Optimization of Number of Operators and Allocation of New Lines in an Oligopolistic Transit Market

Zhi Chun Li, Hing Keung William Lam, S. C. Wong

Research output: Journal article publicationJournal articleAcademic researchpeer-review

18 Citations (Scopus)


This paper proposes a novel model for determining the optimal number of transit operators and the allocation of new lines in an oligopolistic transit market. The proposed model consists of three interrelated sub-models that are associated with three types of players; namely, transit authority, transit operators, and transit passengers. In practice, the operating cost per unit of transit line of each operator is decreasing in the number of lines that it operates. These effects which are referred to as the scale economies of transit operations are explicitly incorporated in the proposed model. On the basis of a logit-type transit passenger travel choice sub-model with elastic demand, the fares and frequencies of transit services are determined by an oligopolistic competitive equilibrium model (i. e. transit operator sub-model). The transit authority sub-model for optimization of the number of operators and the allocation of new lines is expressed as a 0-1 integer programming problem. It can be solved by an implicit enumeration heuristic solution algorithm. Numerical results show that both the scale economies and the market demand level have significant impacts on the optimal number of operators and the allocation schemes of new lines. Ignoring the effects of scale economies on transit operations may lead transit authorities to make biased decisions.
Original languageEnglish
Pages (from-to)1-20
Number of pages20
JournalNetworks and Spatial Economics
Issue number1
Publication statusPublished - 1 Mar 2012


  • Allocation of new lines
  • Implicit enumeration
  • Number of operators
  • Oligopolistic competition
  • Scale economies
  • Transit market

ASJC Scopus subject areas

  • Software
  • Computer Networks and Communications
  • Artificial Intelligence


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