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.
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Bibliographic InfoPaper provided by Department of Economics and Business, Universitat Pompeu Fabra in its series Economics Working Papers with number 1305.
Date of creation: Dec 2011
Date of revision: Nov 2012
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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
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- Joern Meissner & Arne Strauss, 2008.
"Network Revenue Management with Inventory-Sensitive Bid Prices and Customer Choice,"
Working Papers, Department of Management Science, Lancaster University
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, Elsevier, vol. 216(2), pages 459-468.
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