4. Modeling Approach
4.1. Carrier problem
Ocean carriers, port terminal operators and land carriers determine service charges and delivery routes
(port services) in the ocean transportation network, port sub-network and land transportation network,
respectively. There exist hierarchical relationships between ocean carriers and port terminal operators and
between port terminal operators and land carriers, respectively, as these were described earlier. A three-
level hierarchical modeling approach, capturing interactions among the three types of carriers has been
developed (Lee, et al., 2011). The Nash equilibrium principle has been used to formulate the carrier
problem, for each type of carrier at each level of the model. Based on this principle, the optimal service
charge and routing pattern for which each carrier obtains the greatest profit in a competitive environment
is determined. A multi-leader-follower game approach has also been used in the multi-level problem, as
multiple and competing leaders are considered within the carriers' groups. A schematic representation of
the three-level carrier interaction model is shown in Fig. 3.
Fig. 3. Carrier Interactions