Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-22T23:58:53.142Z Has data issue: false hasContentIssue false
  • English
  • Français

A continuous optimization model for a joint problem of pricing and resource allocation

Published online by Cambridge University Press:  28 April 2009

Mustapha Bouhtou  and
Guillaume Erbs
Mustapha Bouhtou
Affiliation:
France Telecom Research and Development, 38-40 rue du Général Leclerc, 92794 Issy les Moulineaux, France; [email protected]
Guillaume Erbs
Affiliation:
France Telecom Research and Development, 38-40 rue du Général Leclerc, 92794 Issy les Moulineaux, France; [email protected] Université Paris 6, 4 place Jussieu, 75005 Paris, France; [email protected]
Get access

Abstract

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.

Keywords

Optimizationbilevel programmingrevenue managementpricingresource allocationtelecommunications.
Type
Research Article
Information
RAIRO - Operations Research , Volume 43 , Issue 2 , April 2009 , pp. 115 - 143
Copyright
© EDP Sciences, ROADEF, SMAI, 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

G. Aydin and J. Ryan, Product line selection with stochastic utility (2000) (submitted).
M. Ben-Akiva and M. Bierlaire, Discrete choice methods and their applications to short term travel decisions, in Handbook of transportation science, edited by R. Hall, International Series in Operations Research and Management Science, Vol. 23. Kluwer Academic Publishers, Dordrecht (1999) 5–34.
Bergstrom, T. and Bagnoli, M., Log-concave probability and its applications. Econ. Theory 26 (2005) 445–469.
M. Bouhtou, M. Diallo and L. Wynter, Capacitated network revenue management through shadow pricing, in Group communications and charges; technology and business models, edited by B. Stiller, G. Carle, M. Karsten and P. Reichl, Lect. Notes Comput. Sci. 2816, Springer-Verlag, Berlin, Heidelberg (2003) 342–352.
M. Bouhtou, M. Diallo and L. Wynter, Fair network resource allocation and link pricing: A numerical study, in Optimization and optimal control, edited by P. Pardalos, I. Tsevendorj and R. Enkhbat, World Scientific Publishing, Singapore (2003) 37–58.
M. Bouhtou, G. Erbs and M. Minoux, Pricing and resource allocation for point-to-point telecommunication services in a competitive market: a bilevel optimization approach, in Telecommunications planning: innovations in pricing, network design and management, edited by G. Anandalingam and S. Raghavan, Operations Research/Computer Science Interfaces Series, Vol. 33. Springer-Verlag, New York (2005) 1–16.
Bouhtou, M., Erbs, G. and Minoux, M., Joint optimization of pricing and resource allocation in competitive telecommunications networks. Networks 50 (2007) 37–49. CrossRef
Bouhtou, M., van Hoesel, S., van der Kraaij, A. and Lutton, J.-L., Tariff optimization in networks. INFORMS J. Comput. 19 (2007) 458–469. CrossRef
Brotcorne, L., Labbé, M., Marcotte, P. and Savard, G., A bilevel model and solution algorithm for a freight tariff setting problem. Transportation Science 34 (2000) 289–302. CrossRef
Brotcorne, L., Labbé, M., Marcotte, P., and Savard, G.. A bilevel model for toll optimization on a multicommodity transportation network. Transportation Science 35 (2001) 1–14. CrossRef
Côté, J.-P., Marcotte, P. and Savard, G., A bilevel modelling approach to pricing and fare optimisation in the airline industry. J. Revenue Pricing Manag. 2 (2003) 23–36. CrossRef
Croxton, K.L., Gendron, B. and Magnanti, T.L., A comparison of mixed-integer programming models for non-convex piecewise linear cost minimization problems. Manage. Sci. 49 (2003) 1268–1273. CrossRef
M. Fortin, P. Marcotte and G. Savard, Pricing a segmented market subject to congestion, in Proceedings of the Fifth Triennal Symposium on Transportation Analysis (TRISTAN V), Le Gosier, Guadeloupe, June 13–18 (2004).
F. Gilbert, P. Marcotte and G. Savard, Global and local approaches to a logit-based pricing problem, in 2006 Optimization Days, Montreal, May 8–10 (2006).
A. Grigoriev, S. van Hoesel, A. van der Kraaij, M. Uetz and M. Bouhtou, Pricing network edges to cross a river, in Approximation and online algorithms, edited by G. Persiano and R. Solis-Oba, Lect. Notes Comput. Sci. 3351 , Springer-Verlag, Berlin, Heidelberg (2004) 140–153.
Justus, C.G., Hargraves, W.R., Mikhail, A. and Graber, D., Methods for estimating wind speed frequency distributions. J. Appl. Meteorol. 17 (1978) 350–353. 2.0.CO;2>CrossRef
Keon, N. and Anandalingam, G., Optimal pricing for multiple services in telecommunications networks offering quality-of-service guarantees. IEEE/ACM Transactions on Networking 11 (2003) 66–80. CrossRef
Keon, N. and Anandalingam, G., A new pricing model for competitive telecommunications services using congestion discounts. INFORMS J. Comput. 17 (2005) 248–262. CrossRef
Labbé, M., Marcotte, P. and Savard, G., A bilevel model of taxation and its application to optimal highway pricing. Manage. Sci. 44 (1998) 1608–1622. CrossRef
M. Labbé, P. Marcotte and G. Savard, On a class of bilevel programs, in Nonlinear optimization and related topics, edited by G.D. Pillo and F. Giannessi, Kluwer Academic Publishers, Dordrecht, Boston (1999) 183–206.
P. Marcotte, G. Savard and D. Zhu, Mathematical structure of a bilevel strategic pricing model. Eur. J. Oper. Res. (2006), (to appear).
P. Marcotte and D. Zhu, Equilibria with infinitely many differentiated classes of customers. In Complementarity and variational problems. State of the art, edited by J.-S. Pang and M. Ferris, SIAM Publications, Philadelphia (1997) 234–258.
McGill, J.I. and van Ryzin, G.J., Revenue management: Research overview and prospects. Transportation Science 33 (1999) 233–256. CrossRef
Nair, S.K. and Bapna, R., An application of yield management for internet service providers. Nav. Res. Logist. 48 (2001) 348–362. CrossRef
Reichl, P., Hausheer, D. and Stiller, B., The cumulus pricing model as an adaptive framework for feasible, efficient and user-friendly tariffing of internet services. Comput. Networks 43 (2003) 3–24. CrossRef
Savickas, R., A simple option-pricing formula. Financ. Rev. 37 (2002) 207–226. CrossRef
Wächter, A. and Biegler, L.T., On the implementation of a primal-dual interior point filter line search algorithm for large-scale nonlinear programming. Math. Program. 106 (2006) 25–57. CrossRef