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On the convex piecewise linear unsplittable multicommodity flow problem

Bernard Fortz 1, 2 Luis Gouveia 3 Martim Joyce-Moniz 4 
1 INOCS - Integrated Optimization with Complex Structure
Inria Lille - Nord Europe, ULB - Université libre de Bruxelles, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
Abstract : We consider the problem of finding the cheapest routing for a set of commodities over a directed graph, such that: i) each commodity flows through a single path, ii) the routing cost of each arc is given by a convex piecewise linear function of the load (i.e. the total flow) traversing it. We propose a new mixed-integer programming formulation for this problem. This formulation gives a complete description of the associated polyhedron for the single commodity case, and produces very tight linear programming bounds for the multi-commodity case.
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Submitted on : Tuesday, December 6, 2016 - 5:03:00 PM
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Bernard Fortz, Luis Gouveia, Martim Joyce-Moniz. On the convex piecewise linear unsplittable multicommodity flow problem. 2016 12th International Conference on the Design of Reliable Communication Networks (DRCN), Mar 2016, Paris, France. pp.9--13, ⟨10.1109/DRCN.2016.7470829⟩. ⟨hal-01410555⟩



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