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Pricing Problems Under the Nested Logit Model with a Quality Consistency Constraint

Author

Listed:
  • James M. Davis

    (Department of Industrial and Enterprise Systems Engineering, University of Illinois at Urbana-Champaign, Champaign, Illinois 61801)

  • Huseyin Topaloglu

    (School of Operations Research and Information Engineering, Cornell Tech, New York, New York 10011)

  • David P. Williamson

    (School of Operations Research and Information Engineering, Cornell University, Ithaca, New York 14853)

Abstract

We consider pricing problems when customers choose among the products according to the nested logit model and there is a quality consistency constraint on the prices charged for the products. We consider two types of quality consistency constraint. In the first, there is an inherent ordering between the qualities of the products in a particular nest and the price for a product of a higher quality should be larger. In the second type of constraint, different nests correspond to different quality levels; the price for any product in a nest corresponding to a higher quality level should be larger than the price for any product in a nest corresponding to a lower quality level. Prices for the products are chosen from a finite set of possible prices. We develop algorithms to find the prices to charge for the products to maximize the expected revenue obtained from a customer, while adhering to a quality consistency constraint. Our algorithms are based on solving linear programs whose sizes scale polynomially with the number of nests, number of products, and number of possible prices for the products. We also give extensions to the cases beyond the two types of quality consistency constraints. Numerical experiments indicate that our algorithms can effectively compute the optimal prices even when there is a large number of products in consideration.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:orijoc:v:29:y:2017:i:1:p:54-76
    DOI: 10.1287/ijoc.2016.0714
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    References listed on IDEAS

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    1. Kyle D. Chen & Warren H. Hausman, 2000. "Technical Note: Mathematical Properties of the Optimal Product Line Selection Problem Using Choice-Based Conjoint Analysis," Management Science, INFORMS, vol. 46(2), pages 327-332, February.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Jacob B. Feldman & Huseyin Topaloglu, 2015. "Capacity Constraints Across Nests in Assortment Optimization Under the Nested Logit Model," Operations Research, INFORMS, vol. 63(4), pages 812-822, August.
    7. 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.
    8. Dan Zhang & Zhaosong Lu, 2013. "Assessing the Value of Dynamic Pricing in Network Revenue Management," INFORMS Journal on Computing, INFORMS, vol. 25(1), pages 102-115, February.
    9. 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.
    10. 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.
    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. Shivaram Subramanian & Hanif Sherali, 2010. "A fractional programming approach for retail category price optimization," Journal of Global Optimization, Springer, vol. 48(2), pages 263-277, October.
    13. 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.
    14. Felipe Caro & Jérémie Gallien, 2012. "Clearance Pricing Optimization for a Fast-Fashion Retailer," Operations Research, INFORMS, vol. 60(6), pages 1404-1422, December.
    15. Ward Hanson & Kipp Martin, 1996. "Optimizing Multinomial Logit Profit Functions," Management Science, INFORMS, vol. 42(7), pages 992-1003, July.
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    Cited by:

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    3. 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.

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