Linear programming and network flows (2nd ed.)
Linear programming and network flows (2nd ed.)
Negative-Cycle Detection Algorithms
ESA '96 Proceedings of the Fourth Annual European Symposium on Algorithms
A heuristic method for the minimum toll booth problem
Journal of Global Optimization
Benders Decomposition for the Hop-Constrained Survivable Network Design Problem
INFORMS Journal on Computing
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We address a toll pricing problem in which the objective is to minimize the number of required toll facilities in a transportation network while inducing drivers to make the most efficient collective use of the network. We formulate the problem as a mixed-integer programming model and propose a solution method using combinatorial Benders cuts. Computational study of real networks as well as randomly generated networks indicates that our proposed method is efficient in obtaining provably optimal solutions for networks with small to medium sizes.