Summary
A version of the toll setting problem consists in determining profit maximizing tolls on a subset of arcs of a transportation network, given that users travel on shortest paths. This yields a bilevel program for which we propose efficient algorithms based on path generation.
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References
Brotcorne, L, Labbé, M., Marcotte, P., Savard, G., “A bilevel model for toll optimization on a multicommodity transportation network”, Transportation Science, 35, 345–358, 2001.
Bouhtou, M., van Hoesel, S., van der Kraaij, A., Lutton, J.-L., “Tariff optimization in networks”, Research Memorandum 041, METEOR, Maastricht Research School of Economics of Technology and Organization, 2003.
CPLEX, ILOG CPLEX, v6.0, 2000.
Dewez, S., On the toll setting problem. PhD thesis, Université Libre de Bruxelles, Institut de Statistique et de Recherche Opérationnelle, 2004.
Grigoriev, A., van Hoesel, S., van der Kraaij, A., Uetz M., Bouhtou, M., “Pricing Network Edges to Cross a River”, Research Memorandum 009, METEOR, Maastricht Research School of Economics of Technology and Organization, 2004.
Grötschel, M., Lovász, L., Schrijver, A., “The ellipsoid method and its consequences in combinatorial optimization”, Combinatorica, 1, 169–197, 1981.
van der Kraaij, A., Pricing in networks. PhD thesis, Proefschrift Universiteit Maastricht, 2004.
Labbé, M., Marcotte, P., Savard, G., “A bilevel model of taxation and its applications to optimal highway pricing”, Management Science, 44, 1608–1622, 1998.
Labbé, M., Marcotte, P., Savard, G., “On a class of bilevel programs”, In: Nonlinear Optimization and Related Topics, Di Pillo and Giannessi eds., Kluwer Academic Publishers, 183–206, 1999.
Lawler, E.L., “A procedure to compute the K best solutions to discrete optimization problems and its application to the shortest path problem”, Management Science, 18, 401–405, 1972.
Marcotte, P., Savard, G. and Semet, F. “A bilevel programming approach to the travelling salesman problem”, Operations Research Letters, 32, 240–248, 2004.
Roch, S., Savard, G., Marcotte, P., “Design and analysis of an algorithm for Stackelberg network pricing”, Networks, 46, 57–67, 2005.
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Didi-Biha, M., Marcotte, P., Savard, G. (2006). Path-based formulations of a bilevel toll setting problem. In: Dempe, S., Kalashnikov, V. (eds) Optimization with Multivalued Mappings. Springer Optimization and Its Applications, vol 2. Springer, Boston, MA . https://doi.org/10.1007/0-387-34221-4_2
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DOI: https://doi.org/10.1007/0-387-34221-4_2
Publisher Name: Springer, Boston, MA
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