Application of Benders decomposition method in solution of a fixed-charge multicommodity network design problem avoiding congestion

By Ashkan Fakhri, Mehdi Ghatee

Published: Applied Mathematical Modelling, Volume 40, Issues 13–14, July 2016, Pages 6468-6476.

Abstract:

In this paper, a new variable partitioning strategy in Benders decomposition method is applied that enables us to deal with a wide class of mixed-integer nonlinear programming problems including fixed-charge multicommodity network design (FMND) problems under congestion effects. It is proved that the proposed technique for an FMND problem leads to a simple branch-and-bound algorithm such that each node of the branching tree includes a single conic quadratic representable problem consisting of only continuous (flow) variables. Preliminary numerical results are reported.

Highlights

  • Using a new variable partitioning strategy in Benders decomposition method.
  • Solving a wide class of mixed-integer nonlinear programming problems.
  • Combining algorithm with Benders decomposition.
  • Solving a single conic quadratic representable problem in each step of algorithm.
  • Getting the results on the fixed-charge multicommodity network design problems.

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