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Revenue management with two market segments and reserved capacity for priority customers

Part of: Stochastic processes

Published online by Cambridge University Press:  01 July 2016

Y Feng  and
B. Xiao
Y Feng*
Affiliation:
National University of Singapore
B. Xiao*
Affiliation:
Long Island University
*
∗ Postal address: Enron Corp., 1400 Smith St., Houston, TX 77002-7361, USA. Email address: [email protected]
∗∗ Postal address: Department of Management, Long Island University, C.W. Post, Brookville, NY 11548, USA. Email address: [email protected]
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Abstract

This paper studies a revenue management problem in which a finite number of substitutable commodities are sold to two different market segments at respective prices. It is required that a certain number of commodities are reserved for the high-price segment to ensure a minimum service level. The two segments are served concurrently at the beginning of the season. To improve revenues, management may choose to close the low-price segment at a time when the chance of selling all items at the high price is promising. The difficulty is determining when such a decision should be made. We derive the exact solution in closed form using the theory of optimal stopping time. We show that the optimal decision is made in reference to a sequence of thresholds in time. These time thresholds take both remaining sales season and inventory into account and exhibit a useful monotone property.

Keywords

Point processyield managementmartingaleoptimal stopping times

MSC classification

Primary: 60G55: Point processes
Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 32 , Issue 3 , September 2000 , pp. 800 - 823
Copyright
Copyright © Applied Probability Trust 2000 

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Footnotes

This research was partly supported by Grant RP3950663 of the National University of Singapore.

References

Belobaba, P. P. (1987). Airline yield management: an overview of seat inventory control. Transportation Sci. 21, 63–73.Google Scholar
Belobaba, P. P. (1989). Application of a probabilistic decision model to airline seat inventory control. Operat. Res. 37, 183–197.Google Scholar
Bitran, G. R. and Gilbert, S. M. (1992). Managing hotel reservations with uncertain arrivals. MIT Sloan School Working Paper.Google Scholar
Bitran, G. R. and Mondschein, S. V. (1995). An application of yield management to the hotel industry considering multiple day stays. Operat. Res. 43, 427–443.Google Scholar
Brémaud, P., (1980). Point Processes and Queues, Martingale Dynamics. Springer, New York.Google Scholar
Brumelle, S. L. and McGill, J. I. (1990). Allocation of airline seats between stochastically dependent demand. Transportation Sci. 24, 183–192.CrossRefGoogle Scholar
Curry, R. (1990). Optimal seat allocation with fare classes nested by origins and destinations. Transportation Sci. 24, 193–204.CrossRefGoogle Scholar
Feldman, J. M. (1991). To rein in those CRSs. Air Transport World 28 (12), 89–92.Google Scholar
Feng, Y. and Gallego, G. (1995). Optimal stopping times for end of season sales and optimal stopping times for promotional fares. Management Sci. 41, 1371–1391.Google Scholar
Feng, Y. and Gallego, G. (2000). Perishable asset revenue management with Markovian time dependent demand intensities. Management Sci. 46, 941–956.CrossRefGoogle Scholar
Feng, Y. and Xiao, B. (1999). Maximizing revenue of perishable assets with risk analysis. Operat. Res. 47, 337–341.Google Scholar
Feng, Y. and Xiao, B. (2000a). A continuous-time yield management model with multiple prices and reversible price changes. Management Sci. 46, 644–657.Google Scholar
Feng, Y. and Xiao, B. (2000b). Optimal policies of yield management with multiple predetermined prices. Operat. Res. 38, 332–343.Google Scholar
Gallego, G. and van Ryzin, G. J. (1994). Optimal dynamic pricing of inventories with stochastic demand over finite horizons. Management Sci. 40, 999–1020.Google Scholar
Glover, F., Glover, R., Lorenzo, J. and McMillan, C. (1982). The passenger-mix problem in the scheduled airlines. Interfaces 12, 73–79.Google Scholar
Ha, A. Y. (1997). Inventory rationing in a make-to-stock production system with several demand classes and lost sales. Management Sci. 43, 1093–1103.Google Scholar
Hersh, M. and Ladany, S. P. (1978). Optimal seat allocation for flights with one intermediate stop. Comput. Operat. Res. 5, 31–37.Google Scholar
Houthakker, H. S., and Taylor, L. D. 1970. Consumer Demand in the United States, Cambridge, MA: Harvard University Press.Google Scholar
Karatzas, I., and Shreve, S. E. 1988. %Brownian Motion and Stochastic Calculus, Springer-Verlag, New York.Google Scholar
Karlin, S. (1968). Total Positivity, Vol. 1. Stanford University Press.Google Scholar
Karr, A. F. 1986. Point Process and their Statistical Inference, Marcel Dekker, Inc., New York and Basel.Google Scholar
Kimes, S. E. (1989). The basics of yield management. Cornell Hotel and Restaurant Administration Quart. 30, 14–19.CrossRefGoogle Scholar
Ladany, S. P. and Arbel, A. (1991). Optimal cruise-liner passenger cabin pricing policy. Eur. J. Operat. Res. 55, 136–147.Google Scholar
Lee, T. C. and Hersh, M. (1993). A model for dynamic airline seat inventory control with multiple seat bookings. Transportation Sci. 27, 252–265.Google Scholar
Liberman, V. and Yechiali, U. (1978). On the hotel overbooking problem—an inventory system with stochastic cancellations. Management Sci. 24, 1117–1126.CrossRefGoogle Scholar
Littlewood, K. (1972). Forecasting and control of passengers. In Proc. 12th AGIFORS Symp. American Airlines, New York, pp. 103–105.Google Scholar
Nicholson, W. 1989. Microeconomic Theory, 4th edition, The Dryden Press.Google Scholar
Peck, J. (1996). Demand uncertainty, incomplete markets, and optimality of rationing. J. Econ. Theory 70, 342–363.CrossRefGoogle Scholar
Pfeifer, P. E. (1989). The airline discount fare allocation problem. Decision Sci. 20, 149–157.Google Scholar
Robinson, L. W. (1995). Optimal and approximate control policies for airline booking with sequential fare classes. Operat. Res. 43, 252–263.CrossRefGoogle Scholar
Rogers, L. C. G. and Williams, D. (1987). Diffusions, Markov Processes, and Martingales, Vol. 2: Itô Calculus. John Wiley, Chichester.Google Scholar
Rothstein, M. (1971). An airline overbooking model. Transportation Sci. 5, 180–192.Google Scholar
Rothstein, M. (1974). Hotel overbooking as a Markovian sequential decision process. Decision Sci. 5, 389–404.CrossRefGoogle Scholar
Smith, B., Leimkuhler, J., Darrow, R. and Samules, J. (1992). Yield management at American airlines. Interface 1, 8–31.Google Scholar
Soumis, F. and Nagurney, A. (1993). A stochastic, multiclass airline network equilibrium model. Operat. Res. 41, 721–730.Google Scholar
Topkis, D. M. (1968). Optimal ordering and rationing policies in a nonstationary dynamic inventory model with n demand classes. Management Sci. 15, 160–176.Google Scholar
Wollmer, R. D. (1992). An airline seat management model for a single leg route when lower fare classes book first. Operat. Res. 40, 26–37.Google Scholar