# Single Resource Revenue Management with Independent Demands

## Abstract

In this chapter, we consider the single resource, independent demand revenue management problem with multiple fare classes. This problem arises in the airline industry where different fares for the same cabin are designed to cater to different market segments. As an example, a low fare may have advance purchase and length of stay restrictions and exclude ancillary services such as advance seat selection, luggage handling, and priority boarding. This low fare may target price-conscious consumers who travel for leisure on restricted budgets. On the other hand, a high fare designed for business consumers may be unrestricted, include ancillary services and be designed to be frequently available for late bookings. If requests for the low fare arrive first, the airline risks selling all of its capacity before seeing requests for the high fare. A key decision in revenue management is how much capacity to reserve for higher fare classes, or equivalently how much capacity to make available for lower fare classes. Throughout the chapter, we will refer to airline applications, but the reader should keep in mind that the models apply more generally.

## References

- M.O. Ball, M. Queyranne, Toward robust revenue management: competitive analysis of online booking. Oper. Res.
**57**(4), 950–963 (2009)Google Scholar - A.V. Bathia, S.C. Prakesh, Optimal allocation of seats by fare, in
*AGIFORS Reservations and Yield Management Study Group Annual Meeting Proceedings*(1973)Google Scholar - P.P. Belobaba, Airline yield management: an overview of seat inventory control. Transp. Sci.
**21**(2), 63–73 (1987)Google Scholar - P.P. Belobaba, Application of a probabilistic decision model to airline seat inventory control. Oper. Res.
**37**(2), 183–197 (1989)Google Scholar - P.P. Belobaba, A. Farkas, Yield management impacts on airline spill estimation. Transp. Sci.
**33**(2), 217–232 (1999)Google Scholar - T. Boyaci, O. Ozer, Information acquisition for capacity planning via pricing and advance selling: when to stop and act? Oper. Res.
**58**(5), 1328–1349 (2010)Google Scholar - S.L. Brumelle, J.I. McGill, Airline seat allocation with multiple nested fare classes. Oper. Res.
**41**(1), 127–137 (1993)Google Scholar - S. Brumelle, D. Walczak, Dynamic airline revenue management with multiple semi-Markov demand. Oper. Res.
**51**(1), 137–148 (2003)Google Scholar - S.L. Brumelle, J.I. McGill, T.H. Oum, M.W. Tretheway, K. Sawaki, Allocation of airline seats between stochastically dependent demands. Transp. Sci.
**24**(3), 183–192 (1990)Google Scholar - G. Cachon, A.G. Kok, Implementation of the newsvendor model with clearance pricing: how to (and how not to) estimate a salvage value. Manuf. Serv. Oper. Manag.
**9**(3), 276–290 (2007a)Google Scholar - S. Chandler, S. Ja, Revenue opportunity modeling at American Airlines, in
*AGIFORS Reservations and Yield Management Study Group Annual Meeting Proceedings*, Jeju (2007)Google Scholar - W.L. Cooper, D. Gupta, Stochastic comparisons in airline revenue management. Manuf. Serv. Oper. Manag.
**8**(3), 221–234 (2006)Google Scholar - R.E. Curry, Optimal airline seat allocation with fare nested by origins and destinations. Transp. Sci.
**24**(3), 193–204 (1990)Google Scholar - S. Diwan. Performance of dynamic programming methods in airline revenue management. Master’s thesis, Massachusetts Institute of Technology, Cambridge, MA (2010)Google Scholar
- Y. Feng, G. Gallego, Optimal starting times of end-of-season sales and optimal stopping times for promotional fares. Manag. Sci.
