How will demand fluctuations, fleet composition, and bunker prices affect deep sea call sizes in Rotterdam?

For a container terminal operator it is of great importance to examine the call size development, since potentially larger call sizes caused by the use of ultra large container vessels (ULCS) put increasing pressure on terminals. Next to that, we expect the use of ULCSs to influence vessel routing and the number of port calls, which in turn indirectly affects the terminal. In order to determine the call size in Rotterdam, we come up with a mixed integer programming formulation which determines the container flow on the network and ship type that minimises total cost, given the demand volumes to the destinations, available fleet, and some routing scenario. The proposed model is able to solve the problem for each scenario within a negligible amount of running time for our problem instance. We observe that fluctuations in bunker prices do not affect routing choices and therefore the call size in Rotterdam at all, while using an ULCS or increasing demand such that an ULCS is needed, affect the routing choice and call size in Rotterdam in case Hamburg is called in the routing without a double call. When Hamburg is not used in the rotation, or a double call in Rotterdam is used, a large demand volume or the use of an ULCS do not affect routing choices or the call size in Rotterdam. We also observe that calling many ports in one rotation is not beneficial in terms of total costs. While executing this research, we discovered that fixed costs such as port call cost, ship operating cost, and fuel cost have a small influence on total costs, and are not likely to affect routing choices and therefore call sizes for our problem instance. On the contrary, costs incurred per TEU such as rail cost, terminal handling cost, and transshipment cost have a significant effect on routing choice. These insights in cost structure are very meaningful for a container terminal operator and can be used to improve its competitive position.