Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  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.  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.
['Bernard Fortz', 'Luis Gouveia', 'Martim Joyce-Moniz']
I am writing a research paper on a idea On the convex piecewise linear unsplittable multicommodity flow problem
[{"from": "human", "value": "I am writing a research paper on a idea On the convex piecewise linear unsplittable multicommodity flow problem"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  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.  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."}]