April  2012, 8(2): 363-378. doi: 10.3934/jimo.2012.8.363

Analysis of airline seat control with region factor

1. 

College of Information Technology, Shanghai Ocean University, Shanghai, 201306, China

Received  January 2011 Revised  September 2011 Published  April 2012

Due to the lower consumption level to the flights in some regions, the flights' vacancy rate is usually very high and the service level is low. To airlines, the common procedure to handle such problems is to employ different price systems. But this in return results in unsatisfying effects. In this paper we discussed the above issue from another standpoint. Firstly, we introduced a parameter, called region factor, and then constructed a stochastic dynamic model of a single-leg flight related to it. Secondly, we derived some monotone properties for the expected revenue functions. These properties ensured that we could choose appropriate region factor to recover the high vacancy rate caused by the lower consumption levels, but also adopt the similar optimal threshold control strategy as the traditional revenue management did. Furthermore, in addition to improving the service levels, the proper region factor can increase the total revenue sometimes. Lastly, Numerical results were used to illustrate properties of the model.
Citation: Yanming Ge. Analysis of airline seat control with region factor. Journal of Industrial and Management Optimization, 2012, 8 (2) : 363-378. doi: 10.3934/jimo.2012.8.363
References:
[1]

P. P. Belobaba, Airline yield management: An overview of seat inventory control, Transportation Science, 21 (1987), 63-73. doi: 10.1287/trsc.21.2.63.

[2]

P. P. Belobaba, Application of a probabilistic decision model to airline seat inventory control, Operations Research, 37 (1989), 183-197. doi: 10.1287/opre.37.2.183.

[3]

S. I. Birbil, J. B. G. Frenk, J. A. S. Gromicho and S. Zhang, The role of robust optimization in single-leg airline evenue management, Management Science, 55 (2009), 148-163. doi: 10.1287/mnsc.1070.0843.

[4]

G. R. Bitran and S. M. Gilbert, Managing hotel reservations with uncertain arrivals, Operations Research, 44 (1996), 35-49. doi: 10.1287/opre.44.1.35.

[5]

R. Boel and P. Varaiya, Optimal control of jump processes, SIAM J. Control Optimization, 15 (1977), 92-119. doi: 10.1137/0315008.

[6]

P. Brémaud, Bang-bang controls of point processes, Adv. Appl. Probab., 8 (1976), 385-394.

[7]

P. Brémaud, "Point Processes and Queues, Martingale Dynamics," Springer-Verlag, New York, 1981.

[8]

Y. Feng and G. Gallego, Optimal stopping times for end of season sales and optimal starting times for promotional fares, Management Science, 41 (1995), 1371-1391. doi: 10.1287/mnsc.41.8.1371.

[9]

Y. Feng and B. Xiao, Maximizing revenue of perishable assets with risk analysis, Operations Research, 47 (1999), 337-341. doi: 10.1287/opre.47.2.337.

[10]

Y. Feng and B. Xiao, Optimal policies of yield management with multiple predetermined prices, Operations Research, 48 (2000), 332-343. doi: 10.1287/opre.48.2.332.13373.

[11]

Y. Feng and B. Xiao, A dynamic airline seat inventory control model and its optimal policy, Operations Research, 49 (2001), 938-949. doi: 10.1287/opre.49.6.938.10026.

[12]

Y. Feng and B. Xiao, A continuous-time seat control model for single-leg flights with no-shows and optimal overbooking upper bound, European Journal of Operational Research, 174 (2006), 1298-1316. doi: 10.1016/j.ejor.2005.05.008.

[13]

Y. Feng, P. Lin and B. Xiao, An analysis of airline seat control with cancellations, in "Stochastic Modelling and Optimization, with Applications in Queues, Finances, and Supply Chains" (eds. D. D. Yao, H. Zhang and X. Y. Zhou), Springer-Verlag, Berlin, 2002.

[14]

W. H. Fleming and H. M. Soner, "Controlled Markov Process and Viscosity Solutions," Second edition, Stochastic Modelling and Applied Probability, 25, Springer, New York, 2006.

[15]

M. k. Geraghty and E. Johnson, Revenue management saves national car rental, Inerfaces, 27 (1997), 107-127. doi: 10.1287/inte.27.1.107.

[16]

Y. Ge, Z. Yin and Y. Xu, Overbooking with transference option for flights, Journal of Industrial and Management Optimization, 7 (2011), 449-465. doi: 10.3934/jimo.2011.7.449.

[17]

S. P. Ladany and A. Arbel, Optimal cruise-liner passenger cabin pricing policy, European Journal of Operational Research, 55 (1991), 136-147. doi: 10.1016/0377-2217(91)90219-L.

[18]

C. J. Lautenbacher, The underlying Markov decision process in the single-leg airline yield management problem, Transportation Science, 34 (1999), 136-146. doi: 10.1287/trsc.33.2.136.

[19]

T. C. Lee and M. Hersh, A model for dynamic airline seat inventory control with multiple seat bookings, Transportation Science, 27 (1993), 252-265. doi: 10.1287/trsc.27.3.252.

