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Pricing Toll Roads under Uncertainty

Authors Trivikram Dokka, Alain Zemkoho, Sonali Sen Gupta, Fabrice Talla Nobibon

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Trivikram Dokka
Alain Zemkoho
Sonali Sen Gupta
Fabrice Talla Nobibon

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Trivikram Dokka, Alain Zemkoho, Sonali Sen Gupta, and Fabrice Talla Nobibon. Pricing Toll Roads under Uncertainty. In 16th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2016). Open Access Series in Informatics (OASIcs), Volume 54, pp. 4:1-4:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016) https://doi.org/10.4230/OASIcs.ATMOS.2016.4

Abstract

We study the toll pricing problem when the non-toll costs on the network are not fixed and can vary over time. We assume that users who take their decisions, after the tolls are fixed, have full information of all costs before making their decision. Toll-setter, on the other hand, do not have any information of the future costs on the network. The only information toll-setter have is historical information (sample) of the network costs. In this work we study this problem on parallel networks and networks with few number of paths in single origin-destination setting. We formulate toll-setting problem in this setting as a distributionally robust optimization problem and propose a method to solve to it. We illustrate the usefulness of our approach by doing numerical experiments using a parallel network.

Subject Classification

Keywords
  • Conditional value at risk
  • robust optimization
  • toll pricing

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References

  1. S.M. Alizadeh, P. Marcotte, and G. Savard. Two-stage stochastic bilevel programming over a transportation network. Transportation Research Part B, 58:92-105, 2013. Google Scholar
  2. M. Bouhtou, G. Erbs, and M. Minoux. Joint optimization of pricing and resource allocation in competitive telecommunication networks. Networks, 50(1):37-49, 2007. Google Scholar
  3. M. Bouhtou, S. van Hoesel, A. Van der Kraaij, and J. Lutton. Tarriff optimization in networks. Informs Journal of Computing, 19:458-469, 2007. Google Scholar
  4. C. Brown. Financing transport infrastructure: For whom the road tolls. Australian Economic Review, 38:431-438, 2005. Google Scholar
  5. J.-P. Coté, P. Marcotte, and G. Savard. A bilevel modeling approach to pricing and fare optimization in the airline industry. Journal of Revenue and Pricing Management, 1:23-36, 2003. Google Scholar
  6. L.M. Gardner, A. Unnikrishnan, and S.T. Waller. Solution methods for robust pricing of transportation networks under uncertain demand. Transportation Research Part C, 18:656-667, 2010. Google Scholar
  7. F. Gilbert, P. Marcotte, and G. Savard. A numerical study of the logit network pricing problem. Transportation Science, 49(3):706-719, 2015. Google Scholar
  8. J. Goh and M. Sim. Distributionally robust optimization and its tractable approximations. Operations Research, 58(4):902-917, 2010. Google Scholar
  9. V. Goyal and R. Ravi. An fptas for minimizing a class of quasi-concave functions over a convex set. Operations Research Letters, 41(2):191-196, 2013. Google Scholar
  10. G. Heilporn, M. Labbé, P. Marcotte, and G. Savard. A parallel between two classes of pricing problems in transportation and marketing. Journal of Revenue and Pricing Management, 9:110-125, 2010. Google Scholar
  11. G. Karakostas and SG. Kolliopoulos. Edge pricing of multicommodity networks for heterogenous selfish users. FOCS, 2004. Google Scholar
  12. M. Labbé, P. Marcotte, and G. Savard. A bilevel model of taxation and its application to optimal highway pricing. Management Science, 44:1608-1622, 1998. Google Scholar
  13. M. Labbé and A. Violin. Bilevel programming and price setting problems. 4OR, 11:1-30, 2013. Google Scholar
  14. T.G.J. Myklebust, M.A. Sharpe, and L. Tuncel. Efficient heuristic algorithms for maximum utility product pricing problems. Computers and Operations Research, 69:25-39, 2016. Google Scholar
  15. RT. Rockafeller and S. Uryasev. Optimization of conditional value-at-risk. Journal of Risk, 2(3):21-42, 2000. Google Scholar
  16. Iakovos Toumazis and Changhyun Kwon. Worst-case conditional value-at-risk minimization for hazardous materials transportation. Transportation Science, http://dx.doi.org/10.1287/trsc.2015.0639:1-14, 2015. Google Scholar
  17. S. van Hoesel. An overview of stackelberg pricing in networks. European Journal of Operational Reseach, 189:1393-1492, 2008. Google Scholar
  18. A. Violin. Mathematical programming approaches to pricing problems. PhD thesis, Universite Libre de Bruxelles, 2014. Google Scholar
  19. Shushang Zhu and Masao Fukushima. Worst-case conditional value-at-risk with application to robust portfolio management. Operations Research, 57(5):1155-1168, 2009. Google Scholar
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