Journal of Revenue and Pricing Management

, Volume 13, Issue 6, pp 440–456 | Cite as

A taxonomy of demand uncensoring methods in revenue management

  • Shadi Sharif Azadeh
  • Patrice Marcotte
  • Gilles Savard
Research Article


Revenue management systems rely on customer data, and are thus affected by the absence of registered demand that arises when a product is no longer available. In the present work, we review the uncensoring (or unconstraining) techniques that have been proposed to deal with this issue, and develop a taxonomy based on their respective features. This study will be helpful in identifying the relative merits of these techniques, as well as avenues for future research.


revenue management demand forecasting uncensoring statistical methods optimization customer choice behaviour 


  1. Andersson, S. (1998) Passenger choice analysis for seat capacity control: A pilot project in Scandinavian Airlines. International Transactions in Operational Research 5 (6): 471–486.CrossRefGoogle Scholar
  2. Armstrong, A. and Meissner, J. (2010) Railway Revenue Management: Overview and Models. UK: Lancaster University Management School. Technical Report.Google Scholar
  3. Armstrong, J. (2001) Principles of Forecasting: A Handbook for Researchers and Practitioners. April 2001 edn. New York, USA: Springer.CrossRefGoogle Scholar
  4. Bansal, M. (2012) Modeling customer behavior for revenue management. PhD thesis, Columbia University.Google Scholar
  5. Belobaba, P. (1987) Air Travel Demand and Airline Seat Inventory Management. Cambridge, MA: Flight Transportation Laboratory, Massachusetts Institute of Technology. Technical Report.Google Scholar
  6. Belobaba, P. and Farkas, A. (1999) Yield management impacts on airline spill estimation. Transportation Science 33 (2): 217–232.CrossRefGoogle Scholar
  7. Belobaba, P. and Hopperstad, C. (1999) Boeing/MIT simulation study: PODS results update. In: AGIFORS Reservations and Yield Management Study Group Symposium Proceedings. Renton, USA.Google Scholar
  8. Besbes, O. and Zeevi, A. (2006) Blind nonparametric revenue management: Asymptotic optimality of a joint learning and pricing method. Working paper.Google Scholar
  9. Bodea, T. (2008) Choice-based revenue management: A hotel perspective. PhD thesis. Georgia Institute of Technology.Google Scholar
  10. Box, G., Jenkins, G. and Reinsel, G. (2011) Time Series Analysis: Forecasting and Control. 4th edn. Vol. 734. Hoboken, New Jersey: Wiley.Google Scholar
  11. Brummer, M. et al. (1988) Determination of potential load capacity based on observed load factor data, a study for Northwest Airlines. Northfield, MN: St. Olaf College Undergraduate Practicum Group. Technical Report.Google Scholar
  12. Cachon, G. and Feldman, P. (2011) Dynamic versus static pricing in the presence of strategic consumers. MSOM. In press, accepted manuscript.Google Scholar
  13. Cachon, G. and Swinney, R. (2009) Purchasing, pricing, and quick response in the presence of strategic consumers. Management Science 55 (3): 497–511.CrossRefGoogle Scholar
  14. Cachon, G. and Swinney, R. (2011) The value of fast fashion: Quick response, enhanced design, and strategic consumer behavior. Management Science 57 (4): 778–795.CrossRefGoogle Scholar
  15. Chen, Y. and Luo, L. (2005) Approach of uncensored demand in airline revenue. Journal of Chengdu University of Information Technology 20 (6): 747–750.Google Scholar
  16. Conlon, C. and Mortimer, J. (2008) Demand Estimation under Incomplete Product Availability. National Bureau of Economic Research. Technical Report.Google Scholar
  17. Cooper, W., Homem-de Mello, T. and Kleywegt, A. (2006) Models of the spiral-down effect in revenue management. Operations Research 54 (5): 968–987.CrossRefGoogle Scholar
