# The Environmental Impact of Inland Empty Container Movements Within Two-Depot Systems
## 4. ABM Formulation  
Traditional optimization approaches such as mixed-integer programming (MIP) and VRP have been widely used in maritime transportation to solve route planning, fleet deployment, and scheduling problems. They typically rely on centralized decision-making, fixed inputs, and deterministic rules, which may not adequately capture the complex, decentralized, and dynamic nature of real-world maritime logistics problems. In contrast, ABM provides a flexible and bottom-up approach that enables the modeling of heterogeneous agents such as shipping lines, ports, terminals, vehicles, and containers, with autonomous behaviours and localized decision-making processes [53].  
ABM is particularly well suited for scenarios where system-level patterns emerge from individual interactions, rather than being dictated by a central planner. Moreover, ABM allows for easy scenario testing under various operational and behavioral assumptions, supporting experimentation with adaptive strategies and policy interventions [54]. This is in contrast to optimization models, which often require reformulation and resolving when system parameters or objectives change.  
This methodological flexibility makes ABM not only a modeling tool but also an exploratory platform to understand the resilience and adaptability of container transportation systems under uncertainty. Therefore, the use of ABM in this paper is not simply a matter of preference but a deliberate choice to better reflect the real-world characteristics of empty container movements. ABM provides a complementary and, in many cases, more realistic alternative to traditional optimization approaches, especially in environments characterized  
Figure 1. Inland empty container flow in a two-depot service, adapted from [52].  
by high uncertainty, heterogeneity, and adaptive behavior [55]. Hence, it is a powerful tool for simulating and optimizing the movement of empty containers within two-depot systems. By modeling these agents and their behaviours, ABM can provide insights into waiting time, container availability, and CO2 emissions.  
In the model, CO2 emissions can be calculated with the CarbonCare CO2 calculator for each move of inland transportation, which estimates emissions based on road distance, truck type, and load factors. This calculator uses the European EN 16258 standard [44]. The calculations were based on the tare weight of an empty twenty-foot equivalent unit (TEU), which is approximately 2300 km [56], and the vehicle type is a 40-tonne truck. The total emissions are calculated by multiplying the number of vehicles by the distance travelled and the emission factor, using the following formula:  
\[\text{Emissions}=\sum\left(\text{Number of vehicles}\times\text{Distance}\times \text{Emission Factor}\right)\]  
JADE, NetLogo, AnyLogic, StarLogo, and RePast are the most frequently mentioned agent-based platforms for supply chain problems. These platforms can be used to track the actions of all supply chain participants throughout time, as well as the supply chain overall. They allow decision-makers to simulate multiple \"what-if\" scenarios involving container repositioning. They can simulate the effect of using different transport modes, optimizing container routes, or adjusting scheduling to reduce emissions. Furthermore, the NetLogo 6.2.2 simulation platform, which is designed to model complex systems using visual shapes and graphs, was chosen in this study. Agents are expressed in the form of turtles, patches, links, and the observer [57]. NetLogo simulates intricate social and ecological systems. Its user-friendly platform allows it to be applied to complex interactions between numerous stakeholders when it is difficult to characterize their patterns of behavior. Numerous scientific fields, including computer science, resource management, and decision-making, have used NetLogo programming.