IDEAS home Printed from https://ideas.repec.org/a/inm/orijoc/v29y2017i1p54-76.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://doi.org/10.1287/ijoc.2016.0714
    Download Restriction: no
    File URL: https://libkey.io/10.1287/ijoc.2016.0714?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. 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.
    2. 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.
    3. 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.
    4. Felipe Caro & Jérémie Gallien, 2012. "Clearance Pricing Optimization for a Fast-Fashion Retailer," Operations Research, INFORMS, vol. 60(6), pages 1404-1422, December.
    5. Ward Hanson & Kipp Martin, 1996. "Optimizing Multinomial Logit Profit Functions," Management Science, INFORMS, vol. 42(7), pages 992-1003, July.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. Guillermo Gallego & Huseyin Topaloglu, 2014. "Constrained Assortment Optimization for the Nested Logit Model," Management Science, INFORMS, vol. 60(10), pages 2583-2601, October.
    14. 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.
    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.
    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. Koch, Sebastian & Klein, Robert, 2020. "Route-based approximate dynamic programming for dynamic pricing in attended home delivery," European Journal of Operational Research, Elsevier, vol. 287(2), pages 633-652.
    2. Anton J. Kleywegt & Hongzhang Shao, 2022. "Revenue Management Under the Markov Chain Choice Model with Joint Price and Assortment Decisions," Papers 2204.04774, arXiv.org.
    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.

    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Hongmin Li, 2020. "Optimal Pricing Under Diffusion-Choice Models," Operations Research, INFORMS, vol. 68(1), pages 115-133, January.
    6. 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.
    7. 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.
    8. 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.
    9. Ruben van de Geer & Arnoud V. den Boer, 2022. "Price Optimization Under the Finite-Mixture Logit Model," Management Science, INFORMS, vol. 68(10), pages 7480-7496, October.
    10. Woonghee T. Huh & Hongmin Li, 2023. "Product‐line pricing with dual objective of profit and consumer surplus," Production and Operations Management, Production and Operations Management Society, vol. 32(4), pages 1223-1242, April.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. Chen, Junlin & Xiong, Jinghong & Chen, Guobao & Liu, Xin & Yan, Peng & Jiang, Hai, 2024. "Optimal instant discounts of multiple ride options at a ride-hailing aggregator," European Journal of Operational Research, Elsevier, vol. 314(2), pages 718-734.
    16. 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.
    17. Xiaobo Li & Hailong Sun & Chung Piaw Teo, 2022. "Convex Optimization for Bundle Size Pricing Problem," Management Science, INFORMS, vol. 68(2), pages 1095-1106, February.
    18. 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.
    19. Daria Dzyabura & Srikanth Jagabathula, 2018. "Offline Assortment Optimization in the Presence of an Online Channel," Management Science, INFORMS, vol. 64(6), pages 2767-2786, June.
    20. Rui Chen & Hai Jiang, 2020. "Assortment optimization with position effects under the nested logit model," Naval Research Logistics (NRL), John Wiley & Sons, vol. 67(1), pages 21-33, February.

    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:inm:orijoc:v:29:y:2017:i:1:p:54-76. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.