, Volume 36, Issue 2, pp 147–165 | Cite as

Second best toll and capacity optimisation in networks: solution algorithm and policy implications

  • Andrew Koh
  • Simon Shepherd
  • Agachai Sumalee


This paper looks at the first and second best jointly optimal toll and road capacity investment problems from both policy and technical oriented perspectives. On the technical side, the paper investigates the applicability of the constraint cutting algorithm for solving the second best problem under elastic demand which is formulated as a bilevel programming problem. The approach is shown to perform well despite several problems encountered by our previous work in Shepherd and Sumalee (Netw. Spat. Econ., 4(2): 161–179, 2004). The paper then applies the algorithm to a small sized network to investigate the policy implications of the first and second best cases. This policy analysis demonstrates that the joint first best structure is to invest in the most direct routes while reducing capacities elsewhere. Whilst unrealistic this acts as a useful benchmark. The results also show that certain second best policies can achieve a high proportion of the first best benefits while in general generating a revenue surplus. We also show that unless costs of capacity are known to be low then second best tolls will be affected and so should be analysed in conjunction with investments in the network.


Second best toll Optimal toll and capacity Bilevel optimization 



The research reported here was funded by the UK Engineering and Physical Science Research Council and the Hong Kong Research Grant Council (PolyU 5261/07E). The authors would also like to thank colleagues Tony May, David Watling and Richard Connors for their support during the course of this research. Also, the third author would like to specially thank Prof. Siriphong Lawphongpanich for his support and suggestion on the application of the CCA. We also sincerely thank the constructive comments from the anonymous three referees which helped improving the paper significantly.


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Copyright information

© Springer Science+Business Media, LLC. 2009

Authors and Affiliations

  1. 1.Institute for Transport StudiesUniversity of LeedsLeedsUK
  2. 2.Department of Civil and Structural EngineeringThe Hong Kong Polytechnic UniversityHung Hom, KowloonHong Kong

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