IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v68y2020i1p134-160.html
   My bibliography  Save this article

Approximation Algorithms for Product Framing and Pricing

Author

Listed:
  • Guillermo Gallego

    (Industrial Engineering and Decision Analytics, Hong Kong University of Science and Technology, Hong Kong)

  • Anran Li

    (London School of Economics and Political Science, London WC2A 2AE, United Kingdom)

  • Van-Anh Truong

    (Industrial Engineering and Operations Research, Columbia University, New York, New York 10027)

  • Xinshang Wang

    (Alibaba Group, San Mateo, California 94402, Antai College of Economics and Management, Shanghai Jiao Tong University, Shanghai 200240, China)

Abstract

We propose one of the first models of “product framing” and pricing. Product framing refers to the way consumer choice is influenced by how the products are framed or displayed. We present a model in which a set of products is displayed or framed into a set of virtual web pages. We assume that consumers consider only products in the top pages with different consumers willing to see different numbers of pages. Consumers select a product, if any, from these pages following a general choice model. We show that the product-framing problem is NP-hard. We derive algorithms with guaranteed performance relative to an optimal algorithm under reasonable assumptions. Our algorithms are fast and easy to implement. We also present structural results and design algorithms for pricing under framing effects for the multinomial logit model. We show that, for profit maximization problems, at optimality, products are displayed in descending order of their value gap and in ascending order of their markups.

Suggested Citation

  • Guillermo Gallego & Anran Li & Van-Anh Truong & Xinshang Wang, 2020. "Approximation Algorithms for Product Framing and Pricing," Operations Research, INFORMS, vol. 68(1), pages 134-160, January.
  • Handle: RePEc:inm:oropre:v:68:y:2020:i:1:p:134-160
    DOI: 10.1287/opre.2019.1875
    as

    Download full text from publisher

    File URL: https://doi.org/10.1287/opre.2019.1875
    Download Restriction: no

    File URL: https://libkey.io/10.1287/opre.2019.1875?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. Eric J. Johnson & Wendy W. Moe & Peter S. Fader & Steven Bellman & Gerald L. Lohse, 2004. "On the Depth and Dynamics of Online Search Behavior," Management Science, INFORMS, vol. 50(3), pages 299-308, March.
    2. Michael R. Baye & J. Rupert J. Gatti & Paul Kattuman & John Morgan, 2009. "Clicks, Discontinuities, and Firm Demand Online," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 18(4), pages 935-975, December.
    3. John R. Hauser & Steven P. Gaskin, 1984. "Application of the “Defender” Consumer Model," Marketing Science, INFORMS, vol. 3(4), pages 327-351.
    4. 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.
    5. 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.
    6. Shugan, Steven M, 1980. "The Cost of Thinking," Journal of Consumer Research, Oxford University Press, vol. 7(2), pages 99-111, Se.
    7. Juan Feng & Hemant K. Bhargava & David M. Pennock, 2007. "Implementing Sponsored Search in Web Search Engines: Computational Evaluation of Alternative Mechanisms," INFORMS Journal on Computing, INFORMS, vol. 19(1), pages 137-148, February.
    8. John R. Hauser, 1978. "Testing the Accuracy, Usefulness, and Significance of Probabilistic Choice Models: An Information-Theoretic Approach," Operations Research, INFORMS, vol. 26(3), pages 406-421, June.
    9. Manrai, Ajay K. & Andrews, Rick L., 1998. "Two-stage discrete choice models for scanner panel data: An assessment of process and assumptions," European Journal of Operational Research, Elsevier, vol. 111(2), pages 193-215, December.
    10. Garrett van Ryzin & Siddharth Mahajan, 1999. "On the Relationship Between Inventory Costs and Variety Benefits in Retail Assortments," Management Science, INFORMS, vol. 45(11), pages 1496-1509, November.
    11. 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.
    12. 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.
    13. Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, vol. 63(4), pages 841-890, July.
    14. Guillermo Gallego & Huseyin Topaloglu, 2014. "Constrained Assortment Optimization for the Nested Logit Model," Management Science, INFORMS, vol. 60(10), pages 2583-2601, October.
    15. Erik Brynjolfsson & Astrid Dick & Michael Smith, 2010. "A nearly perfect market?," Quantitative Marketing and Economics (QME), Springer, vol. 8(1), pages 1-33, March.
    16. Chiang, Jeongwen & Chib, Siddhartha & Narasimhan, Chakravarthi, 1998. "Markov chain Monte Carlo and models of consideration set and parameter heterogeneity," Journal of Econometrics, Elsevier, vol. 89(1-2), pages 223-248, November.
    17. 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.
    18. Paat Rusmevichientong & Zuo-Jun Max Shen & David B. Shmoys, 2010. "Dynamic Assortment Optimization with a Multinomial Logit Choice Model and Capacity Constraint," Operations Research, INFORMS, vol. 58(6), pages 1666-1680, December.
    19. Gérard P. Cachon & Christian Terwiesch & Yi Xu, 2005. "Retail Assortment Planning in the Presence of Consumer Search," Manufacturing & Service Operations Management, INFORMS, vol. 7(4), pages 330-346, August.
    20. Tversky, Amos & Kahneman, Daniel, 1986. "Rational Choice and the Framing of Decisions," The Journal of Business, University of Chicago Press, vol. 59(4), pages 251-278, October.
    21. Ward Hanson & Kipp Martin, 1996. "Optimizing Multinomial Logit Profit Functions," Management Science, INFORMS, vol. 42(7), pages 992-1003, July.
    22. Shashi Mittal & Andreas S. Schulz, 2013. "A General Framework for Designing Approximation Schemes for Combinatorial Optimization Problems with Many Objectives Combined into One," Operations Research, INFORMS, vol. 61(2), pages 386-397, April.
    23. Anindya Ghose & Sha Yang, 2009. "An Empirical Analysis of Search Engine Advertising: Sponsored Search in Electronic Markets," Management Science, INFORMS, vol. 55(10), pages 1605-1622, October.
    24. Animesh Animesh & Siva Viswanathan & Ritu Agarwal, 2011. "Competing “Creatively” in Sponsored Search Markets: The Effect of Rank, Differentiation Strategy, and Competition on Performance," Information Systems Research, INFORMS, vol. 22(1), pages 153-169, March.
    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. Gerardo Berbeglia & Alvaro Flores & Guillermo Gallego, 2021. "The Refined Assortment Optimization Problem," Papers 2102.03043, arXiv.org.
    2. Mahsa Derakhshan & Negin Golrezaei & Vahideh Manshadi & Vahab Mirrokni, 2022. "Product Ranking on Online Platforms," Management Science, INFORMS, vol. 68(6), pages 4024-4041, June.
    3. Ningyuan Chen & Adam N. Elmachtoub & Michael L. Hamilton & Xiao Lei, 2021. "Loot Box Pricing and Design," Management Science, INFORMS, vol. 67(8), pages 4809-4825, August.
    4. Ali Aouad & Daniela Saban, 2023. "Online Assortment Optimization for Two-Sided Matching Platforms," Management Science, INFORMS, vol. 69(4), pages 2069-2087, April.
    5. Ali Aouad & Danny Segev, 2021. "Display Optimization for Vertically Differentiated Locations Under Multinomial Logit Preferences," Management Science, INFORMS, vol. 67(6), pages 3519-3550, June.
    6. Guillermo Gallego & Gerardo Berbeglia, 2021. "Bounds, Heuristics, and Prophet Inequalities for Assortment Optimization," Papers 2109.14861, arXiv.org, revised Oct 2023.
    7. Santiago R. Balseiro & Antoine Désir, 2023. "Incentive-Compatible Assortment Optimization for Sponsored Products," Management Science, INFORMS, vol. 69(8), pages 4668-4684, August.
    8. Kris J. Ferreira & Sunanda Parthasarathy & Shreyas Sekar, 2022. "Learning to Rank an Assortment of Products," Management Science, INFORMS, vol. 68(3), pages 1828-1848, March.
    9. Berbeglia, Franco & Berbeglia, Gerardo & Van Hentenryck, Pascal, 2021. "Market segmentation in online platforms," European Journal of Operational Research, Elsevier, vol. 295(3), pages 1025-1041.

