# Integrated Simulation-Based Optimization of Operational Decisions at Container Terminals
## 1 Introduction  
Seaports are the interface between various transport modes in the maritime supply chain. In 2019, the volume of global maritime containerized trade had tripled to 152 million TEU (Twenty-foot Equivalent Unit, the size of a standard container) from its value in 1997 [1]. Moreover, ship sizes have also tripled in the past 20 years, from an 8000 TEU capacity to around 24,000 TEU. This implies that, in addition to adjustments to the port's infrastructure and superstructure, container terminals have to substantially increase their efficiency in ship handling in order to keep unproductive berthing times as short as possible while container volumes that are handled during one ship call increase. Thus, the challenge for terminals is to handle a large number of containers within a very short period of time. Terminals can address this challenge by creating technical prerequisites (i.e., using more and higher-performance equipment) and by optimizing operational processes. While the use of more equipment entails correspondingly more investment and higher running costs, intelligent control of operational processes leads to more efficient cargo handling without additional costs. Therefore, it is reasonable to minimize the amount of necessary equipment and to coordinate operational processes. Container handling requires a large number of process steps in the terminal. When a ship is berthed, Quay Cranes (QCs) unload the containers and set them onto waitingYard Trucks (YTs), which then transport them to the storage area. There, Rubber-Tired Gantry (RTGs) cranes lift the containers into the respective Yard Block (YB) for short-term storage until the container is picked up. The steps in the process of loading a ship run in the opposite direction. The processes are coupled because YTs are passive equipment and are not able to lift the containers themselves. As a result, waiting times and utilization of the respective equipment must be weighed against each other. In order to perform ship handling as quickly as possible and to reduce the waiting times of the QCs, it is preferable to use more YTs however, this leads to longer waiting times and lower utilization of YTs. Furthermore, using too many YTs leads to congestion and, therefore, to delays in ship handling [2]. The better the balance between these conflicting objectives, the more efficiently the terminal works. There are several decision problems in the design and operation of container terminals, which strongly influence the efficiency of container handling. Figure 1 shows an overview of typical decision problems at container terminals. Decisions regarding the design of the terminal layout (e.g., location and size of the YBs) or the equipment that must be used and how much of it to procure have a rather long-term influence (refer to [3] for a recent overview). From a short-term perspective, on the quayside, decisions include berth allocation, stowage planning, and QC assignment and scheduling (refer to [4] for an overview). In horizontal transport, the decision problems are dispatching or scheduling (assigning vehicles and transport orders) and routing. Dispatching (assigning RTGs and storage orders), YB assignment, and YB position assignment are the primary decision problems in the storage area. On the land side, there are also questions of order assignment and gate control. [PERSON] and [PERSON] [5] provide a recent overview of container terminal decision problems. These decision problems influence each other [6]. For example, berth allocation directly influences the YB assignment and vice versa. The distances between the ship at the berth and the assigned YBs should be as short as possible, and at the same time, sufficient YBs should be assigned to a berth or QC. RTGs in the yard can typically move 15 containers within one hour, while QCs have a productivity of around 30 moves/h. Thus, at least two YBs (each being served by at least one RTG) have to be connected to one QC.