  18. Crevier, B., Cordeau, J. and Savard, G. (2012) Integrated operations planning and revenue management for rail freight transportation. Transportation Research Part B: Methodological 46 (1): 100–119.CrossRefGoogle Scholar
  19. Dantas, A., Yamamoto, K., Lamar, M. and Yamashita, Y. (2000) Neural network for travel demand forecast using GIS and remote sensing. In: INNS-ENNS International Joint Conference on Neural Networks. Japan: IEEE.Google Scholar
  20. Dempster, A.P., Laird, N.M. and Rubin, D.B. (1977) Maximum likelihood from incomplete data via the em algorithm. Journal of the Royal Statistical Society Series B: Methodological 39 (1): 1–38.Google Scholar
  21. Eijken, T. (2009) The spiral-down effect in revenue management. Master’s thesis. BMI, Vrije Universiteit Amsterdam.Google Scholar
  22. Eren, S. and Maglaras, C. (2009) A Maximum Entropy Joint Demand Estimation and Capacity Control Policy. Columbia Business School, Center for Pricing and Revenue Management. Technical Report.Google Scholar
  23. Farias, V. (2007) Revenue management beyond ‘estimate, then optimize’. PhD thesis, Stanford University.Google Scholar
  24. Farias, V., Jagabathula, S. and Shah, D. (2013) A nonparametric approach to modeling choice with limited data. Management Science 59 (2): 305–322.CrossRefGoogle Scholar
  25. Ferguson, M. and Queenan, C. (2009) Starting with good inputs: Unconstraining demand data in revenue management. INFORMS Transactions on Education 9 (3): 180–187.CrossRefGoogle Scholar
  26. Gallego, G. and Hu, M. (2014) Dynamic pricing of perishable assets under competition. Management Science.Google Scholar
  27. Gorin, T. (2000) Airline revenue management: Sell-up and forecasting algorithms. PhD thesis, Massachusetts Institute of Technology.Google Scholar
  28. Guo, P., Xiao, B. and Li, J. (2008) Research on the method of demand forecasting without constraint for airline passenger revenue management. Journal of Transportation Engineering and Information 2 (6): 71–78.Google Scholar
  29. Guo, P., Xiao, B. and Li, J. (2011) The research on unconstraining methods based on multi-distribution of demand in revenue management systems. Applications of Statistics and Management 30 (6): 1077–1088.Google Scholar
  30. Gurbuz, E. et al. (2011) Revenue management operations in hotel chains in Finland. Master’s thesis. Imatra, Finland: Saimaa University of Applied Sciences.Google Scholar
  31. Haensel, A. and Koole, G. (2010) Estimating unconstrained demand rate functions using customer choice sets. Journal of Revenue and Pricing Management 10 (5): 438–454.CrossRefGoogle Scholar
  32. Haensel, A., Koole, G. and Erdman, J. (2011) Estimating unconstrained customer choice set demand: A case study on airline reservation data. Journal of Choice Modelling 4 (3): 75–87.CrossRefGoogle Scholar
  33. He, D. and Luo, L. (2006) An improved winters model for airline demand forecast. Journal of Transportation Systems Engineering and Information Technology 6 (6): 103–107.Google Scholar
  34. Hopperstad, C. (1995) An Alternative Detruncation Method. Boeing Commercial Aircraft Company. Technical Report.Google Scholar
  35. Hopperstad, C. (1996) Passenger O/D simulator–PODS. In: AGIFORS Proceedings, Zurich, Switzerland.Google Scholar
  36. Hopperstad, C. (1997) PODS update: Simulation of O/D revenue management schemes. In: AGIFORS Proceedings Yield Management Study Group. Renton, USA.Google Scholar
  37. Hopperstad, C., Zerbib, G. and Belobaba, P. (2007) Methods for estimating sell-up. In: AGIFORS Yield Management Study Group Meeting. Jeju Island, Korea.Google Scholar
  38. Huh, W., Levi, R., Rusmevichientong, P. and Orlin, J. (2011) Adaptive data-driven inventory control with censored demand based on Kaplan-Meier estimator. Operations Research 59 (4): 929–941.CrossRefGoogle Scholar
