Build-operate-transfer Schemes for Road Franchising with Road Deterioration and Maintenance Effects

  • Zhijia Tan
  • Hai Yang
  • Xiaolei Guo


Private provision of public roads through build-operate-transfer (BOT) approaches is increasing around the world. By considering both social welfare gain and profitability, the BOT problem is to determine the optimal BOT contract which can be viewed as a combination of three primary variables of concession period, road capacity and toll charge. This paper models the BOT problem as the isoperimetric problem in calculus of variations to maximize the social welfare with a profit constraint. The model explicitly incorporates the effect of road deterioration and maintenance over the years, which is assumed to depend on the traffic loads, road capacity and road natural deterioration. We find that an optimal pricing policy requires toll increase over calendar time to reduce traffic load due to time-increasing and load-increasing maintenance cost. If, however, the marginal user damage on road is independent of time, then the optimal toll charge is free from the effect of road natural deterioration and thus time-invariant. We also discuss how to reach an optimal contract through government regulations and investigate the effects of economic growth on the solution properties of the problem.


Traffic Load Private Firm Transportation Research Part Road Capacity Road Life 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



The research described here was supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. HKUST6215 / 06E).


  1. Arnott, R., and Kraus, M. (1998). Self-financing of congestible facilities in a growing economy.Public Economics Theoretical and Applied Analysis,161-184.Google Scholar
  2. Chu, C.P. and Tsai, J.F. (2004). Road pricing models with maintenance cost. Transportation,31(4), 457-477.CrossRefGoogle Scholar
  3. de Palma, A., Kilani, M. and Lindsey, R. (2007). Maintenance, service quality and congestion pricing with competing roads. Transportation research Part B, 41(5), 573-591.CrossRefGoogle Scholar
  4. Durango, P. and Madanat, S. (2008). Optimization of inspection and maintenance decisions for infrastructure facilities under performance model uncertainty: a quasi-bayes approach. Transportation Research Part A, 42(8), 1074-1085.Google Scholar
  5. Engel, E., Fischer, R. and Galetovic, A. (1997). Highway franchising: pitfalls and opportunities. American Economic Review,87(2), 68-72.Google Scholar
  6. Engel, E. Fischer, R. and Galetovic, A. (2001). Least-present-value-of-revenue auctions and highway franchising. Journal of Political Economy,109, 993-1020.CrossRefGoogle Scholar
  7. Guo, X.L. and Yang, H. (2008). Analysis of a build-operate-transfer scheme for road franchising. International Journal of Sustainable Transportation,in press.Google Scholar
  8. Keeler, T.E. and Small, K.A. (1977). Optimal peak-load pricing, investment, and service levels on urban expressways. Journal of Political Economy, 85(1), 1-25.CrossRefGoogle Scholar
  9. Levinson, D. and Gillen, D. (1998). The full cost of intercity highway transportation. Transportation Research Part D, 3(4), 207-223.CrossRefGoogle Scholar
  10. Li, Y. and Madanat, S. (2002). A steady-state solution for the optimal pavement resurfacing problem. Transportation ResearchPart A, 36(6), 525-535.Google Scholar
  11. Mohring, H. (1976). Transportation Economics. Cambridge.Google Scholar
  12. Mohring, H. and Harwitz, M. (1962). Highway Benefits: an Analytical Framework. Northwestern University Press, Evanston, IL.Google Scholar
  13. Newbery, D.M. (1988). Road damage externalities and road user charges. Econometrica, 56(2), 295-316.CrossRefGoogle Scholar
  14. Newbery, D.M. (1989). Cost recovery from optimally designed roads. Economica, 56 (222), 165-185.CrossRefGoogle Scholar
  15. Nombela G. and de Rus, G. (2004). Flexible-term contracts for road franchising. Transportation ResearchPart A, 38(3), 163-179.Google Scholar
  16. Paterson, W.D.O. (1987). Road Deterioration and Maintenance Effects, Models for Planning and Management. the Johns Hopkins University Press.Google Scholar
  17. Small, K.A., Winston, C. and Evans, C.A. (1989). Road Works. The Brookings Institution Washington, D. C.Google Scholar
  18. Talluri, K.T. and van Ryzin, G.J. (2004) The Theory and Practice of Revenue Management.Kluwer Academic. Publishers.Google Scholar
  19. van Brunt, B. (2004). The Calculus of Variations. Springer.Google Scholar
  20. Yang, H. and Meng, Q. (2000). Highway pricing and capacity choice in a road network under a build-operate-transfer scheme. Transportation Research Part A,34(3), 207-222.Google Scholar
  21. Yang, H. and Meng, Q. (2002). A note on “highway pricing and capacity choice in a road network under a build-operate-transfer scheme”. Transportation ResearchPart A, 36(7), 659-663.Google Scholar
  22. Yang, H. and Huang, H.J. (2005). Mathematical and Economic Theory of Road Pricing.Elsevier, Oxford.Google Scholar
  23. Verhoef, E.T. (2007). Second-best road pricing through highway franchising. Journal of Urban Economics, 62(2), 337-361.CrossRefGoogle Scholar
  24. Ubbels, B. and Verhoef, E.T. (2008). Auctioning concessions for private roads. Transportation Research Part A, 42(1), 155-172.Google Scholar

Copyright information

© Springer-Verlag US 2009

Authors and Affiliations

  • Zhijia Tan
    • 1
  • Hai Yang
    • 1
  • Xiaolei Guo
    • 1
  1. 1.The Hong Kong University of Science and TechnologyHong KongChina

Personalised recommendations