Advertisement

Transportation

, Volume 44, Issue 4, pp 731–752 | Cite as

Joint road toll pricing and capacity development in discrete transport network design problem

  • Meng Xu
  • Guangmin Wang
  • Susan Grant-Muller
  • Ziyou Gao
Article

Abstract

The paper demonstrates a method to determine road network improvements that also involve the use of a road toll charge, taking the perspective of the government or authority. A general discrete network design problem with a road toll pricing scheme, to minimize the total travel time under a budget constraint, is proposed. This approach is taken in order to determine the appropriate level of road toll pricing whilst simultaneously addressing the need for capacity. The proposed approach is formulated as a bi-level programming problem. The optimal road capacity improvement and toll level scheme is investigated with respect to the available budget levels and toll revenues.

Keywords

Toll pricing Road development Discrete network design problem (DNDP) Bilevel programming Relaxation algorithm 

Notes

Acknowledgments

The work described in this paper was jointly supported by the National Natural Science Foundation of China (71361130016, 71422010, 71471167), the National Basic Research Program of China (2012CB725401), and the EU Marie Curie IIF (MOPED, 300674). The content is solely the responsibility of the authors and does not necessarily represent the views of the funding sources. Any remaining errors or shortcomings are our own. Any views or conclusions expressed in this paper do not represent those of funding sources.

