Discrete intermodal freight transportation network design with route choice behavior of intermodal operators

We consider a discrete intermodal network design problem for freight transportation, in which the network planner needs to determine whether or not to build up or expand a link to minimize the total operating cost of carriers and hub operators under a general route choice model of intermodal operators. We formulate the problem as a mixed-integer nonlinear and non-convex program that involves congestion effects, piecewise linear cost functions, and a fixed-point constraint. We develop a series of relaxed and equivalent models to reduce the hardness of the problem and provide theoretical results to show the equivalences. We present two solution methods to solve the problem with one returning heuristic solutions and the other generating a globally optimal solution. We offer two numerical experiments to test the two solution algorithms and also shed light on their performance comparisons.