| The Stackelberg game between shippers and carriers in an intermodal network is formulated as a bi-level program. In this network, shippers make production, consumption, and routing decisions while carriers make pricing and routing decisions. The oligopolistic carrier pricing and routing problem, which comprises the upper level of the bi-level program, is formulated either as a nonlinear constrained optimization problem or as a variational inequality problem, depending on whether the oligopolistic carriers choose to collude or compete with each other in their pricing decision. The shippers' decision behavior is defined by the spatial price equilibrium principle. For the spatial price equilibrium problem, which is the lower level of the bi-level program, a variational inequality formulation is used to account for the asymmetric interactions between flows of different commodity types. A sensitivity analysis-based heuristic algorithm is proposed to solve the program. An example application of the bi-level programming approach analyzes the behavior of two marine terminal operators. The terminal operators are considered to be under the same Port Authority. The bi-level programming approach is then used to evaluate the Port Authority's alternative investment strategies. |
