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

Andrew Koh, Simon Shepherd, Agachai Sumalee

Research output: Journal article publicationJournal articleAcademic researchpeer-review

14 Citations (Scopus)


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. 2009.
Original languageEnglish
Pages (from-to)147-165
Number of pages19
Issue number2
Publication statusPublished - 13 Feb 2009


  • Bilevel optimization
  • Optimal toll and capacity
  • Second best toll

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Development
  • Transportation

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