# Integrated Simulation-Based Optimization of Operational Decisions at Container Terminals
## 1 Introduction
### Literature Review on Integrated Decision Problems  
There are two main approaches to addressing the operational decision problems of container terminals [8]. The first approach takes into account the complex dynamic environment of a container terminal. It typically uses priority rules, which are analyzed with the help of simulation models that can represent stochastic processes. Simulation models involving container terminals are reviewed in [9; 10]. In the second approach, a simplified deterministic mathematical model is formulated. Either the model can be solved optimally for small instances, or an approximation can be found with the help of heuristics. While the first approach is better suited to volatile processes at container terminals, simulation studies that aim to investigate several decision problems quickly become very complex [11]. The second approach also quickly reaches its limits. In this context, [PERSON] et al. [12] showed that the integrated QC and YT scheduling problem is non-deterministic polynomial-time hard, which means that the computing time required to optimally solve the problem is too long to be used in practice. To take advantage of both approaches, especially in order to investigate integrated decision problems that influence each other, the approach of combining simulation and optimization has been developed in recent years. [PERSON] et al. [13] addressed integrated QC, YT, and RTG scheduling. They developed a mixed-integer programming model and proposed a simulation-based optimization method. Their optimization algorithm integrates genetic and particle swarm optimization algorithms. [PERSON] et al. [14] aimed to schedule RTGs and YTs simultaneously in order to decrease the ship turnaround time. They introduced a multi-layer genetic algorithm to solve the scheduling problem and designed an algorithm-accelerating strategy. [PERSON] et al. [15] focused on the QC scheduling problem: They integrated artificial intelligence techniques and simulation, combining an evolutionary algorithm with a simulation model to embed uncertainty. [PERSON] et al. [16] studied the integrated problem of QC assignment and scheduling, YB assignment, and YT dispatching. They proposed a mixed-integer programming and constraint programming model and showed that the constraint programming model performed much better in terms of calculating time. Integrated quayside problems can also be investigated with other aims, such as saving costs and energy simultaneously [17] or exploring different modes of integration [18]. [PERSON] et al. [19] combined discrete event simulation, data envelopment analysis, and cost-efficiency analysis to investigate different investment alternatives based on the number of QCs, total length of a quay, YTs, and RTGs. They applied their model to 16 different scenarios but did not modify the operating policies. Furthermore, other research has combined different simulation paradigms to solve optimization problems at different decision levels. For example, in [20], a system-dynamic model was used to optimize the main parameters of a dry port, and in [21], a combination of system-dynamic and discrete-event simulation models was used. [PERSON] et al. [22] provide a literature overview of simulation-based optimization at container terminals. They focused on the covered problems, chosen meta-heuristics, and the shapes of the parameter configuration space in the respective publications. Similarly, [PERSON] et al. [23] present a summary of publications on the integration of simulation and optimization for maritime logistics. They classified five modes of integration according to the interaction of the two techniques. [PERSON] et al. [24] proposed applying the Tree-structured Parzen Estimation (TPE) approach to scale the amount of utilized equipment in a simulation model. With the help of simulation-based optimization, only a subset of the experiments was executed. At the same time, a fine search grid (all equipment was scaled in step sizes of 1) enabled a very good approximation of the unknown optimum.