**41**(8), 1371–1391 (1995)Google Scholar - Y. Feng, G. Gallego, Perishable asset revenue management with Markovian time-dependent demand intensities. Manag. Sci.
**46**(7), 941–956 (2000)Google Scholar - Y. Feng, B. Xiao, Optimal policies of yield management with multiple predetermined prices. Oper. Res.
**48**(2), 332–343 (2000)Google Scholar - G. Gallego, I. Moon, The distribution free newsboy problem: review and extensions. J. Oper. Res. Soc.
**44**(8), 824–834 (1993)Google Scholar - G. Gallego, S. Kou, R. Phillips, Revenue management of callable products. Manag. Sci.
**54**(3), 550–564 (2008a)Google Scholar - D. Gupta, W.L. Cooper, Stochastic comparisons in product yield management. Oper. Res.
**53**(2), 377–384 (2005)Google Scholar - M. Hu, J. Milner, J. Wu, Liking and following and the newsvendor: operations and marketing policies under social influence. Manag. Sci.
**62**(3), 867–879 (2016a)Google Scholar - A.J. Kleywegt, J.D. Papastavrou, The dynamic and stochastic knapsack problem. Oper. Res.
**46**(1), 17–35 (1998)Google Scholar - S. Kunnumkal, H. Topaloglu, A stochastic approximation method for the revenue management problem on a single flight leg with discrete demand distributions. Math. Meth. Oper. Res.
**70**(3), 477–504 (2009)Google Scholar - C.T. Lee, M. Hersh, A model for dynamic airline seat inventory control with multiple seat bookings. Transp. Sci.
**27**(3), 252–265 (1993)Google Scholar - R. Levi, G. Perakis, J. Uichanco, The data-driven newsvendor problem: new bounds and insights. Oper. Res.
**63**(6), 1294–1306 (2015)Google Scholar - K. Littlewood, Forecasting and control of passenger bookings, in
*AGIFORS Reservations and Yield Management Study Group Annual Meeting Proceedings*, Nathanya (1972)Google Scholar - W. Ma, D. Simchi-Levi, C.-P. Teo, On policies for single-leg revenue management with limited demand information. Technical report, MIT, Cambridge, MA (2018)Google Scholar
- J.I. McGill, G.J. van Ryzin, Revenue management: research overview and prospects. Transp. Sci.
**33**(2), 233–256 (1999)Google Scholar - O. Ozer, R. Phillips (eds.),
*The Oxford Handbook of Pricing Management*(Oxford University Press, Oxford, 2012)Google Scholar - G. Perakis, G. Roels, Regret in the newsvendor problem with partial information. Oper. Res.
**56**(1), 188–203 (2008)Google Scholar - R.L. Phillips,
*Pricing and Revenue Optimization*(Stanford University Press, Stanford, 2005)Google Scholar - R. Ratliff, Revenue management demand distributions, in
*AGIFORS Reservations and Yield Management Study Group Annual Meeting Proceedings*, Cape Town, South Africa (2005)Google Scholar - H. Richter, The differential revenue method to determine optimal seat allotments by fare type, in
*Proceedings 22nd AGIFORS Symposium*, Lagonissi (1982), pp. 339–362Google Scholar - L.W. Robinson, Optimal and approximate control policies for airline booking with sequential nonmonotonic fare classes. Oper. Res.
**43**(3), 252–263 (1995)Google Scholar - R. Simpson, Theoretical concepts for capacity/yield management, in
*Proceedings 25th AGIFORS Symposium*(1985), pp. 281–293Google Scholar - K. Talluri, G. van Ryzin,
*The Theory and Practice of Revenue Management*(Springer Science+Business Media, New York, 2004b)Google Scholar - C. Temath, S. Polt, L. Suhi, On the robustness of the network-based revenue opportunity model. J. Revenue Pricing Manag.
**9**(4), 341–355 (2010)Google Scholar - G.J. van Ryzin, J. McGill, Yield management without forecasting or optimization: an adaptive algorithm for protection level optimization. Manag. Sci.
**46**(6), 568–573 (2000)Google Scholar - G.J. van Ryzin, K.T. Talluri, Revenue management, in
*Handbook of Transportation*, ed. by R. Hall (Springer, New York, 2003)Google Scholar - G.J. van Ryzin, K.T. Talluri, An introduction to revenue management, in
*Tutorials in Operations Research*(INFORMS, New Orleans, 2005)Google Scholar - L.R. Weatherford, S.E. Bolidy, A taxonomy and research overview of perishable-asset revenue management: yield management, overbooking, and pricing. Oper. Res.
**40**(5), 831–844 (1992)Google Scholar - L.R. Weatherford, S.E. Bolidy, P.E. Pfeifer, Modeling the customer arrival process and comparing decision rules in perishable asset revenue management situations. Transp. Sci.
**27**(3), 239–251 (1993)Google Scholar - R.D. Wollmer, An airline seat management model for a single leg route when lower fare classes book first. Oper. Res.
**40**(1), 26–37 (1992)Google Scholar - W. Zhao, Y.-S. Zheng, A dynamic model for airline seat allocation with passenger diversion and no-shows. Transp. Sci.
**35**(1), 80–98 (2001)Google Scholar - P. Zipkin,
*Foundations of Inventory Management*(McGraw-Hill/Irwin, Boston, 2000)Google Scholar