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Maximum likelihood approach for demand unconstraining problem with censoring information incompleteness

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Journal of Revenue and Pricing Management Aims and scope

Abstract

The forecast of passenger demand in Revenue Management is usually based on historical booking data that reflects the number of sales rather than true demand which is constrained by booking limits. That is why the process of demand forecasting under such circumstances is called unconstraining. The goal of every unconstraining approach is to get empirical or theoretical estimation of true demand. The application of the maximum likelihood method to unconstraining problems in Revenue Management is advocated in the article based on the construction of the distribution function for the censored demand depending on availability of the censoring information. Numerical results are presented on comparative analysis of existing unconstraining methods and the method used in the article. It is demonstrated that maximum likelihood method proves to be more efficient in case of high percentage of censoring. Another important advantage of the method connected to the fact that it enables one to process the situation of censoring information incompleteness when some elements of the observed sample data are known to be censored or not and for the others this information is not available. Mathematical computer environment Wolfram Mathematica has been used for obtaining all the numerical results presented in the article.

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References

  • Aranda-Ordaz, F.J. (1987) Relative efficiency of the Kaplan-Meier estimator under contamination. Communications in Statistics-Simulation and computations 16 (4): 987–997.

    Article  Google Scholar 

  • Davison, A.C. (2008) Statistical Models. Cambridge University press.

    Google Scholar 

  • Guo, P., Xiao, B. and Li, J. (2012) Unconstraining methods in revenue management systems: Research overview and prospects. Advances in Operations Research 2012 (2012): 1–23.

    Article  Google Scholar 

  • Harris, J.W. and Stocker, H. (1998) Handbook of Mathematics and Computational Science. New York: Springer-Verlag.

    Book  Google Scholar 

  • Heitjan, D.F. (1994) Ignorability in general incomplete-data models. Biometrika 81 (4): 701–708.

    Article  Google Scholar 

  • Hopperstad, C. (1995) An alternative detruncation method. Boeing Commercial Aircraft Company Internal Document, Boeing, Renton, Washington DC.

  • Kaplan, E.L. and Meier, P. (1958) Nonparametric estimation from incomplete observations. Journal of the American Statistical Association 53 (282): 457–481.

    Article  Google Scholar 

  • Klein, J.P. and Moeschberger, M.L. (1989) The robustness of several estimators of the survivorship function with randomly censored data. Communications in Statistics-Simulation and computations 18 (3): 1087–1112.

    Article  Google Scholar 

  • Klein, J.P. and Moeschberger, M.L. (2005) Survival Analysis. New York: Springer.

    Google Scholar 

  • Lapina, M.G. and Fridman, G.M. (forthcoming) Relative Asymptotic Efficiency of the Kaplan-Meier and Maximum Likelihood Methods for Demand Unconstraining Problems. Finance and Business. Moscow, Russia: Prospect Publishing House.

  • Lee, E.T. and Wang, J.W. (2003) Statistical Methods for Survival Data Analysis. 3rd edn. Hoboken, NJ: John Wiley & Sons.

    Book  Google Scholar 

  • McLachlan, G.J. and Krishnan, T. (1997) The EM Algorithm and Extensions. New York: Wiley.

    Google Scholar 

  • Meier, P., Karrison, T., Chappell, R. and Xie, H. (2004) The price of Kaplan-Meier. Journal of the American Statistical Association 99 (467): 890–896.

    Article  Google Scholar 

  • Miller, R.G. (1983) What price Kaplan-Meier? Biometrics 39 (4): 1077–1081.

    Article  Google Scholar 

  • Miller, R.G. (2011) Survival Analysis. 2nd edn. Hoboken, NJ: John Wiley & Sons.

    Google Scholar 

  • Salch, J. (1997) Unconstraining passenger demand using the EM algorithm, in Proceedings of the INFORMS Conference, Dallas, TX.

  • Talluri, K. and van Ryzin, G.J. (2004) The Theory and Practice of Revenue Management. Boston, MA: Kluwer Academic Publishers.

    Book  Google Scholar 

  • Tukey, J.W. (1977) Exploratory Data Analysis. Reading, MA: Addison-Wesley, pp. 39–43.

    Google Scholar 

  • Weatherford, L.R. and Pölt, S. (2002) Better unconstraining of airline demand data in revenue management systems for improved forecast accuracy and greater revenues. Journal of Revenue and Pricing Management 1 (3): 234–254.

    Article  Google Scholar 

  • Zeni, R.H. (2001) Improved forecast accuracy in revenue management by unconstraining demand estimates from censored data, Ph.D. thesis, Rutgers University, Rutgers, NJ.

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Authors and Affiliations

  1. Department of Applied Mathematics and Mathematical Modeling in Economics, St.Petersburg State University of Economics, St Petersburg, Russia

    Gregory Fridman

  2. National Research University Higher School of Economics (HSE), St Petersburg, Russia

    Maria Lapina

Authors
  1. Gregory Fridman
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  2. Maria Lapina
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Correspondence to Gregory Fridman.

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Fridman, G., Lapina, M. Maximum likelihood approach for demand unconstraining problem with censoring information incompleteness. J Revenue Pricing Manag 15, 37–51 (2016). https://doi.org/10.1057/rpm.2015.23

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  • DOI: https://doi.org/10.1057/rpm.2015.23

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