A stochastic approximation method for the single-leg revenue management problem with discrete demand distributions

Kunnumkal, S and Topaloglu, H (2009) A stochastic approximation method for the single-leg revenue management problem with discrete demand distributions. Mathematical Methods of Operations Research, 70 (3). pp. 477-504.

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We consider the problem of optimally allocating the seats on a single flight leg to the demands from multiple fare classes that arrive sequentially. It is well-known that the optimal policy for this problem is characterized by a set of protection levels. In this paper, we develop a new stochastic approximation method to compute the optimal protection levels under the assumption that the demand distributions are not known and we only have access to the samples from the demand distributions. The novel aspect of our method is that it works with the nonsmooth version of the problem where the capacity can only be allocated in integer quantities. We show that the sequence of protection levels generated by our method converges to a set of optimal protection levels with probability one. We discuss applications to the case where the demand information is censored by the seat availability. Computational experiments indicate that our method is especially advantageous when the total expected demand exceeds the capacity by a significant margin and we do not have good a priori estimates of the optimal protection levels.

ISB Creiators:
ISB Creators
Kunnumkal, S
Item Type: Article
Uncontrolled Keywords: Dynamic programming; Revenue management; Stochastic approximation; Subgradient optimization
Subjects: Business and Management
Depositing User: Veeramani R
Date Deposited: 03 Nov 2014 14:22
Last Modified: 03 Nov 2014 17:18
URI: http://eprints.exchange.isb.edu/id/eprint/140
Publisher URL: http://dx.doi.org./10.1007/s00186-008-0278-x
Publisher OA policy: http://www.sherpa.ac.uk/romeo/issn/1432-2994/
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