Solving a mixed integer linear program approximation of the toll design problem using constraint generation within a branch-and-cut algorithm

Joakim Ekström, Clas Rydergren, Agachai Sumalee

Research output: Journal article publicationJournal articleAcademic researchpeer-review

9 Citations (Scopus)


This paper addresses the global optimality of the toll design problem (TDP) by formulating a mixed integer linear program (MILP) approximation. In the TDP, the objective is to maximise the social surplus by adjusting toll locations and levels in a road traffic network. The resulting optimisation problem can be formulated as a mathematical program with equilibrium constraints. An MILP is obtained by piecewise linear approximation of the nonlinear functions in the TDP, and we present a domain reduction scheme to reduce the error introduced by these approximations. Previous approaches for solving the MILP approximation have been relying on a large number of MILPs to be solved iteratively within a cutting constraint algorithm (CCA). This paper instead focuses on the development of a solution algorithm for solving the MILP approximation in which the CCA is integrated within a branch-and-cut algorithm, which only requires one MILP to be solved.
Original languageEnglish
Pages (from-to)791-819
Number of pages29
JournalTransportmetrica A: Transport Science
Issue number9
Publication statusPublished - 1 Jan 2014


  • bilevel optimisation
  • global optimisation
  • road pricing
  • toll design

ASJC Scopus subject areas

  • Transportation
  • Engineering(all)

Cite this