  39. Hyndman, R., Koehler, A., Ord, J. and Snyder, R. (2008) Forecasting with Exponential Smoothing: The State Space Approach. Berlin, Germany: Springer.CrossRefGoogle Scholar
  40. Ja, S., Rao, B. and Chandler, S. (2001) Passenger recapture estimation in airline revenue management. In: AGIFORS 41st Annual Symposium. Sydney, Australia.Google Scholar
  41. Jiang, H. (2007) Network Capacity Management Competition. Judge Business School at University of Cambridge, UK. Technical Report.Google Scholar
  42. Jiang, H. and Pang, Z. (2011) Network capacity management under competition. Computational Optimization and Applications 50 (2): 287–326.CrossRefGoogle Scholar
  43. Kachitvichyanukul, V., Luong, H. and Pitakaso, R. (2012) Hotel room demand forecasting via observed reservation information. Asia Pacific Industrial Engineering and Management Systems Conference 2012.Google Scholar
  44. Kaplan, E. and Meier, P. (1958) Nonparametric estimation from incomplete observations. Journal of the American statistical association 53 (282): 457–481.CrossRefGoogle Scholar
  45. Karmarkar, S., Goutam, D. and Tathagata, B. (2010) Revenue impacts of demand unconstraining and accounting for dependency. Journal of Revenue and Pricing Management 10 (4): 367–381.CrossRefGoogle Scholar
  46. Kuhlmann, R. (2004) Why is revenue management not working? Journal of Revenue and Pricing Management 2 (4): 378.CrossRefGoogle Scholar
  47. Kunnumkal, S. and Topaloglu, H. (2010) A randomized linear program for the network revenue management problem with customer choice behavior. Journal of Revenue and Pricing Management 10 (5): 455–470.CrossRefGoogle Scholar
  48. Kwon, C., Friesz, T., Mookherjee, R., Yao, T. and Feng, B. (2009) Non-cooperative competition among revenue maximizing service providers with demand learning. European Journal of Operational Research 197 (3): 981–996.CrossRefGoogle Scholar
  49. Lee, A. (1990) Airline Reservations Forecasting: Probabilistic and Statistical Models of the Booking Process. Flight Transportation Laboratory, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology. Technical Report.Google Scholar
  50. Lee, C., Lin, T. and Lin, C. (2005) Pattern analysis on the booking curve of an inter-city railway. Journal of the Eastern Asia Society for Transportation Studies 6: 303–317.Google Scholar
  51. Levin, Y., McGill, J. and Nediak, M. (2010) Optimal dynamic pricing of perishable items by a monopolist facing strategic consumers. Production and Operations Management 19 (1): 40–60.CrossRefGoogle Scholar
  52. L’Heureux, E. (1986) A new twist in forecasting short-term passenger pickup. In: AGIFORS Annual Meeting. Northwestern University, USA.Google Scholar
  53. Little, R. and Rubin, D. (2002) Statistical Analysis with Missing Data. 2nd edn. New York: Wiley.CrossRefGoogle Scholar
  54. Littlewood, K. (2005) Special issue papers: Forecasting and control of passenger bookings. Journal of Revenue and Pricing Management 4 (2): 111–123.CrossRefGoogle Scholar
  55. Liu, P. (2004) Hotel demand/cancellation analysis and estimation of unconstrained demand using statistical methods. In: Revenue Management and Pricing: Case Studies and Applications. London Thompson.Google Scholar
  56. Liu, P., Smith, S., Orkin, E. and Carey, G. (2002) Estimating unconstrained hotel demand based on censored booking data. Journal of Revenue and Pricing Management 1 (2): 121–138.CrossRefGoogle Scholar
  57. Liu, Q. and van Ryzin, G. (2008) On the choice-based linear programming model for network revenue management. Manufacturing & Service Operations Management 10 (2): 288–310.CrossRefGoogle Scholar
  58. Liu, Q. and Zhang, D. (2011) Dynamic Pricing Competition with Strategic Customers under Vertical Product Differentiation. Hong Kong University of Science and Technology, Kowloon. Technical Report.Google Scholar
