Abstract
In this paper, we survey applications and algorithms pertaining to an important class of price setting problems formulated as bilevel programs.
À Alain, en souvenir de randonnées bien arrosées sur la rivière l’Assomption et dans la réserve Mastigouche, aux temps héroïques du GERAD.
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References
Bencheick, A., “Conception et tarification d’un réseau privé mul-tidébit à large bande dans un environnement concurrentiel”, Ph.D. thesis, Institut National de Recherche Scientifique, INRS-Télécommunication (1997).
Brotcorne, L., Labbé, M., Marcotte, P. and Savard, G., “A bilevel model for toll optimization on a multicommodity transportation network”, forthcoming in Transportation Science.
Brotcorne, L., “Approches opérationnelles et stratégiques des problèmes de trafic routier”, Ph.D. thesis, Université Libre de Bruxelles, February 1998.
Cocchi, R., Shenker, S., Estrin, D. and Zhang, L., “Pricing in computer networks: motivation, formulation, and example”, IEEE/ACM Transactions on Networking 1 (1993) 614–627.
Dial, R. B., “Minimal-revenue congestion pricing Part II: An efficient algorithm for the general case”, Transportation Research B 34 (2000) 645–665.
Dial, R. B.J “Minimal-revenue congestion pricing part I: A fast algorithm for the single-origin casse case”, Transportation Research B 33 (1999) 189–202.
Fukushima, M., “Equivalent differentiate optimization problems and descent methods for asymmetric variational inequality problems”, Mathematical Programming 53 (1992) 99–110.
Gendreau, M., Marcotte, P. and Savard, G., “A Hybrid tabu-ascent algorithm for the linear bilevel programming problem”, Journal of Global Optimization 8 (1996) 217–232.
Girard, A. and Zidane, R., “Revenue Optimization of B-ISDN Networks”, IEEE Transactions on Communications 43 (1995) 15–25.
Hansen, P., Jaumard, B. and Savard, G., “New branch-and-bound rules for linear bilevel programming”, JOTA 22 (1992) 1194–1217.
Hearn, D.W. and Ramana, M.V., “Solving congestion toll pricing models”, in: Equilibrium and Advanced Transportation Modelling, Patrice Marcotte and Sang Nguyen (eds.), Kluwer, Dordrecht, pp. 109–123, 1998.
Kocvara, M. and Outrata, J.V., “A nonsmooth approach to optimization problems with equilibrium constraints”, in Complementarity and variational problems. State of the art, M.C. Ferris and J.S. Pang (eds.), SIAM, Philadelphia (1997).
Julsain, H., “Tarification dans les réseaux de télécommunications: une approche par programmation mathématique à deux niveaux”, Mémoire de maîtrise, École Polytechnique de Montréal, 1999.
Labbé, M., Marcotte, P. and Savard, G., “A bilevel model of taxation and its application to optimal highway pricing”, Management Science 44 (1998) 1595–1607.
Larsson, T. and Patriksson, M., “Traffic management through link tolls - an approach utilizing side constrained traffic equilibrium models”, in: Equilibrium and Advanced Transportation Modelling, Patrice Marcotte and Sang Nguyen (eds.), Kluwer, Dordrecht, pp. 125–151, 1998.
Loridan, P. and Morgan, J., “E-regularized two-level optimization problems: approximation and existence results”, Fifth French-German Conference on Optimization, Lecture Notes in Mathematics 1405, Springer-Verlag (1989) 99–113.
Luo, Z.Q., Pang, J.S. and Ralph, D., Mathematical Programs with Equilibrium Constraints, Cambridge University Press, Cambridge (1996).
Mitchell, B.M. and Vogelsang, I., Telecommunications pricing: Theory and practice, Cambridge University Press, (1992).
Outrata, J.V., Kocvara, M. and Zowe, J., Nonsmooth Approach to Optimization Problems with Equilibrium Constraints. Kluwer Academic Publishers, Dordrecht, (1998).
Shimizu, K., Ishizuka, Y. and Bard, J.F., Nondifferentiable and Two-Level Mathematical Programming, Kluwer, Boston (1997).
Scholtes, S. and Stohr, M., “Exact penalization of mathematical programs with equilibrium constraints” SIAM J. Control and Optimization 37, pp.617–652, (1999).
Special issue on Yield Management, Transportation Science 33 (1999).
Wang, Q., Peha, J.M. and Sirbu, M., “Optimal Pricing for Integrated-Services Networks”, in Internet Economics, Joseph Bailey and Lee McKnight editors, MIT Press, (1997) 353–376.
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Marcotte, P., Savard, G. (2002). A Bilevel Programming Approach to Optimal Price Setting. In: Zaccour, G. (eds) Decision & Control in Management Science. Advances in Computational Management Science, vol 4. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3561-1_6
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DOI: https://doi.org/10.1007/978-1-4757-3561-1_6
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-4995-0
Online ISBN: 978-1-4757-3561-1
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