Shippers produce goods and deliver them to customer locations using the transportation services
provided the carriers. They coordinate freight movements to explore the potential economic benefit from
the price differences between different regions. Shippers decide a sequence of carriers based upon the
carriers' pricing and routing decisions. Therefore, hierarchical interactions also occur between shippers
and carriers. This paper presents a bi-level modeling approach to capture the carrier-shipper relationships,
focusing on the shippers' behavior. Spatial price equilibrium (SPE) is used to find the optimal production,
shipment and consumption pattern of shippers in a global maritime shipping setting.
Several shipper models have been formulated applying the concept of SPE over the past decades.
Through the early 1980s, most of the models haven't considered the carriers' behavior, defining arc and
node transportation cost functions. Research efforts to include carriers' decisions in the shipper problem
have emerged to analyze the simultaneous shipper-carrier interactions, via generalized SPE models that
capture the profit maximization behavior of carriers explicitly. Limited research work has focused on
sequential interactions between shippers and carriers considering carriers as the leading players in an
international trade network model. Existing literature, however, does not differentiate among different
types of carriers and their interactions, which is the issue addressed in this paper.
The structure of the paper is as follows. The next section presents an up-to-date literature review of
shipper and shipper-carrier models. The third section defines the general maritime freight transportation
network structures. The fourth section proposes modeling approaches for the shipper problem, carrier
problem and shipper-carrier problem, and makes solution algorithm recommendations. The next section
presents a numerical example, demonstrating the applicability of the model. The last section summarizes
and concludes the paper.