Network design and flow problems with cross-arc costs

Network design and flow problems appear in a wide variety of transportation applications. We consider a new variation to this important class of problems, in which the cost associated with an arc depends not only on the amount of flow moving across that arc, but on the amount of flow on other arcs in the network as well. We formulate an integer program to address this problem, discuss a real-world application in which cross-arc costs are found, and conduct computational experiments on a broad class of problems to analyze how the model performs as network characteristics vary.