References

  1. Adler, N., Proost, S.: Introduction to special issue of transportation research part B modelling non-urban transport investment and pricing. Transp. Res. Part B 44, 791–794 (2010)CrossRefGoogle Scholar
  2. Ban, J.X., Liu, H.X., Ferris, M.C., et al.: A general MPCC model and its solution algorithm for continuous network design problem. Math. Comput. Model. 43(5–6), 493–505 (2006)CrossRefGoogle Scholar
  3. Bouza, G., Still, G.: Mathematical programs with complementarity constraints: convergence properties of a smoothing method. Math. Oper. Res. 32(2), 467–483 (2007)CrossRefGoogle Scholar
  4. Boyce, D.E., Janson, B.N.: A discrete transportation network design problem with combined trip distribution and assignment. Transp. Res. Part B 14(1), 147–154 (1980)CrossRefGoogle Scholar
  5. Chen, Y., Florian, M.: The nonlinear bilevel programming problem: formulations, regularity and optimality conditions. Optimization 32, 193–209 (1995)CrossRefGoogle Scholar
  6. Colson, B., Marcotte, P., Savard, G.: Bilevel programming: a survey. A Quart. J. Oper. Res. 3, 87–107 (2005)CrossRefGoogle Scholar
  7. Dimitriou, L., Tsekeris, T., Stathopoulos, A.: Joint pricing and design of urban highways with spatial and user group heterogeneity. Netnomics 10, 141–160 (2009)CrossRefGoogle Scholar
  8. Fan, W., Gurmu, Z.: Combined decision making of congestion pricing and capacity expansion: genetic algorithm approach. J. Transp. Eng. 140(8), 04014031 (2014)CrossRefGoogle Scholar
  9. Farvaresh, H., Sepehri, M.M.: A single-level mixed integer linear formulation for a bi-level discrete network design problem. Transp. Res. Part E 47(5), 623–640 (2011)CrossRefGoogle Scholar
  10. Farvaresh, H., Sepehri, M.M.: A branch and bound algorithm for bilevel discrete network design problem. Netw. Spat. Econ. 13(1), 67–106 (2013)CrossRefGoogle Scholar
  11. Farahani, R.Z., Miandoabchi, E., Szeto, W.Y., Rashidi, H.: A review of urban transportation network design problems. Eur. J. Oper. Res. 229(2), 281–302 (2013)CrossRefGoogle Scholar
  12. Fortuny-Amat, J., McCarl, B.: A representation and economic interpretation of two-level programming problem. J. Oper. Res. Soc. 32, 783–792 (1981)CrossRefGoogle Scholar
  13. GAMS: GAMS The Solver Manuals. GAMS Development Corporation, Washington, DC (2009)Google Scholar
  14. Gao, Z.Y., Wu, J.J., Sun, H.J.: Solution algorithm for the bilevel discrete network design problem. Transp. Res. Part B 39(6), 479–495 (2005)CrossRefGoogle Scholar
  15. Givoni, M.: Addressing transport policy challenges through policy-packaging. Transp. Res. Part A 60, 1–8 (2014)CrossRefGoogle Scholar
  16. Givoni, M., Macmillen, J., Banister, D., Feitelson, E.: From policy measures to policy packages. Transp. Rev. 33(1), 1–20 (2013)CrossRefGoogle Scholar
  17. Grant-Muller, S., Xu, M.: The role of tradable credit schemes in road traffic congestion management. Transp. Rev. 34(2), 128–149 (2014)CrossRefGoogle Scholar
  18. Gümüş, Z.H., Floudas, C.A.: Global optimization of mixed-integer bilevel programming problems. CMS 2(3), 181–212 (2005)CrossRefGoogle Scholar
  19. Hearn, D.W., Ramana, M.V.: Solving congestion toll pricing models. In: Marcotte, P., Nguyen, S. (eds.) Equilibrium and Advanced Transportation Modeling, pp. 109–124. Kluwer Academic Publishers, Boston (1998)CrossRefGoogle Scholar
  20. Hoheisel, T., Kanzow, C., Schwartz, A.: Theoretical and numerical comparison of relaxation methods for mathematical programs with complementarity constraints. Math. Progr. 137, 257–288 (2013)CrossRefGoogle Scholar
  21. Jan, R.H., Chern, M.S.: Nonlinear integer bilevel programing. Eur. J. Oper. Res. 72(3), 574–587 (1994)CrossRefGoogle Scholar
  22. Kadrani, A., Dussault, J.P., Benchakroun, A.: A new regularization scheme for mathematical programs with complementarity constraints. SIAM J. Optim. 20, 78–103 (2009)CrossRefGoogle Scholar
  23. Kanzow, C., Schwartz, A.: A New Regularization Method for Mathematical Programs with Complementarity Constraints with Strong Convergence Properties. Preprint 296. Institute of Mathematics. University of Wrzburg, Wrzburg (2010)Google Scholar