[20]

Y. Liang, Solution to the continuous time dynamic yield management model, Transportation Science, 33 (1999), 117-123. doi: 10.1287/trsc.33.1.117.

[21]

K. Littlewood, Forecasting and control of passenger bookings, 12th AGIFORS Symposium Proceedings, (1972), 103-105.

[22]

K. T. Talluri and G. J. Van Ryzin, "The Theory and Practice of Revenue Management," International Series in Operations Research & Management Science, 68, Kluwer Academic Publishers, Boston, MA, 2004.

show all references

References:
[1]

P. P. Belobaba, Airline yield management: An overview of seat inventory control, Transportation Science, 21 (1987), 63-73. doi: 10.1287/trsc.21.2.63.

[2]

P. P. Belobaba, Application of a probabilistic decision model to airline seat inventory control, Operations Research, 37 (1989), 183-197. doi: 10.1287/opre.37.2.183.

[3]

S. I. Birbil, J. B. G. Frenk, J. A. S. Gromicho and S. Zhang, The role of robust optimization in single-leg airline evenue management, Management Science, 55 (2009), 148-163. doi: 10.1287/mnsc.1070.0843.

[4]

G. R. Bitran and S. M. Gilbert, Managing hotel reservations with uncertain arrivals, Operations Research, 44 (1996), 35-49. doi: 10.1287/opre.44.1.35.

[5]

R. Boel and P. Varaiya, Optimal control of jump processes, SIAM J. Control Optimization, 15 (1977), 92-119. doi: 10.1137/0315008.

[6]

P. Brémaud, Bang-bang controls of point processes, Adv. Appl. Probab., 8 (1976), 385-394.

[7]

P. Brémaud, "Point Processes and Queues, Martingale Dynamics," Springer-Verlag, New York, 1981.

[8]

Y. Feng and G. Gallego, Optimal stopping times for end of season sales and optimal starting times for promotional fares, Management Science, 41 (1995), 1371-1391. doi: 10.1287/mnsc.41.8.1371.

[9]

Y. Feng and B. Xiao, Maximizing revenue of perishable assets with risk analysis, Operations Research, 47 (1999), 337-341. doi: 10.1287/opre.47.2.337.

[10]

Y. Feng and B. Xiao, Optimal policies of yield management with multiple predetermined prices, Operations Research, 48 (2000), 332-343. doi: 10.1287/opre.48.2.332.13373.

[11]

Y. Feng and B. Xiao, A dynamic airline seat inventory control model and its optimal policy, Operations Research, 49 (2001), 938-949. doi: 10.1287/opre.49.6.938.10026.

[12]

Y. Feng and B. Xiao, A continuous-time seat control model for single-leg flights with no-shows and optimal overbooking upper bound, European Journal of Operational Research, 174 (2006), 1298-1316. doi: 10.1016/j.ejor.2005.05.008.

[13]

Y. Feng, P. Lin and B. Xiao, An analysis of airline seat control with cancellations, in "Stochastic Modelling and Optimization, with Applications in Queues, Finances, and Supply Chains" (eds. D. D. Yao, H. Zhang and X. Y. Zhou), Springer-Verlag, Berlin, 2002.

[14]

W. H. Fleming and H. M. Soner, "Controlled Markov Process and Viscosity Solutions," Second edition, Stochastic Modelling and Applied Probability, 25, Springer, New York, 2006.

[15]

M. k. Geraghty and E. Johnson, Revenue management saves national car rental, Inerfaces, 27 (1997), 107-127. doi: 10.1287/inte.27.1.107.

[16]

Y. Ge, Z. Yin and Y. Xu, Overbooking with transference option for flights, Journal of Industrial and Management Optimization, 7 (2011), 449-465. doi: 10.3934/jimo.2011.7.449.

[17]

S. P. Ladany and A. Arbel, Optimal cruise-liner passenger cabin pricing policy, European Journal of Operational Research, 55 (1991), 136-147. doi: 10.1016/0377-2217(91)90219-L.

[18]

C. J. Lautenbacher, The underlying Markov decision process in the single-leg airline yield management problem, Transportation Science, 34 (1999), 136-146. doi: 10.1287/trsc.33.2.136.

[19]

T. C. Lee and M. Hersh, A model for dynamic airline seat inventory control with multiple seat bookings, Transportation Science, 27 (1993), 252-265. doi: 10.1287/trsc.27.3.252.

[20]

Y. Liang, Solution to the continuous time dynamic yield management model, Transportation Science, 33 (1999), 117-123. doi: 10.1287/trsc.33.1.117.

[21]

K. Littlewood, Forecasting and control of passenger bookings, 12th AGIFORS Symposium Proceedings, (1972), 103-105.

[22]

K. T. Talluri and G. J. Van Ryzin, "The Theory and Practice of Revenue Management," International Series in Operations Research & Management Science, 68, Kluwer Academic Publishers, Boston, MA, 2004.

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