    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. Gallego, Guillermo & Li, Anran & Truong, Van-Anh & Wang, Xinshang, 2020. "Approximation algorithms for product framing and pricing," LSE Research Online Documents on Economics 101983, London School of Economics and Political Science, LSE Library.
    2. 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.
    3. 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.
    4. Aydın Alptekinoğlu & John H. Semple, 2016. "The Exponomial Choice Model: A New Alternative for Assortment and Price Optimization," Operations Research, INFORMS, vol. 64(1), pages 79-93, February.
    5. 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.
    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. 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.
    8. Xi Chen & Zachary Owen & Clark Pixton & David Simchi-Levi, 2022. "A Statistical Learning Approach to Personalization in Revenue Management," Management Science, INFORMS, vol. 68(3), pages 1923-1937, March.
    9. 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.
    10. 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.
    11. 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.
    12. Ruxian Wang & Ozge Sahin, 2018. "The Impact of Consumer Search Cost on Assortment Planning and Pricing," Management Science, INFORMS, vol. 64(8), pages 3649-3666, August.
    13. 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.
    14. Guillermo Gallego & Huseyin Topaloglu, 2014. "Constrained Assortment Optimization for the Nested Logit Model," Management Science, INFORMS, vol. 60(10), pages 2583-2601, October.
    15. Ruxian Wang & Zizhuo Wang, 2017. "Consumer Choice Models with Endogenous Network Effects," Management Science, INFORMS, vol. 63(11), pages 3944-3960, November.
    16. Chenhao Du & William L. Cooper & Zizhuo Wang, 2016. "Optimal Pricing for a Multinomial Logit Choice Model with Network Effects," Operations Research, INFORMS, vol. 64(2), pages 441-455, April.
    17. Pol Boada-Collado & Victor Martínez-de-Albéniz, 2020. "Estimating and Optimizing the Impact of Inventory on Consumer Choices in a Fashion Retail Setting," Manufacturing & Service Operations Management, INFORMS, vol. 22(3), pages 582-597, May.
    18. Sumit Kunnumkal & Victor Martínez-de-Albéniz, 2019. "Tractable Approximations for Assortment Planning with Product Costs," Operations Research, INFORMS, vol. 67(2), pages 436-452, March.
    19. H. Sebastian Heese & Victor Martínez-de-Albéniz, 2018. "Effects of Assortment Breadth Announcements on Manufacturer Competition," Manufacturing & Service Operations Management, INFORMS, vol. 20(2), pages 302-316, May.
    20. 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.

    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:oropre:v:68:y:2020:i:1:p:134-160. 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.