  24. Keeler, T.E., Small, K.A.: Optimal peak-load pricing, investment, and service levels on urban expressways. J. Polit. Econ. 85, 1–25 (1977)CrossRefGoogle Scholar
  25. Kelly, C., May, A., Jopson, A.: The development of an option generation tool to identify potential transport policy packages. Transp. Policy 15(6), 361–371 (2008)CrossRefGoogle Scholar
  26. Koh, A., Shepherd, S.P., Sumalee, A.: Second best toll and capacity optimisation in networks: solution algorithm and policy implications. Transportation 36(2), 147–165 (2009)CrossRefGoogle Scholar
  27. LeBlanc, L.J.: An algorithm for the discrete network design problem. Transp. Sci. 9(3), 183–199 (1975)CrossRefGoogle Scholar
  28. Leyffer, S.: Mathematical programs with complementarity constraints. SIAG/OPT Views News 14(1), 15–18 (2003)Google Scholar
  29. Lin, G.H., Fukushima, M.: A modified relaxation scheme for mathematical programs with complementarity constraints. Ann. Oper. Res. 133, 63–84 (2005)CrossRefGoogle Scholar
  30. Luo, Z.Q., Pang, J.S., Ralph, D.: Mathematical Programs with Equilibrium Constraints. Cambridge University Press, Cambridge (1996)CrossRefGoogle Scholar
  31. Marsden, G., Frick, K.T., May, A.D., Deakin, E.: Transfer of innovative policies between cities to promote sustainability: case study evidence. Transp. Res. Rec. 21, 89–96 (2010)CrossRefGoogle Scholar
  32. May, A.D., Karlstrom, A., Marler, N., Matthews, B., Minken, H., Monzon, A., Page, M., Pfaffenbichler, P., Shepherd, S.: Developing sustainable urban land use and transport strategies: a decision-makers’ guidebook. Institute for Transport Studies, Leeds. Working paper (2005b)Google Scholar
  33. May, A.D., Kelly, C., Shepherd, S.P.: The principles of integration in urban transport strategies. Transp. Policy 13(4), 319–327 (2006)CrossRefGoogle Scholar
  34. May, A.D., Shepherd, S.P., Emberger, G., Ash, A., Zhang, X., Paulley, N.: Optimal land use and transport strategies: methodology and application to European cities. Transp. Res. Rec. 1924, 129–138 (2005)CrossRefGoogle Scholar
  35. May, A.D., Still, B.J.: The Instruments of Transport Policy. Working Paper WP545. Institute for Transport Studies, Leeds (2000)Google Scholar
  36. Meng, Q., Liu, Z.Y., Wang, S.A.: Optimal distance tolls under congestion pricing and continuously distributed value of time. Transp. Res. Part E 48(5), 937–957 (2012)CrossRefGoogle Scholar
  37. Mitsos, A.: Global solution of nonlinear mixed-integer bilevel programs. J. Global Optim. 47, 557–582 (2010)CrossRefGoogle Scholar
  38. Mohring, H., Harwitz, M.: HighWay Benefits. Northwestern University Press, Evanston (1962)Google Scholar
  39. Moore, J.T., Bard, F.J.: The mixed integer linear bilevel programming problem. Oper. Res. 38(5), 911–921 (1990)CrossRefGoogle Scholar
  40. Niu, B.Z., Zhang, J.: Price, capacity and concession period decisions of Pareto-efficient BOT contracts with demand uncertainty. Transp. Res. Part E 53, 1–14 (2013)CrossRefGoogle Scholar
  41. Sahin, K.H., Ciric, A.R.: A dual temperature simulated annealing approach for solving bilevel programming problems. Comput. Chem. Eng. 23(1), 11–25 (1998)CrossRefGoogle Scholar
  42. Scheel, H., Scholtes, S.: Mathematical programs with complementarity constraints: stationarity, optimality, and sensitivity. Math. Oper. Res. 22(1), 1–22 (2000)CrossRefGoogle Scholar
  43. Scholtes, S.: Convergence properties of a regularization scheme for mathematical programs with complementarity constraints. SIAM J. Optim. 11(4), 918–936 (2001)CrossRefGoogle Scholar
  44. Sheffi, Y.: Urban Transportation Networks: Equilibrium Analysis with Mathematical Programming Methods. Prentice-Hall, Englewood Cliffs (1985)Google Scholar
  45. Shepherd, S.P., Zhang, X., Emberger, G., May, A.D., Hudson, M., Paulley, N.: Designing optimal urban transport strategies: the role of individual policy instruments and the impact of financial constraints. Transp. Policy 13(1), 49–65 (2006)CrossRefGoogle Scholar
  46. Steffensen, S., Ulbrich, M.: A new relaxation scheme for mathematical programs with equilibrium constraints. SIAM J. Optim. 20, 2504–2539 (2010)CrossRefGoogle Scholar
