The extended gate problem: Intermodal hub location with multiple actors

Hinterland transportation has become increasingly critical for global container supply chain performance. However, the literature on the management of the container supply chain tends to overlook the issues related to hinterland transportation. The problem we consider here is faced by a deep-sea terminal operator who wants to open an inland terminal to facilitate its operations. When developed by a deep-sea terminal operator, such an inland terminal directly related to a deep-sea port is called an extended gate. In this setting, the shippers can decide to take their containers either directly at the deep-sea terminal or at the inland terminal. In this latter case, train transportation is used from the deep-sea terminal to the inland terminal. Intermodal hub location problems are usually solved by considering a single decision maker even though several actors often interact in practice. We analyze here the impact of having multiple actors involved by proposing a formulation of the problem based on game theory. We develop structural properties of the shippers’ behavior. These properties enable us to identify the existing equilibria for the game and to solve the problem optimally. We apply the results to an example based on the features of the hinterland network in the Netherlands and we provide related insights. We show that the multiple actors feature of intermodal hinterland networks is critical and needs to be accounted for. Our results serve as a basis for appropriately taking multiple actors into account in hub location problems.