Products can be transported in containers from one port to another. At a container terminal these containers are transshipped from one mode of transportation to another. Cranes remove containers from a ship and put them at a certain time (i.e., release time) into a buffer area with limited capacity. A vehicle lifts a container from the buffer area before the buffer area is full (i.e., in due time) and transports the container from the buffer area to the storage area. At the storage area the container is placed in another buffer area. The advantage of using these buffer areas is the resultant decoupling of the unloading and transportation processes. We study the case in which each container has a time window [release time, due time] in which the transportation should start. The objective is to minimize the vehicle fleet size such that the transportation of each container starts within its time window. No literature has been found studying this relevant problem. We have developed an integer linear programming model to solve the problem of determining vehicle requirements under time-window constraints. We use simulation to validate the estimates of the vehicle fleet size by the analytical model. We test the ability of the model under various conditions. From these numerical experiments we conclude that the results of the analytical model are close to the results of the simulation model. Furthermore, we conclude that the analytical model performs well in the context of a container terminal. © 2005 INFORMS.