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Network design problem with congestion effects: A case of bilevel programming

Abstract

Recently much attention has been focused on multilevel programming, a branch of mathematical programming that can be viewed either as a generalization of min-max problems or as a particular class of Stackelberg games with continuous variables. The network design problem with continuous decision variables representing link capacities can be cast into such a framework. We first give a formal description of the problem and then develop various suboptimal procedures to solve it. Worst-case behaviour results concerning the heuristics, as well as numerical results on a small network, are presented.

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Additional information

Research supported by SSHRC-Canada Grant #410-81-0722 and FCAC-Québec grant #83-AS-26.

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Marcotte, P. Network design problem with congestion effects: A case of bilevel programming. Mathematical Programming 34, 142–162 (1986). https://doi.org/10.1007/BF01580580

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Key words

  • Network Design
  • Bilevel Programming
  • Variational Inequalities
  • Stackelberg Games