## 2 The Theoretical Background
### The Physical Internet (PI) Paradigm  
This subsection delves into the concept of the Physical Internet, aiming to establish a digitally standardised and sustainable approach to supply chain management. The Physical Internet (PI) promises a paradigm shift in global logistics, inspired by the Digital Internet's ideas, to build an open and interconnected system [8]. Implementing \begin{table}
\begin{tabular}{l l c c c l} \hline \hline
**Authors** & **Type of Hub** & \multicolumn{3}{c}{**Key Performance Indicators (KPI)**} & \multicolumn{1}{l}{**Method/Tool**} \\ \cline{3-6}  & & **Environmental** & **Performance** & **Social** & \\ \hline [PERSON] et al., 2017 [4] & Maritime transport & — & ✓ & — & Heuristic method/Tabu Search \\ [PERSON] and [PERSON], & & Intermodal & — & ✓ & — & Heuristic method \\
2013 [7] & transportation & — & ✓ & — & Agent-based modelling \\ [PERSON] and [PERSON], & & Intermodal & ✓ & ✓ & ✓ & Agent-based modelling \\
2015 [9] & transportation & ✓ & ✓ & — & Agent-based and discrete-event \\ [PERSON] et al., 2023 [3] & transportation & ✓ & ✓ & — & modelling \\ [PERSON] et al., 2008 [13] & Maritime ports & — & ✓ & — & Integer programming/CPLEX \\ [PERSON] et al., 2007 [23] & Maritime ports & — & ✓ & — & optimisation \\ [PERSON], 2012 [24] & Intermodal & — & ✓ & — & Integer programming/heuristic \\  & transportation & & & & rule-based method \\ [PERSON] et al., 2024 [1] & Intermodal & — & ✓ & — & Mathematical model \\ [PERSON], 2013 [18] & Maritime ports & — & ✓ & — & Mathematical model/heuristic \\ [PERSON] et al., 2024 [5] & Multi-modal transport & — & ✓ & — & Integer programming model \\ \hline \hline \end{tabular} Note: The checkmark (✓) indicates that the authors validate the corresponding KPI. A dash (—) indicates that the KPI is not addressed in the respective study.  
\end{table} 
Table 1: Approaches to empty container (EC) management. global standardisation, modularity, and interoperability is its main objective in order to remove the inefficiencies present in current logistics networks [25]. Through a worldwide interconnected logistics network, these principles facilitate the smooth movement of commodities across many means of transportation, including air, sea, train, and road. The fundamental principle of the PI od universal interconnection guarantees that, independent of ownership or location, logistics hubs, vehicles, and storage facilities function as a single, cohesive system [25]. The PI has revolutionised logistics and supply chain management by emphasising digital interoperability as the key to sustainability and efficiency. It challenges current digital solutions with its unique requirements, uncovering new research opportunities and gaps [26]. In a recent study by [PERSON] et al. [27], the authors explored the transformation of cross-docking practices towards PI-cross-dock solutions, delineating their unique features and optimisation challenges. Their study underscores the importance of addressing these challenges across strategic, tactical, and operational decision levels while also evaluating the sustainability of PI-cross-dock solutions through mathematical models. Additionally, their study emphasises the need to consider the human and social dimensions in future research on these highly automated platforms. Digital interoperability plays an important role in logistics and supply chain management, particularly in the context of the PI paradigm. Innovative avenues such as cooperative networks, autonomous systems, digital twins, and smart infrastructures can address these challenges of sustainability in logistics and SCM [26]. Recent studies have highlighted using diverse methodologies to address inefficiencies in the PI paradigm. The diverse approaches and methodologies employed in addressing logistical inefficiencies within the PI paradigm are summarised in Table 2, highlighting key studies, their focus areas, and the tools or models utilised to optimise logistics operations. For instance, [PERSON] et al.