class of Nonparametric Choice Models," Management Science, INFORMS, vol. 61(2), pages 281-300, February.
    20. Srikanth Jagabathula & Gustavo Vulcano, 2018. "A Partial-Order-Based Model to Estimate Individual Preferences Using Panel Data," Management Science, INFORMS, vol. 64(4), pages 1609-1628, April.
    21. Mehrani, Saharnaz & Sefair, Jorge A., 2022. "Robust assortment optimization under sequential product unavailability," European Journal of Operational Research, Elsevier, vol. 303(3), pages 1027-1043.
    22. Omar Besbes & Assaf Zeevi, 2009. "Dynamic Pricing Without Knowing the Demand Function: Risk Bounds and Near-Optimal Algorithms," Operations Research, INFORMS, vol. 57(6), pages 1407-1420, December.

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