IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v65y2017i2p396-407.html
   My bibliography  Save this article

Technical Note—An Expectation-Maximization Method to Estimate a Rank-Based Choice Model of Demand

Author

Listed:
  • Garrett van Ryzin

    (Graduate School of Business, Columbia University, New York, New York 10027)

  • Gustavo Vulcano

    (Leonard N. Stern School of Business, New York University, New York, New York 10012; School of Business, Universidad Torcuato di Tella, Buenos Aires, Argentina)

Abstract

We propose an expectation-maximization (EM) method to estimate customer preferences for a category of products using only sales transaction and product availability data. The demand model combines a general, rank-based discrete choice model of preferences with a Bernoulli process of customer arrivals over time. The discrete choice model is defined by a probability mass function (pmf) on a given set of preference rankings of alternatives, including the no-purchase alternative. Each customer is represented by a preference list, and when faced with a given choice set is assumed to either purchase the available option that ranks highest in her preference list, or not purchase at all if no available product ranks higher than the no-purchase alternative. We apply the EM method to jointly estimate the arrival rate of customers and the pmf of the rank-based choice model, and show that it leads to a remarkably simple and highly efficient estimation procedure. All limit points of the procedure are provably stationary points of the associated incomplete data log-likelihood function, and the output produced are maximum likelihood estimates (MLEs). Our numerical experiments confirm the practical potential of the proposal.

Suggested Citation

  • Garrett van Ryzin & Gustavo Vulcano, 2017. "Technical Note—An Expectation-Maximization Method to Estimate a Rank-Based Choice Model of Demand," Operations Research, INFORMS, vol. 65(2), pages 396-407, April.
    • Handle: RePEc:inm:oropre:v:65:y:2017:i:2:p:396-407
    DOI: 10.1287/opre.2016.1559
    as

