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A finite-population revenue management model and a risk-ratio procedure for the joint estimation of population size and parameters

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  • Kalyan Talluri

Abstract

Many dynamic revenue management models divide the sale period into a finite number of periods T and assume, invoking a fine-enough grid of time, that each period sees at most one booking request. These Poisson-type assumptions restrict the variability of the demand in the model, but researchers and practitioners were willing to overlook this for the benefit of tractability of the models. In this paper, we criticize this model from another angle. Estimating the discrete finite-period model poses problems of indeterminacy and non-robustness: Arbitrarily fixing T leads to arbitrary control values and on the other hand estimating T from data adds an additional layer of indeterminacy. To counter this, we first propose an alternate finite-population model that avoids this problem of fixing T and allows a wider range of demand distributions, while retaining the useful marginal-value properties of the finite-period model. The finite-population model still requires jointly estimating market size and the parameters of the customer purchase model without observing no-purchases. Estimation of market-size when no-purchases are unobservable has rarely been attempted in the marketing or revenue management literature. Indeed, we point out that it is akin to the classical statistical problem of estimating the parameters of a binomial distribution with unknown population size and success probability, and hence likely to be challenging. However, when the purchase probabilities are given by a functional form such as a multinomial-logit model, we propose an estimation heuristic that exploits the specification of the functional form, the variety of the offer sets in a typical RM setting, and qualitative knowledge of arrival rates. Finally we perform simulations to show that the estimator is very promising in obtaining unbiased estimates of population size and the model parameters.

Suggested Citation

  • 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.
  • Handle: RePEc:upf:upfgen:1141
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    References listed on IDEAS

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    1. S. L. Brumelle & J. I. McGill, 1993. "Airline Seat Allocation with Multiple Nested Fare Classes," Operations Research, INFORMS, vol. 41(1), pages 127-137, February.
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    Cited by:

    1. Omar Besbes & Assaf Zeevi, 2011. "On the Minimax Complexity of Pricing in a Changing Environment," Operations Research, INFORMS, vol. 59(1), pages 66-79, February.
    2. Shivaram Subramanian & Pavithra Harsha, 2021. "Demand Modeling in the Presence of Unobserved Lost Sales," Management Science, INFORMS, vol. 67(6), pages 3803-3833, June.
    3. 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.
    4. Sumit Kunnumkal & Kalyan Talluri, 2014. "On the Tractability of the Piecewiselinear Approximation for General Discrete-Choice Network Revenue Management," Working Papers 749, Barcelona School of Economics.
    5. 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.
    6. Johannes F. Jörg & Catherine Cleophas, 2022. "Nonparametric estimation of customer segments from censored sales panel data," Journal of Revenue and Pricing Management, Palgrave Macmillan, vol. 21(4), pages 393-417, August.
    7. Sumit Kunnumkal & Kalyan Talluri, 2014. "On the tractability of the piecewise-linear approximation for general discrete-choice network revenue management," Economics Working Papers 1409, Department of Economics and Business, Universitat Pompeu Fabra.

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    More about this item

    Keywords

    Revenue management; estimation; multi-nomial logit; risk-ratio;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • L93 - Industrial Organization - - Industry Studies: Transportation and Utilities - - - Air Transportation
    • L83 - Industrial Organization - - Industry Studies: Services - - - Sports; Gambling; Restaurants; Recreation; Tourism
    • M11 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Administration - - - Production Management

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