## 2 The Theoretical Background
### The Empty Container (EC) Problem  
Currently, container logistics are one of the most essential methods for transporting commodities globally. According to [PERSON] and [PERSON] [10], container operations have a significant global impact but face a fundamental imbalance due to uneven global trade flows. An example of this imbalance is the logistics challenge where containers often travel without cargo [3; 5; 6]. ECs are frequently the outcome of trade flow imbalances, in which products are transferred in one direction but containers must return empty. These mismatches occur more frequently on international routes and in industries with substantial export and import volumes.  
Transporting ECs is not only a logistical challenge but also poses significant economic implications. Transport operators incur additional costs related to fuel, maintenance, and tolls without generating additional revenue when moving an EC. These inefficiencies are compounded by the fragmented nature of supply chains, in which a lack of coordination between actors prevents more efficient solutions to reduce empty runs.  
In addition, low truck capacity utilisation directly affects the operational efficiency of trucking companies, which increases their total operating costs [11; 12].  
Various approaches, such as heuristic methods, cost reduction, and container distribution optimisation, have been explored. For instance, [PERSON] et al. [4] proposed a heuristic model using Tabu Search to address imbalances in maritime transport networks. This study showed that this approach significantly reduced the costs associated with the return of ECs, more effectively meeting customer demands.  
Similarly, [PERSON] et al. [13] explored a solution for EC interchange at the Port of Los Angeles/Long Beach using an integer programming model in CPLEX. This study concluded that substitution between different container types could further reduce operating costs.  
Additionally, [PERSON] et al. [7] approached the problem from a truck scheduling perspective in intermodal transportation, proposing a two-stage heuristic method to minimise the total truck operation time. Their computational experiments showed that this approach outperformed the other methods in terms of its computational efficiency, suggesting that it was a viable solution for reducing the operation times in complex logistics networks.  
The unnecessary transport of ECs not only affects companies financially but also has a considerable environmental impact. Each kilometre travelled with an EC generates greenhouse gas emissions, increasing the logistics sector's carbon footprint. Road transport is one of the largest contributors to CO\({}_{2}\) emissions, accounting for almost 25% of global energy-related emissions [14]. A recent study by [PERSON] et al. [15] showed that using the PI-containers at a water-road hub reduces CO\({}_{2}\) emissions by 27% and improves the efficiency, highlighting the PI's potential within sustainable supply chains. A study by [PERSON] et al. [3] investigated the environmental and economic implications of EC repositioning strategies in an intermodal context. Their results revealed that EC repositioning strategies could reduce emissions by 32% and costs by more than 50% compared to the baseline scenario, demonstrating the potential of these strategies to improve eco-efficiency.