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Dantzig-Wolfe Reformulation for the Network Pricing Problem with Connected Toll Arcs

par Deleplanque, Samuel ;Fortz, Bernard ;Labbé, Martine ;Violin, Alessia
Publication Non publié, 2017-10-05

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Résumé :

This paper considers a pricing problem on a network with connected toll arcsand proposes a Dantzig-Wolfe reformulation for it. First, the relaxation ofthis formulation is theoretically shown to be at least as good as the referenceproposed in the literature. Then, we detail the particularities of the imple-mentation of a branch-and-price algorithm for solving it such as a primalheuristic, the branching rules, the stabilization process, and an algorithmfor fixing variables using Lagrangian duality. Finally, numerical results ontwo types of instances, real and pseudo-randomly generated, are reported,confirming numerically the main theoretical results.