IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v67y2021i6p3803-3833.html
   My bibliography  Save this article

Demand Modeling in the Presence of Unobserved Lost Sales

Author

Listed:
  • Shivaram Subramanian

    (IBM T. J. Watson Research Center, Yorktown Heights, New York 10598)

  • Pavithra Harsha

    (IBM T. J. Watson Research Center, Yorktown Heights, New York 10598)

Abstract

We present an integrated optimization approach to parameter estimation for discrete choice demand models where data for one or more choice alternatives are censored. We employ a mixed-integer program (MIP) to jointly determine the prediction parameters associated with the customer arrival rate and their substitutive choices. This integrated approach enables us to recover proven, (near-) optimal parameter values with respect to the chosen loss-minimization (LM) objective function, thereby overcoming a limitation of prior multistart heuristic approaches that terminate without providing precise information on the solution quality. The imputations are done endogenously in the MIP by estimating optimal values for the probabilities of the unobserved choices being selected. Under mild assumptions, we prove that the approach is asymptotically consistent. For large LM instances, we derive a nonconvex-contvex alternating heuristic that can be used to obtain quick, near-optimal solutions. Partial information, user acceptance criteria, model selection, and regularization techniques can be incorporated to enhance practical efficacy. We test the LM model on simulated and real data and present results for a variety of demand-prediction scenarios: single-item, multi-item, time-varying arrival rate, large-scale instances, and a dual-layer estimation model extension that learns the unobserved market shares of competitors.

Suggested Citation

  • Shivaram Subramanian & Pavithra Harsha, 2021. "Demand Modeling in the Presence of Unobserved Lost Sales," Management Science, INFORMS, vol. 67(6), pages 3803-3833, June.
    • Handle: RePEc:inm:ormnsc:v:67:y:2021:i:6:p:3803-3833
    DOI: 10.1287/mnsc.2020.3667
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.2020.3667
    Download Restriction: no
    File URL: https://libkey.io/10.1287/mnsc.2020.3667?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. Peter M. Guadagni & John D. C. Little, 1983. "A Logit Model of Brand Choice Calibrated on Scanner Data," Marketing Science, INFORMS, vol. 2(3), pages 203-238.
    2. Chris Tofallis, 2015. "A better measure of relative prediction accuracy for model selection and model estimation," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 66(8), pages 1352-1362, August.
    3. Gustavo Vulcano & Garrett van Ryzin & Richard Ratliff, 2012. "Estimating Primary Demand for Substitutable Products from Sales Transaction Data," Operations Research, INFORMS, vol. 60(2), pages 313-334, April.
    4. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521766555, September.
    5. 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.
    6. 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.
    7. Gustavo Vulcano & Garrett van Ryzin & Wassim Chaar, 2010. "OM Practice--Choice-Based Revenue Management: An Empirical Study of Estimation and Optimization," Manufacturing & Service Operations Management, INFORMS, vol. 12(3), pages 371-392, February.
    8. 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.
    9. 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.
    10. 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.
    11. Jeffrey P. Newman & Mark E. Ferguson & Laurie A. Garrow & Timothy L. Jacobs, 2014. "Estimation of Choice-Based Models Using Sales Data from a Single Firm," Manufacturing & Service Operations Management, INFORMS, vol. 16(2), pages 184-197, May.
    12. 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.
    13. Chris Tofallis, 2015. "A better measure of relative prediction accuracy for model selection and model estimation," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 66(3), pages 524-524, March.
    14. Kalyan Talluri, 2009. "A finite-population revenue management model and a risk-ratio procedure for the joint estimation of population size and parameters," Economics Working Papers 1141, Department of Economics and Business, Universitat Pompeu Fabra.
    15. Steven T. Berry, 1994. "Estimating Discrete-Choice Models of Product Differentiation," RAND Journal of Economics, The RAND Corporation, vol. 25(2), pages 242-262, Summer.
    16. Pavithra Harsha & Shivaram Subramanian & Joline Uichanco, 2019. "Dynamic Pricing of Omnichannel Inventories," Service Science, INFORMS, vol. 21(1), pages 47-65, January.
    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. Tran, Minh Tam & Rekik, Yacine & Hadj-Hamou, Khaled, 2024. "Optimal pricing for dual-channel retailing with stochastic attraction demand model," International Journal of Production Economics, Elsevier, vol. 268(C).

    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. 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.
    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. Jeffrey P. Newman & Mark E. Ferguson & Laurie A. Garrow & Timothy L. Jacobs, 2014. "Estimation of Choice-Based Models Using Sales Data from a Single Firm," Manufacturing & Service Operations Management, INFORMS, vol. 16(2), pages 184-197, May.
    5. C. I. Chiang, 2023. "Availability control under online reviews in hospitality," Journal of Revenue and Pricing Management, Palgrave Macmillan, vol. 22(5), pages 385-398, October.
    6. 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.
    7. 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.
    8. Antoine Désir & Vineet Goyal & Danny Segev & Chun Ye, 2020. "Constrained Assortment Optimization Under the Markov Chain–based Choice Model," Management Science, INFORMS, vol. 66(2), pages 698-721, February.
    9. Shipra Agrawal & Vashist Avadhanula & Vineet Goyal & Assaf Zeevi, 2019. "MNL-Bandit: A Dynamic Learning Approach to Assortment Selection," Operations Research, INFORMS, vol. 67(5), pages 1453-1485, September.
    10. Ali Aouad & Vivek Farias & Retsef Levi, 2021. "Assortment Optimization Under Consider-Then-Choose Choice Models," Management Science, INFORMS, vol. 67(6), pages 3368-3386, June.
    11. 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.
    12. Qiu, Jiaqing & Li, Xiangyong & Duan, Yongrui & Chen, Mengxi & Tian, Peng, 2020. "Dynamic assortment in the presence of brand heterogeneity," Journal of Retailing and Consumer Services, Elsevier, vol. 56(C).
    13. Boxiao Chen & Xiuli Chao, 2020. "Dynamic Inventory Control with Stockout Substitution and Demand Learning," Management Science, INFORMS, vol. 66(11), pages 5108-5127, November.
    14. Jacob B. Feldman & Huseyin Topaloglu, 2017. "Revenue Management Under the Markov Chain Choice Model," Operations Research, INFORMS, vol. 65(5), pages 1322-1342, October.
    15. 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.
    16. 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.
    17. Wan, Mingchao & Huang, Yihui & Zhao, Lei & Deng, Tianhu & Fransoo, Jan C., 2018. "Demand estimation under multi-store multi-product substitution in high density traditional retail," European Journal of Operational Research, Elsevier, vol. 266(1), pages 99-111.
    18. 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.
    19. 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.
    20. 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.

    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:ormnsc:v:67:y:2021:i:6:p:3803-3833. 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.