Equivalence of Piecewise-Linear Approximation and Lagrangian Relaxation for Network Revenue Management
AbstractThe network revenue management (RM) problem arises in airline, hotel, media, and other industries where the sale products use multiple resources. It can be formulated as a stochastic dynamic program but the dynamic program is computationally intractable because of an exponentially large state space, and a number of heuristics have been proposed to approximate it. Notable amongst these (both for their revenue performance, as well as their theoretically sound basis) are approximate dynamic programming methods that approximate the value function by basis functions (both affine functions as well as piecewise-linear functions have been proposed for network RM) and decomposition methods that relax the constraints of the dynamic program to solve simpler dynamic programs (such as the Lagrangian relaxation methods). In this paper we show that these two seemingly distinct approaches coincide for the network RM dynamic program, i.e., the piecewise-linear approximation method and the Lagrangian relaxation method are one and the same.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Barcelona Graduate School of Economics in its series Working Papers with number 608.
Date of creation: Dec 2011
Date of revision:
network revenue management; linear programming; approximate dynamic programming; Lagrangian relaxation methods;
Find related papers by JEL classification:
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
- L93 - Industrial Organization - - Industry Studies: Transportation and Utilities - - - Air Transportation
- L83 - Industrial Organization - - Industry Studies: Services - - - Sports; Gambling; Restaurants; Recreation; Tourism
- M11 - Business Administration and Business Economics; Marketing; Accounting - - Business Administration - - - Production Management
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-05-15 (All new papers)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Joern Meissner & Arne Strauss, 2008.
"Network Revenue Management with Inventory-Sensitive Bid Prices and Customer Choice,"
MRG/0008, Department of Management Science, Lancaster University, revised Apr 2010.
- Meissner, Joern & Strauss, Arne, 2012. "Network revenue management with inventory-sensitive bid prices and customer choice," European Journal of Operational Research, Elsevier, vol. 216(2), pages 459-468.
- Sumit Kunnumkal & Kalyan Talluri, 2014. "On the tractability of the piecewise-linear approximation for general discrete-choice network revenue management," Economics Working Papers 1409, Department of Economics and Business, Universitat Pompeu Fabra.
- Sumit Kunnumkal & Kalyan Talluri, 2014. "On the Tractability of the Piecewiselinear Approximation for General Discrete-Choice Network Revenue Management," Working Papers 749, Barcelona Graduate School of Economics.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Bruno Guallar).
If references are entirely missing, you can add them using this form.