    Download full text from publisher

    File URL: https://doi.org/10.1287/opre.2016.1559
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.2016.1559?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. Ravi Anupindi & Maqbool Dada & Sachin Gupta, 1998. "Estimation of Consumer Demand with Stock-Out Based Substitution: An Application to Vending Machine Products," Marketing Science, INFORMS, vol. 17(4), pages 406-423.
    2. Tudor Bodea & Mark Ferguson & Laurie Garrow, 2009. "Data Set--Choice-Based Revenue Management: Data from a Major Hotel Chain," Manufacturing & Service Operations Management, INFORMS, vol. 11(2), pages 356-361, December.
    3. Christopher T. Conlon & Julie Holland Mortimer, 2013. "Demand Estimation under Incomplete Product Availability," American Economic Journal: Microeconomics, American Economic Association, vol. 5(4), pages 1-30, November.
    4. 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.
    5. Sumit Kunnumkal, 2014. "Randomization Approaches for Network Revenue Management with Customer Choice Behavior," Production and Operations Management, Production and Operations Management Society, vol. 23(9), pages 1617-1633, September.
    6. Dorothée Honhon & Vishal Gaur & Sridhar Seshadri, 2010. "Assortment Planning and Inventory Decisions Under Stockout-Based Substitution," Operations Research, INFORMS, vol. 58(5), pages 1364-1379, October.
    7. Garrett van Ryzin & Gustavo Vulcano, 2008. "Computing Virtual Nesting Controls for Network Revenue Management Under Customer Choice Behavior," Manufacturing & Service Operations Management, INFORMS, vol. 10(3), pages 448-467, October.
    8. Dorothee Honhon & Sreelata Jonnalagedda & Xiajun Amy Pan, 2012. "Optimal Algorithms for Assortment Selection Under Ranking-Based Consumer Choice Models," Manufacturing & Service Operations Management, INFORMS, vol. 14(2), pages 279-289, April.
    9. Chen, Lijian & Homem-de-Mello, Tito, 2010. "Mathematical programming models for revenue management under customer choice," European Journal of Operational Research, Elsevier, vol. 203(2), pages 294-305, June.
    10. Juan M. Chaneton & Gustavo Vulcano, 2011. "Computing Bid Prices for Revenue Management Under Customer Choice Behavior," Manufacturing & Service Operations Management, INFORMS, vol. 13(4), pages 452-470, October.
    11. 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.
    12. A. Gürhan Kök & Marshall L. Fisher, 2007. "Demand Estimation and Assortment Optimization Under Substitution: Methodology and Application," Operations Research, INFORMS, vol. 55(6), pages 1001-1021, December.
    13. Tallys H. Yunes & Dominic Napolitano & Alan Scheller-Wolf & Sridhar Tayur, 2007. "Building Efficient Product Portfolios at John Deere and Company," Operations Research, INFORMS, vol. 55(4), pages 615-629, August.
    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 & Agustín Garassino & Gustavo Vulcano, 2022. "A Comparative Empirical Study of Discrete Choice Models in Retail Operations," Management Science, INFORMS, vol. 68(6), pages 4005-4023, June.
    2. Flores, Alvaro & Berbeglia, Gerardo & Van Hentenryck, Pascal, 2019. "Assortment optimization under the Sequential Multinomial Logit Model," European Journal of Operational Research, Elsevier, vol. 273(3), pages 1052-1064.
    3. Ningyuan Chen & Guillermo Gallego & Zhuodong Tang, 2019. "The Use of Binary Choice Forests to Model and Estimate Discrete Choices," Papers 1908.01109, arXiv.org, revised Apr 2024.
    4. Xiang Zhao & Xinghua Shan & Jinfei Wu, 2023. "The Impact of Seat Resource Fragmentation on Railway Network Revenue Management," Networks and Spatial Economics, Springer, vol. 23(1), pages 135-177, March.
    5. Thibault Barbier & Miguel Anjos & Fabien Cirinei & Gilles Savard, 2019. "Fluid arrivals simulation for choice network revenue management," Journal of Revenue and Pricing Management, Palgrave Macmillan, vol. 18(2), pages 164-180, April.
    6. Doust, Negin Ahmadi Saber & van Esch, Patrick & Kemper, Joya & Franklin, Drew & Casserly, Shane, 2021. "Marketing the use of headgear in high contact sports," Journal of Retailing and Consumer Services, Elsevier, vol. 59(C).
    7. 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.
    8. Qi Feng & J. George Shanthikumar & Mengying Xue, 2022. "Consumer Choice Models and Estimation: A Review and Extension," Production and Operations Management, Production and Operations Management Society, vol. 31(2), pages 847-867, February.
    9. Yi-Chun Akchen & Dmitry Mitrofanov, 2023. "Consider or Choose? The Role and Power of Consideration Sets," Papers 2302.04354, arXiv.org, revised Jun 2024.
    10. Milad HajMirzaei & Koorush Ziarati & Alireza Nikseresht, 0. "Discovering customer types using sales transactions and product availability data of 5 hotel datasets with genetic algorithm," Journal of Revenue and Pricing Management, Palgrave Macmillan, vol. 0, pages 1-15.
    11. Milad HajMirzaei & Koorush Ziarati & Alireza Nikseresht, 2020. "Discovering customer types using sales transactions and product availability data of 5 hotel datasets with genetic algorithm," Journal of Revenue and Pricing Management, Palgrave Macmillan, vol. 19(6), pages 386-400, December.
    12. Milad HajMirzaei & Koorush Ziarati & Alireza Nikseresht, 2022. "A customer type discovery algorithm in hotel revenue management systems," Journal of Revenue and Pricing Management, Palgrave Macmillan, vol. 21(2), pages 200-211, April.
    13. Hamed Sherafat Moula & S. Hadi Yaghoubyan & Razieh Malekhosseini & Karamollah Bagherifard, 2023. "Customer type discovery in hotel revenue management by Memetic algorithm," Journal of Revenue and Pricing Management, Palgrave Macmillan, vol. 22(6), pages 470-481, December.
    14. Qi Feng & J. George Shanthikumar, 2022. "Developing operations management data analytics," Production and Operations Management, Production and Operations Management Society, vol. 31(12), pages 4544-4557, December.
    15. Barbier, Thibault & Anjos, Miguel F. & Cirinei, Fabien & Savard, Gilles, 2020. "Product-closing approximation for ranking-based choice network revenue management," European Journal of Operational Research, Elsevier, vol. 286(3), pages 1002-1017.
    16. 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.

