Using Lagrangian Relaxation to Compute Capacity-Dependent Bid Prices in Network Revenue Management

We propose a new method to compute bid prices in network revenue management problems. The novel aspect of our method is that it explicitly considers the temporal dynamics of the arrivals of the itinerary requests and generates bid prices that depend on the remaining leg capacities. Our method is bas...

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Bibliographic Details
Published in:Operations research Vol. 57; no. 3; pp. 637 - 649
Main Author: Topaloglu, Huseyin
Format: Journal Article
Language:English
Published: Hanover, MD INFORMS 01.05.2009
Institute for Operations Research and the Management Sciences
Subjects:
Air transportation and traffic
Analysis
applications
Applied sciences
Approximation
Bid prices
Determinism
Dynamic programming
dynamic programming/optimal control
Exact sciences and technology
Ground, air and sea transportation, marine construction
Lagrange multiplier
Lagrange multipliers
Lagrangian function
Lagrangian functions
Mathematical programming
Matrices
Operational research and scientific management
Operational research. Management science
Optimal solutions
Portfolio management
Pricing
probability
Revenue
Revenue management
stochastic model applications
Stochastic models
Studies
Total revenue
Vehicular flight
United States
Stochastic model
Probabilistic approach
Income
Linear programming
Network management
Upper bound
Lagrange multiplier
Load capacity
Optimal control
Relaxation method
Air transportation
Dynamic programming
Tariffication
dynamic programming/optimal control: applications
probability: stochastic model applications
ISSN:0030-364X, 1526-5463
Online Access:Get full text
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Summary:We propose a new method to compute bid prices in network revenue management problems. The novel aspect of our method is that it explicitly considers the temporal dynamics of the arrivals of the itinerary requests and generates bid prices that depend on the remaining leg capacities. Our method is based on relaxing certain constraints that link the decisions for different flight legs by associating Lagrange multipliers with them. In this case, the network revenue management problem decomposes by the flight legs, and we can concentrate on one flight leg at a time. When compared with the so-called deterministic linear program, we show that our method provides a tighter upper bound on the optimal objective value of the network revenue management problem. Computational experiments indicate that the bid prices obtained by our method perform significantly better than the ones obtained by standard benchmark methods.
Bibliography:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0030-364X
1526-5463
DOI:10.1287/opre.1080.0597