  59. Martínez, V. and Talluri, K. (2011) Dynamic price competition with fixed capacities. Management Science 57 (6): 1078–1093.CrossRefGoogle Scholar
  60. McFadden, D. (2001) Disaggregate behavioral travel demand’s RUM side. In: Travel Behaviour Research. Oxford: Pergamon Press, UC Berkeley, USA.Google Scholar
  61. McGill, J. (1995) Censored regression analysis of multiclass passenger demand data subject to joint capacity constraints. Annals of Operations Research 60 (1): 209–240.CrossRefGoogle Scholar
  62. McGill, J. and van Ryzin, G. (1999) Revenue management: Research overview and prospects. Transportation science 33 (2): 233–256.CrossRefGoogle Scholar
  63. Meissner, J. and Strauss, A. (2009) Choice-Based Network Revenue Management under Weak Market Segmentation. Lancaster University Management School. Technical Report.Google Scholar
  64. Meissner, J. and Strauss, A. (2012a) Improved bid prices for choice-based network revenue management. European Journal of Operational Research 217 (2): 417–427.CrossRefGoogle Scholar
  65. Meissner, J. and Strauss, A. (2012b) Network revenue management with inventory-sensitive bid prices and customer choice. European Journal of Operational Research 216 (2): 459–468.CrossRefGoogle Scholar
  66. Meissner, J., Strauss, A. and Talluri, K. (2012) An Enhanced Concave Program Relaxation for Choice Network Revenue Management. Lancaster University Management School. Technical Report.Google Scholar
  67. Mishra, S. and Viswanathan, V. (2003) Revenue management with restriction-free pricing. In: AGIFORS Revenue Management and Distribution Study Group Meeting, Honolulu, USA.Google Scholar
  68. Naim, I. and Gildea, D. (2012) Convergence of the em algorithm for gaussian mixtures with unbalanced mixing coefficients. ArXiv preprint ArXiv 1206: 6427.Google Scholar
  69. Netessine, S. and Shumsky, R. (2005) Revenue management games: Horizontal and vertical competition. Management Science 51 (5): 813–831.CrossRefGoogle Scholar
  70. Orkin, E. (1998) Wishful thinking and rocket science the essential matter of calculating unconstrained demand for revenue management. Cornell Hotel and Restaurant Administration Quarterly 39 (4): 15–19.Google Scholar
  71. Perakis, G. and Sood, A. (2006) Competitive multi-period pricing for perishable products: A robust optimization approach. Mathematical Programming 107 (1): 295–335.CrossRefGoogle Scholar
  72. Pölt, S. (2000) From Bookings to Demand: The Process of Unconstraining. New York: AGIFORS Reservations and Yield Management Study Group.Google Scholar
  73. Popescu, A., Barnes, E., Johnson, E. and Keskinocak, P. (2013) Bid prices when demand is a mix of individual and batch bookings. Transportation Science 47 (2): 198–213.CrossRefGoogle Scholar
  74. Queenan, C., Ferguson, M., Higbie, J. and Kapoor, R. (2009) A comparison of unconstraining methods to improve revenue management systems. Production and Operations Management 16 (6): 729–746.CrossRefGoogle Scholar
  75. Ratliff, R., Rao, B., Narayan, C. and Yellepeddi, K. (2008) A multi-flight recapture heuristic for estimating unconstrained demand from airline bookings. Journal of Revenue and Pricing Management 7 (2): 153–171.CrossRefGoogle Scholar
  76. Sa, J. (1987) Reservations Forecasting in Airline Yield Management. Cambridge, MA: Flight Transportation Laboratory, Massachusetts Institute of Technology. Technical Report.Google Scholar
  77. Salch, J. (1997) Unconstraining passenger demand using the em algorithm. In: Proceedings of the INFORMS Conference. Dallas, USA.Google Scholar
  78. Saleh, R. (1997) Estimating lost demand with imperfect availability indicators. In: Proceedings of the AGIFORS Reservations and Yield Management Study Group. Montreal, Canada.Google Scholar