  47. Strotz, R.H.: Urban transportation parables. In: Margolis, J. (ed.) The Public Economy of Urban Communities. Resources for the Future, Washington, DC (1965)Google Scholar
  48. Subprasom, K., Chen, A.: Effects of regulation on highway pricing and capacity choice of a build-operate-transfer scheme. J. Constr. Eng. Manag. 133(1), 64–71 (2007)CrossRefGoogle Scholar
  49. Tan, Z.J., Yang, H., Guo, X.L.: Properties of Pareto efficient contracts and regulations for road franchising. Transp. Res. Part B 44(4), 415–433 (2010)CrossRefGoogle Scholar
  50. Tan, Z.J., Yang, H.: Flexible build-operate-transfer contracts for road franchising under demand uncertainty. Transp. Res. Part B 46(10), 1419–1439 (2012)CrossRefGoogle Scholar
  51. Verhoef, E., Koh, A., Shepherd, S.: Pricing, capacity and long-run cost functions for first-best and second-best network problems. Transp. Res. Part B 44, 870–885 (2010)CrossRefGoogle Scholar
  52. Wang, G.M., Gao, Z.Y., Xu, M., Sun, H.J.: Models and a relaxation algorithm for continuous network design problem with a tradable credit scheme and equity constraints. Comput. Oper. Res. 41(1), 252–261 (2014a)CrossRefGoogle Scholar
  53. Wang, G.M., Gao, Z.Y., Xu, M., Sun, H.J.: Joint link-based credit charging and road capacity improvement in continuous network design problem. Transp. Res. Part A 67, 1–14 (2014b)CrossRefGoogle Scholar
  54. Wang, S.A., Meng, Q., Yang, H.: Global optimization methods for the discrete network design problem. Transp. Res. Part B 50, 42–60 (2013)CrossRefGoogle Scholar
  55. Wen, U.P., Hsu, S.T.: Linear bi-level programming problem: a review. J. Oper. Res. Soc. 42(2), 125–133 (1991)Google Scholar
  56. Xu, M., Gao, Z.Y.: Multi-class multi-modal network equilibrium with regular behaviors: a general fixed point approach. In: Lam, W.H.K., Wong, S.C., Lo, H.K. (eds.) Proceedings of 18th International Symposium on Transportation and Traffic Theory, Springer, pp. 301–326 (2009)Google Scholar
  57. Xu, M., Grant-Muller, S., Gao, Z.Y.: Evolution and assessment of economic regulatory policies for expressway infrastructure in China. Transp. Policy 41, 50–63 (2015a)CrossRefGoogle Scholar
  58. Xu, M., Grant-Muller, S., Huang, H.J., Gao, Z.Y.: Transport management measures in the post-olympic games period: supporting sustainable urban mobility for Beijing? Int. J. Sustain. Dev. World Ecol. 22(1), 50–63 (2015b)Google Scholar
  59. Yang, H., Bell, M.G.H.: Models and algorithms for road network design: a review and some new developments. Transp. Rev. 18(3), 257–278 (1998)CrossRefGoogle Scholar
  60. Yang, H., Huang, H.J.: Mathematical and Economic Theory of Road Pricing. Elsevier Ltd., Oxford (2005)CrossRefGoogle Scholar
  61. Yang, H., Meng, Q.: Highway pricing and capacity choice in a road network under a build-operate-transfer scheme. Transp. Res. A 34, 207–222 (2000)Google Scholar
  62. Yang, H., Xu, W., Heydecker, B.: Bounding the efficiency of road pricing. Transp. Res. E 46(1), 90–108 (2010)CrossRefGoogle Scholar
  63. Yin, Y., Li, Z.C., Lam, W.H.K., Choi, K.: Sustainable toll pricing and capacity investment in a congested road network: a goal programming approach. J. Transp. Eng. 140, 95–100 (2014)Google Scholar
  64. Zhang, L., Lawphongpanich, S., Yin, Y.: Reformulating and solving discrete network design problem via an active set technique. In: Lam, W.H.K., Wong, S.C., Lo, H.K. (eds.) Proceedings of 18th International Symposium on Transportation and Traffic Theory, Springer, pp. 283–300 (2009)Google Scholar
  65. Zhang, X.N., Wee, B.: Enhancing transportation network capacity by congestion pricing with simultaneous toll location and toll level optimization. Eng. Optim. 44(4), 477–488 (2012)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Meng Xu
    • 1
  • Guangmin Wang
    • 2
  • Susan Grant-Muller
    • 3
  • Ziyou Gao
    • 4
  1. 1.State Key Laboratory of Rail Traffic Control and SafetyBeijing Jiaotong UniversityBeijingChina
  2. 2.School of Economics and ManagementChina University of GeosciencesWuhanChina
  3. 3.Institute for Transport StudiesUniversity of LeedsLeedsUK
  4. 4.School of Traffic and TransportationBeijing Jiaotong UniversityBeijingChina

Personalised recommendations