    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. 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.
    2. 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.
    3. Gerardo Berbeglia & Agustín Garassino & Gustavo Vulcano, 2022. "A Comparative Empirical Study of Discrete Choice Models in Retail Operations," Management Science, INFORMS, vol. 68(6), pages 4005-4023, June.
    4. Qi Feng & J. George Shanthikumar & Mengying Xue, 2022. "Consumer Choice Models and Estimation: A Review and Extension," Production and Operations Management, Production and Operations Management Society, vol. 31(2), pages 847-867, February.
    5. Joonkyum Lee & Vishal Gaur & Suresh Muthulingam & Gary F. Swisher, 2016. "Stockout-Based Substitution and Inventory Planning in Textbook Retailing," Manufacturing & Service Operations Management, INFORMS, vol. 18(1), pages 104-121, February.
    6. 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.
    7. Amr Farahat & Joonkyum Lee, 2018. "The Multiproduct Newsvendor Problem with Customer Choice," Operations Research, INFORMS, vol. 66(1), pages 123-136, January.
    8. Boxiao Chen & Xiuli Chao, 2020. "Dynamic Inventory Control with Stockout Substitution and Demand Learning," Management Science, INFORMS, vol. 66(11), pages 5108-5127, November.
    9. Ali Aouad & Retsef Levi & Danny Segev, 2019. "Approximation Algorithms for Dynamic Assortment Optimization Models," Mathematics of Operations Research, INFORMS, vol. 44(2), pages 487-511, May.
    10. Sanjay Dominik Jena & Andrea Lodi & Claudio Sole, 2021. "On the estimation of discrete choice models to capture irrational customer behaviors," Papers 2109.03882, arXiv.org.
    11. Morad Hosseinalifam & Gilles Savard & Patrice Marcotte, 2016. "Computing booking limits under a non-parametric demand model: A mathematical programming approach," Journal of Revenue and Pricing Management, Palgrave Macmillan, vol. 15(2), pages 170-184, April.
    12. Aditya Jain & Nils Rudi & Tong Wang, 2015. "Demand Estimation and Ordering Under Censoring: Stock-Out Timing Is (Almost) All You Need," Operations Research, INFORMS, vol. 63(1), pages 134-150, February.
    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. Kameng Nip & Zhenbo Wang & Zizhuo Wang, 2021. "Assortment Optimization under a Single Transition Choice Model," Production and Operations Management, Production and Operations Management Society, vol. 30(7), pages 2122-2142, July.
    15. Barbier, Thibault & Anjos, Miguel F. & Cirinei, Fabien & Savard, Gilles, 2020. "Product-closing approximation for ranking-based choice network revenue management," European Journal of Operational Research, Elsevier, vol. 286(3), pages 1002-1017.
    16. Transchel, Sandra, 2017. "Inventory management under price-based and stockout-based substitution," European Journal of Operational Research, Elsevier, vol. 262(3), pages 996-1008.
    17. Yalçın Akçay & Yunke Li & Harihara Prasad Natarajan, 2020. "Category Inventory Planning With Service Level Requirements and Dynamic Substitutions," Production and Operations Management, Production and Operations Management Society, vol. 29(11), pages 2553-2578, November.
    18. Jacob Feldman & Alice Paul & Huseyin Topaloglu, 2019. "Technical Note—Assortment Optimization with Small Consideration Sets," Operations Research, INFORMS, vol. 67(5), pages 1283-1299, September.
    19. Milad HajMirzaei & Koorush Ziarati & Alireza Nikseresht, 0. "Discovering customer types using sales transactions and product availability data of 5 hotel datasets with genetic algorithm," Journal of Revenue and Pricing Management, Palgrave Macmillan, vol. 0, pages 1-15.
    20. Ding, Xiaohui & Chen, Caihua & Li, Chongshou & Lim, Andrew, 2021. "Product demand estimation for vending machines using video surveillance data: A group-lasso method," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 150(C).

    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:65:y:2017:i:2:p:396-407. 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.