  79. Sharif Azadeh, S., Labib, R. and Savard, G. (2012) Railway demand forecasting in revenue management using neural networks. International Journal of Revenue Management 7 (1): 18–36.CrossRefGoogle Scholar
  80. Shen, Z. and Su, X. (2007) Customer behavior modeling in revenue management and auctions: A review and new research opportunities. Production and Operations Management 16 (6): 713–728.CrossRefGoogle Scholar
  81. Skwarek, D. (1996a) Competitive Impacts of Yield Management System Components: Forecasting and Sell-Up Models. Cambridge, MA: Massachusetts Institute of Technology, Flight Transportation Laboratory. Technical Report.Google Scholar
  82. Skwarek, D. (1996b) Revenue and traffic impacts of alternative detruncation methods. In: Proceedings of the AGIFORS Reservations and Yield Management Study Group. Zurich, Switzerland.Google Scholar
  83. Stefanescu, C. (2009) Multivariate Customer Demand: Modeling and Estimation from Censored Sales. London Business School. Technical Report.Google Scholar
  84. Stefanescu, C., DeMiguel, V., Fridgeirsdottir, K. and Zenios, S. (2004) Revenue management with correlated demand forecasting. In: Proceedings of the American Statistical Association, Business and Economics Statistics Section. Alexandria, VA.Google Scholar
  85. Su, X. (2007) Intertemporal pricing with strategic customer behavior. Management Science 53 (5): 726–741.CrossRefGoogle Scholar
  86. Swan, M. (1999) Spill modeling for airlines. In: 8th World Conference on Transport Research Proceedings, pp. 225–237.Google Scholar
  87. Swan, W. (1979) A Systems Analysis of Scheduled Air Transportation Networks. Massachusetts Institute of Technology, Flight Transportation Laboratory. Technical Report.Google Scholar
  88. Swan, W. (2002) Airline demand distributions: Passenger revenue management and spill. Transportation Research Part E: Logistics and Transportation Review 38 (3): 253–263.CrossRefGoogle Scholar
  89. Swinney, R. (2011) Selling to strategic consumers when product value is uncertain: The value of matching supply and demand. Management Science 57 (10): 1737–1751.CrossRefGoogle Scholar
  90. Talluri, K. (2009) A Finite-Population Revenue Management Model and A Risk-Ratio Procedure for The Joint Estimation of Population Size and Parameters. Universitat Pompeu Fabra. Technical Report.Google Scholar
  91. Talluri, K. (2010) A Randomized Concave Programming Method for Choice Network Revenue Management. Universitat Pompeu Fabra. Technical Report.Google Scholar
  92. Talluri, K. and van Ryzin, G. (2004) Revenue management under a general discrete choice model of consumer behavior. Management Science 50 (1): 15–33.CrossRefGoogle Scholar
  93. Talluri, K. and van Ryzin, G. (2005) The Theory and Practice of Revenue Management, Vol. 68, New York: Springer.Google Scholar
  94. Train, K. (2009) Discrete Choice Methods with Simulation. 2nd edn. Cambridge, UK: Cambridge University Press.CrossRefGoogle Scholar
  95. van Ryzin, G. and McGill, J. (2000) Revenue management without forecasting or optimization: An adaptive algorithm for determining airline seat protection levels. Management Science 46 (6): 760–775.CrossRefGoogle Scholar
  96. van Ryzin, G. (2005) Future of revenue management: Models of demand. Journal of Revenue and Pricing Management 4 (2): 204–210.CrossRefGoogle Scholar
  97. Vulcano, G., van Ryzin, G. and Chaar, W. (2010) Om practice-choice-based revenue management: An empirical study of estimation and optimization. Manufacturing & Service Operations Management 12 (3): 371–392.CrossRefGoogle Scholar
  98. Vulcano, G., van Ryzin, G. and Ratliff, R. (2012) Estimating primary demand for substitutable products from sales transaction data. Operations Research 60 (2): 313–334.CrossRefGoogle Scholar
