This Article Full Text (PDF) e-companion References Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via HighWire Citing Articles via Google Scholar Google Scholar Articles by van Ryzin, G. Articles by Vulcano, G. Search for Related Content

Simulation-Based Optimization of Virtual Nesting Controls for Network Revenue Management

Graduate School of Business, Columbia University, New York, New York 10027
Stern School of Business, New York University, New York, New York 10012
gjv1{at}columbia.edu
gvulcano{at}stern.nyu.edu

Virtual nesting is a popular capacity control strategy in network revenue management. In virtual nesting, products (itinerary-fare-class combinations) are mapped ("indexed") into a relatively small number of "virtual classes" on each resource (flight leg) of the network. Nested protection levels are then used to control the availability of these virtual classes; specifically, a product request is accepted if and only if its corresponding virtual class is available on each resource required. Bertsimas and de Boer proposed an innovative simulation-based optimization method for computing protection levels in a virtual nesting control scheme [Bertsimas, D., S. de Boer. 2005. Simulation-based booking-limits for airline revenue management. Oper. Res. 53 90–106]. In contrast to traditional heuristic methods, this simulation approach captures the true network revenues generated by virtual nesting controls. However, because it is based on a discrete model of capacity and demand, the method has both computational and theoretical limitations. In particular, it uses first-difference estimates, which are computationally complex to calculate exactly. These gradient estimates are then used in a steepest-ascent-type algorithm, which, for discrete problems, has no guarantee of convergence.

In this paper, we analyze a continuous model of the problem that retains most of the desirable features of the Bertsimas-de Boer method, yet avoids many of its pitfalls. Because our model is continuous, we are able to compute gradients exactly using a simple and efficient recursion. Indeed, our gradient estimates are often an order of magnitude faster to compute than first-difference estimates, which is an important practical feature given that simulation-based optimization is computationally intensive. In addition, because our model results in a smooth optimization problem, we are able to prove that stochastic gradient methods are at least locally convergent. On several test problems using realistic networks, the method is fast and produces significant performance improvements relative to the protection levels produced by heuristic virtual nesting schemes. These results suggest it has good practical potential.

Subject classifications: stochastic algorithm; stochastic gradients; revenue management; capacity control.
History: Received January 2003; revision received May 2006; accepted September 2006.

This article has been cited by other articles:

				J. Patrick, M. L. Puterman, and M. Queyranne Dynamic Multipriority Patient Scheduling for a Diagnostic Resource Operations Research, November 1, 2008; 56(6): 1507 - 1525. [Abstract] [PDF]