×

A stochastic dynamic pricing model for the multiclass problems in the airline industry. (English) Zbl 1341.91081

Summary: In the airline industry, deciding the ticket price for each flight directly affects the number of people that in the future will try to buy a ticket. Depending on the willingness-to-pay of the customers the flight might take off with empty seats or seats sold at a lower price. Therefore, based on the behavior of the customers, a price must be fixed for each type of product in each period. We propose a stochastic dynamic pricing model to solve this problem, applying phase type distributions and renewal processes to model the inter-arrival time between two customers that book a ticket and the probability that a customer buys a ticket. We test this model in a real-world case where as a result the revenue is increased on average by 31 percent.

MSC:

91B24 Microeconomic theory (price theory and economic markets)
91B74 Economic models of real-world systems (e.g., electricity markets, etc.)
91B42 Consumer behavior, demand theory
60K10 Applications of renewal theory (reliability, demand theory, etc.)
90C15 Stochastic programming

Software:

EMpht
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Asmussen, S.; Nerman, O.; Olsson, M., Fitting phase-type distributions via the EM algorithm, Scandinavian Journal of Statistics, 23, 4, 419-441 (1996) · Zbl 0898.62104
[2] Bertesaks, D., Dynamic programming and optimal control (2000), Athena Scientific
[3] Bobbio, A.; Horváth, A.; Scarpa, A.; Telek, M., Acyclic discrete phase type distributions: Properties and a parameter estimation algorithm, Performance Evaluation, 54, 1, 1-32 (2003)
[4] Bobbio, A.; Horváth, A.; Telek, M., Matching three moments with minimal acyclic phase type distributions, Stochastic Models, 21, 1, 303-326 (2005) · Zbl 1069.60013
[5] Chen, L., Dynamic pricing with active learning under twosided censoring, Working paper, 1-33 (2012), The Fuqua School of Business Duke University
[6] Ernst, R.; Kamrad, B., Estimating demand by using sales information: Inaccuracies encountered, European Journal of Operational Research, 174, 2, 675-688 (2006) · Zbl 1110.90030
[7] Fiig, T.; Isler, K.; Hopperstad, C.; Belobaba, P., Optimization of mixed fare structures: Theory and applications, Journal of Revenue and Pricing Management, 9, 1, 152-170 (2010)
[8] Haensel, A.; Koole, G., Estimating unconstrained demand rate functions using customer choice sets, Journal of Revenue and Pricing Management, 10, 5, 1-17 (2011)
[9] Johnson, M.; Taaffe, M., Mathcing moments to phase distributions: Nonlinear programming approaches, Communications in Statistics - Stochastic Models, 6, 2, 259-281 (1990) · Zbl 0708.60019
[10] Khayari, R.; Sadre, R.; Haverkort, B., Fitting world-wide web request traces with the em-algorithm, Performance Evaluation, 52, 1, 175-191 (2003)
[11] Latouche, G.; Ramaswami, V., Introduction to matrix analytic methods in stochastic modeling (1999), ASA-SIAM · Zbl 0922.60001
[13] Li, L.; Ji-hua, P., Dynamic pricing model for airline revenue management under competition, Systems Engineering - Theory and Practice, 27, 11, 15-25 (2007)
[14] Maglaras, C.; Meissner, J., Dynamic pricing strategies for multi-product revenue management problems, Manufacturing & Service Operations Management (MSOM), 8, 2, 136-148 (2006)
[15] Osogami, T.; Harchol-Balter, M., A closed-form solution for mapping general distributions to minimal PH distributions, Computer performance evaluation. Modelling techniques and tools, 200-217 (2003), North-Holland · Zbl 1274.60041
[16] Parr, W.; Shucanny, W., Minimum distance and robust optimization, Working paper, 1-39 (1979), Department of Statistics, Shouthern Methodist University
[17] Perez, J.; Riaño, G., Benchmarking of fitting algorithms for continuous phase-type distributions, Working paper, 1-20 (2007), COPA Universidad de los Andes
[18] Phillips, R., Pricing and revenue optimization (2005), Stanford Business Books
[19] Puterman, M., Markov decision process: Discrete stochastic dynamic programming (2005), Wiley Interscience · Zbl 1184.90170
[20] Ross, S., Introduction to probability models (2007), Elsevier
[21] Talluri, K.; Van Ryzin, G., The theory and practice of revenue management (2004), Springer · Zbl 1083.90024
[22] Telek, M.; Heindl, A., Matching moments for acyclic discrete and continuous phase type distributions of second order, International Journal of Simulation, 3, 3, 1-11 (2003)
[23] Thummler, A.; Buchholz, P.; Telek, M., A novel approach for phase-type fitting with the EM algorithm, IEEE Computer Society, 3, 3, 1-35 (2005)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.