  99. Weatherford, L. (2000) Unconstraining methods. In: AGIFORS Reservations and Yield Management Study Group. New York.Google Scholar
  100. Weatherford, L. and Belobaba, P. (2002) Revenue impacts of fare input and demand forecast accuracy in airline yield management. Journal of the Operational Research Society 53 (8): 811–821.CrossRefGoogle Scholar
  101. Weatherford, L., Gentry, T. and Wilamowski, B. (2003) Neural network forecasting for airlines: A comparative analysis. Journal of Revenue and Pricing Management 1 (4): 319–331.CrossRefGoogle Scholar
  102. Weatherford, L. and Kimes, S. (2003) A comparison of forecasting methods for hotel revenue management. International Journal of Forecasting 19 (3): 401–415.CrossRefGoogle Scholar
  103. Weatherford, L. and Polt, 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.CrossRefGoogle Scholar
  104. Weatherford, L. and Ratliff, R. (2010) Review of revenue management methods with dependent demands. Journal of Revenue and Pricing Management 9 (4): 326–340.CrossRefGoogle Scholar
  105. Wickham, R. (1995) Evaluation of Forecasting Techniques for Short-Term Demand of Air Transportation. Massachusetts Institute of Technology, Flight Transportation Laboratory. Technical Report.Google Scholar
  106. Xu, L. (1997) Comparative analysis on convergence rates of the em algorithm and its two modifications for gaussian mixtures. Neural Processing Letters 6 (3): 69–76.CrossRefGoogle Scholar
  107. Yang, H., Song, H. and Zhang, S. (2010) Dynamic pricing with strategic and myopic consumers. In: Business Intelligence and Financial Engineering (BIFE), Hong Kong: IEEE.Google Scholar
  108. Yin, R., Aviv, Y., Pazgal, A. and Tang, C. (2009) Optimal markdown pricing: Implications of inventory display formats in the presence of strategic customers. Management Science 55 (8): 1391–1408.CrossRefGoogle Scholar
  109. Zakhary, A., El Gayar, N. and Atiya, A.F. (2008) A comparative study of the pickup method and its variations using a simulated hotel reservation data. ICGST International Journal on Artificial Intelligence and Machine Learning, Special Issue on Computational Methods for the Tourism Industry 8: 15–21.Google Scholar
  110. Zeni, R. (2001) Improved forecast accuracy in airline revenue management by unconstraining demand estimates from censored data. PhD thesis, MIT.Google Scholar
  111. Zeni, R. and Lawrence, K. (2004) Unconstraining demand data at us airways. In: Revenue Management and Pricing: Case Studies and Applications. Chapter 11, London, UK: Thomson, Cengage Learning Business Press, pp. 124–136.Google Scholar
  112. ZF Li, M. and Hoon Oum, T. (2000) Airline spill analysis–beyond the normal demand. European Journal of Operational Research 125 (1): 205–215.CrossRefGoogle Scholar
  113. Zhang, D. and Cooper, W. (2005) Revenue management for parallel flights with customer-choice behavior. Operations Research 53 (3): 415–431.CrossRefGoogle Scholar
  114. Zhang, D. and Cooper, W. (2009) Pricing substitutable flights in airline revenue management. European Journal of Operational Research 197 (3): 848–861.CrossRefGoogle Scholar
  115. Zhu, J. (2006) Using turndowns to estimate the latent demand in a car rental unconstrained demand forecast. Journal of Revenue and Pricing Management 4 (4): 344–353.CrossRefGoogle Scholar
  116. Zickus, J. (1998) Forecasting for Airline Network Revenue Management: Revenue and Competitive Impacts. Massachusetts Institute of Technology, Transportation Laboratory. Technical Report.Google Scholar

Copyright information

© Palgrave Macmillan, a division of Macmillan Publishers Ltd 2014

Authors and Affiliations

  • Shadi Sharif Azadeh
    • 1
  • Patrice Marcotte
    • 2
  • Gilles Savard
    • 1
  1. 1.Polytechnique MontrealMontrealCanada
  2. 2.University of MontrealMontrealCanada

Personalised recommendations