# Optimal Deployment of Container Weighing Equipment: Models and Properties
## 1 Introduction  
Over the past five decades, technological advancements in container manufacturing and regulatory improvements have significantly enhanced the container shipping industry, establishing it as a crucial player in international freight transport [1]. Figure 1 depicts a bustling container port scene, highlighting the crucial role of container transportation within the global supply chain. Its prominence stems from cost-effectiveness, price stability, and improved safety. However, the maritime industry faces significant challenges, such as the risk of pandemic [2], the threat of piracy, global trade uncertainty, and the common practice among shippers of overloading containers to cut logistics costs. This tendency of carrying overweight containers not only compromises the structural integrity and safety during loading and stowage on vessels, but also poses severe risks. Improper stowage--such as placing a large number of heavy containers on one side of the vessel and lighter ones on the other--can cause an increased list, alter the vessel's metacentric height, and reduce stability, frequently leading to accidents.  
At the same time, we need to realize that marine chokepoints are important to the international trade and the global economic security [3]. If an accident occurs on a ship due to overweight containers and results in the closure of a maritime chokepoint, there will be a significant impact on the international trade and the global economy. The adverse effects of overweight containers, coupled with the challenges in verifying accurate cargo weights, have escalated concerns about maritime safety, highlighting the urgent need for precise container weighing methods.  
Moreover, transportation modes are now more interactive and collaborative than ever before [4], and the integration of container shipping with other modes of transport, known as intermodal transportation, has become increasingly vital for efficient global logistics [5].  
Ensuring accurate container weights is essential not only for maritime safety but also for the seamless transfer of containers between ships, trucks, and trains, thereby enhancing the overall efficiency and reliability of the intermodal transport system.  
Accurate weighing of containers significantly enhances the safety and stability of the shipping system. The earlier a container is weighed, the greater its contribution to the overall safety of the maritime system. Ideally, all of the containers should be weighed at their ports of origin. However, due to constraints such as the limited number and capacity of weighing machines, practical implementation necessitates optimization. This involves making strategic decisions about the number of weighing machines that each port should have and determining the optimal locations for weighing containers. The primary objective is to maximize the contribution of weighing containers to the safety of the maritime system, which we quantify in terms of \"benefits.\" When containers are weighed at their origin ports, the benefits are maximized. Conversely, weighing containers at the destination ports results in the lowest benefits, leading to increased transportation risks due to the lack of weight measurements before the travel.  
Despite the benefits, strategic planning for container weighing is under-researched. Based on the evidenced efficiency of advanced analytics in improving the efficiency and safety of transportation systems [6], this paper addresses the gap in container weighing by proposing an optimization model. This model aims to maximize the safety benefits of container weighing for the maritime system.  
To address this gap, this paper proposes a container weighing scheme within the shipping system that aims to maximize the safety benefits of container weighing for the maritime system.