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This paper investigates the problem of maximizing the revenue of a telecommunications operator by simultaneously pricing point-to-point services and allocating bandwidth in its network, while facing competition. Customers are distributed into market segments, i.e., groups of customers with a similar preference for the services. This preference is expressed using utility functions, and customers choose between the offers of the operator and of the competition according to their utility. We model the problem as a leader-follower game between the operator and the customers. This kind of problem has classically been modeled as a bilevel program. A market segmentation is usually defined by a discrete distribution function of the total demand for a service; in this case, the problem can be modeled as a combinatorial optimization problem. In this paper, however, we motivate the use of a continuous distribution function and investigate the nonlinear continuous optimization problem obtained in this case. We analyze the mathematical properties of the problem, and in particular we give a necessary and sufficient condition for its convexity. We introduce methods to solve the problem and we provide encouraging numerical results on realistic telecommunications instances of the problem, showing that it can be solved efficiently.
@article{RO_2009__43_2_115_0,
author = {Bouhtou, Mustapha and Erbs, Guillaume},
title = {A continuous optimization model for a joint problem of pricing and resource allocation},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {115--143},
publisher = {EDP-Sciences},
volume = {43},
number = {2},
year = {2009},
doi = {10.1051/ro/2009008},
mrnumber = {2527859},
zbl = {1176.90683},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/ro/2009008/}
}
TY - JOUR AU - Bouhtou, Mustapha AU - Erbs, Guillaume TI - A continuous optimization model for a joint problem of pricing and resource allocation JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2009 SP - 115 EP - 143 VL - 43 IS - 2 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/ro/2009008/ DO - 10.1051/ro/2009008 LA - en ID - RO_2009__43_2_115_0 ER -
%0 Journal Article %A Bouhtou, Mustapha %A Erbs, Guillaume %T A continuous optimization model for a joint problem of pricing and resource allocation %J RAIRO - Operations Research - Recherche Opérationnelle %D 2009 %P 115-143 %V 43 %N 2 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/ro/2009008/ %R 10.1051/ro/2009008 %G en %F RO_2009__43_2_115_0
Bouhtou, Mustapha; Erbs, Guillaume. A continuous optimization model for a joint problem of pricing and resource allocation. RAIRO - Operations Research - Recherche Opérationnelle, Tome 43 (2009) no. 2, pp. 115-143. doi: 10.1051/ro/2009008
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