Benchmarking filter-based demand estimates for airline revenue management

  • Philipp Bartke
  • Natalia Kliewer
  • Catherine CleophasEmail author
Research Paper


In recent years, revenue management research developed increasingly complex demand forecasts to model customer choice. While the resulting systems should easily outperform their predecessors, it appears difficult to achieve substantial improvement in practice. At the same time, interest in robust revenue maximization is growing. From this arises the challenge of creating versatile and computationally efficient approaches to estimate demand and quantify demand uncertainty. Motivated by this challenge, this paper introduces and benchmarks two filter-based demand estimators: the unscented Kalman filter and the particle filter. It documents a computational study, which is set in the airline industry and compares the estimators’ efficiency to that of sequential estimation and maximum-likelihood estimation. We quantify estimator efficiency through the posterior Cramér–Rao bound and compare revenue performance to the revenue opportunity. Both indicate that unscented Kalman filter and maximum-likelihood estimation outperform the alternatives. In addition, the Kalman filter requires comparatively little computational effort to update and quantifies demand uncertainty.


Revenue management Demand estimation Uncertainty Kalman filter Particle filter Simulation 


  1. Araman VF, Caldentey R (2011) Revenue management with incomplete demand information. Encyclopedia of Operations Research WileyGoogle Scholar
  2. Azadeh SS, Marcotte P, Savard G (2014) A taxonomy of demand uncensoring methods in revenue management. J Revenue Pricing Manag 13(6):440–456CrossRefGoogle Scholar
  3. Ball MO, Queyranne M (2009) Toward robust revenue management: competitive analysis of online booking. Oper Res 57(4):950–963CrossRefGoogle Scholar
  4. Besbes O, Zeevi A (2009) Dynamic pricing without knowing the demand function: risk bounds and near-optimal algorithms. Oper Res 57(6):1407–1420CrossRefGoogle Scholar
  5. Carvalho A, Puterman M (2015) Dynamic optimization and learning: how should a manager set prices when the demand function is unknown? Instituto de Pesquisa Econômica Aplicada (Ipea)Google Scholar
  6. Chung B, Li J, Yao T, Kwon C, Friesz T (2012) Demand learning and dynamic pricing under competition in a state-space framework. Eng Manag IEEE Trans 59(2):240–249CrossRefGoogle Scholar
  7. Doucet A, Godsill S, Andrieu C (2000) On sequential Monte Carlo sampling methods for Bayesian filtering. Stat Comput 10(3):197–208CrossRefGoogle Scholar
  8. Farias VF, Jagabathula S, Shah D (2013) A nonparametric approach to modeling choice with limited data. Manag Sci 59(2):305–322CrossRefGoogle Scholar
  9. Fiig T, Isler K, Hopperstad C, Belobaba P (2009) Optimization of mixed fare structures: theory and applications. J Revenue Pricing Manag 9(1):152–170Google Scholar
  10. Gerlach M, Cleophas C, Frank M (2010) Introducing REMATE: revenue management simulation in practice. In: AGIFORS working group revenue management and cargo, New YorkGoogle Scholar
  11. Gordon N, Salmond D, Smith A (1993) Novel approach to nonlinear/non-Gaussian Bayesian state estimation. Radar Signal Process IEE Proc 140:107–113CrossRefGoogle Scholar
  12. Haensel A, Koole G (2011) Estimating unconstrained demand rate functions using customer choice sets. J Revenue Pricing Manag 10(5):438–454CrossRefGoogle Scholar
  13. Julier S, Uhlmann J (2004) Unscented filtering and nonlinear estimation. Proc IEEE 92(3):401–422CrossRefGoogle Scholar
  14. Julier S, Uhlmann J (1997) a new extension of the kalman filter to nonlinear systems. In: Signal processing, sensor fusion, and target recognition VI; Proceedings of the conference, pp 182–193Google Scholar
  15. Kalman R (1960) A new approach to linear filtering and prediction problems. Trans ASME J Basic Eng 82(Series D):35–45Google Scholar
  16. Keskin NB, Zeevi A (2014) Dynamic pricing with an unknown demand model: asymptotically optimal semi-myopic policies. Oper Res 62(5):1142–1167CrossRefGoogle Scholar
  17. Kitagawa G (1996) Monte Carlo filter and smoother for non-gaussian nonlinear state space models. J Comput Graph Stat 5(1):1–25Google Scholar
  18. Kwon C, Friesz T, Mookherjee R, Yao T, Feng B (2009) Non-cooperative competition among revenue maximizing service providers with demand learning. Eur J Oper Res 197(3):981–996CrossRefGoogle Scholar
  19. Lan Y, Gao H, Ball MO, Karaesmen I (2008) Revenue management with limited demand information. Manag Sci 54(9):1594–1609CrossRefGoogle Scholar
  20. Li J, Yao T, Gao H (2009) A revenue maximizing strategy based on bayesian analysis of demand dynamics. In: SIAM Proceedings: mathematics for industry, society for industrial and applied mathematics, San Francisco, pp 174–181Google Scholar
  21. Lobo M, Boyd S (2003) Pricing and learning with uncertain demand. Fuqua School of Business, Duke University (Preprint) Google Scholar
  22. Mukhopadhyay S, Samaddar S, Colville G (2007) Improving revenue management decision making for airlines by evaluating analyst-adjusted passenger demand forecasts. Decis Sci 38(2):309–327CrossRefGoogle Scholar
  23. Müller P (1991) Monte Carlo integration in general dynamic models. In: Statistical multiple integration: Proceedings of an AMS-IMS-SIAM joint research conference, pp 145–162Google Scholar
  24. Perakis G, Roels G (2010) Robust controls for network revenue management. Manuf Serv Oper Manag 12(1):56–76CrossRefGoogle Scholar
  25. Scholz FW (2004) Maximum likelihood estimation. Wiley. doi: 10.1002/0471667196.ess1571.pub2
  26. Stefanescu C (2009) Multivariate customer demand: modeling and estimation from censored sales. Available at SSRN 1334353Google Scholar
  27. Talluri K, van Ryzin GJ (2005) The theory and practice of revenue management. Springer, New YorkGoogle Scholar
  28. Tichavsky P, Muravchik C, Nehorai A (1998) Posterior Cramér-Rao bounds for discrete-time nonlinear filtering. IEEE Trans Signal Process 46(5):1386–1396CrossRefGoogle Scholar
  29. van Ryzin GJ, McGill J (2000) Revenue management without forecasting or optimization: an adaptive algorithm for determining airline seat protection levels. Manag Sci 46(6):760–775CrossRefGoogle Scholar
  30. van Ryzin GJ, Vulcano G (2015) A market discovery algorithm to estimate a general class of nonparametric choice models. Manag Sci 61(2):281–300CrossRefGoogle Scholar
  31. Vulcano G, van Ryzin GJ, Ratliff R (2012) Estimating primary demand for substitutable products from sales transaction data. Oper Res 60(2):313–334CrossRefGoogle Scholar
  32. Weatherford L (2016) The history of unconstraining models in revenue management. J Revenue Pricing Manag 15(3):222–228CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg and EURO - The Association of European Operational Research Societies 2017

Authors and Affiliations

  • Philipp Bartke
    • 1
  • Natalia Kliewer
    • 2
  • Catherine Cleophas
    • 3
    Email author
  1. 1.Information Systems DepartmentFreie Universität BerlinBerlinGermany
  2. 2.Information Systems DepartmentFreie Universität BerlinBerlinGermany
  3. 3.School of Business and EconomicsRWTH Aachen UniversityAachenGermany

Personalised recommendations