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The ever increasing number of containers to be transported necessitates expanding the capacity of container terminals. This can be achieved either by enlarging the container terminals physically or by managing the container terminals better. Since the first alternative is costly, and sometimes not possible due to limited land, container terminal managers focus on the second alternative. One possible way to increase the capacity of a container terminal is to reduce the vessel handling times. By that way, containers will spend little or no time at the yard storage phase, which will directly enhance the capability of container terminals to compete with each other. This setting is applicable to large transhipment hubs where many vessels can be moored and processed at the same time and discharged containers can directly go to their outbound vessels. Since the yard is a critical resource for the container terminal management, this environment will result in less cost and better utilization of the yard space. In this study, we consider a transshipment container terminal where all containers must be loaded to their outbound vessels directly after being unloaded from their incoming vessels. Our aim is to determine a schedule of unloading and loading times of containers while minimizing the makespan, which is the total completion time of all operations. This problem has not been studied before. The most related work deals with a case where there are two vessels and three types of containers, which are loaded, unloaded and directly transshipped ones. In our study, we consider just the transshipment containers but the number of vessels is not restricted to two. We develop a mathematical model to represent the system and analyse its performance through computational studies. We create instances from different sizes to understand the limits of the mathematical model. After identifying these limits for the model, we study possible solution methodologies.