# Optimal Deployment of Container Weighing Equipment: Models and Properties
## 5 Discussion  
In this paper, we introduce a container weighing optimization model and validate several propositions derived from this model. A case study conducted on ports along the Yangtze River, coupled with sensitivity analyses of the model, yields the following conclusions, along with practical guidelines for port managers to directly improve operations in the discussed areas.  
First, the model proves capable of addressing large-scale port container optimization challenges, offering practical solutions to real-world problems. Port managers can use this model to develop more effective container weighing strategies, thereby enhancing overall operational efficiency.  
Second, as the number of weighing machines increases, the strategy for container weighing transitions. When the number of machines is insufficient, only a subset of containers is weighed, but these are all weighed at their origin ports. In this scenario, port managers should prioritize weighing containers that have a significant impact on the total weight. When there are more weighing machines available, more containers can be weighed, but some of them are weighed at transshipment or destination ports. In this case, port managers should strategically allocate weighing locations to ensure that transshipment weighing spots are as close as possible to the destination ports. Ultimately, sufficient machine availability ensures that all of the containers can be weighed at their origin ports. In this context, port managers should focus on maintaining and scheduling weighing equipment to ensure that the weighing process remains efficient and stable.  
Third, ports can increase the capacity of each weighing machine, which allows for an increased number of containers to be weighed. When the capacity of the machine is increased, the objective function value increases in a fashion similar to that when the number of machines is increased. Specifically, the objective function value transitions from steady to decelerating before stabilizing. Port managers can increase weighing capacity through upgrading weighing technology, enhancing personnel training, and implementing intelligent management. By implementing these measures, port managers can effectively increase the capacity and accuracy of container weighing machines, thereby improving port operations and enhancing overall competitiveness.  
The mathematical model and methodology presented in this paper are not limited to the Yangtze River. The same methods can be applied to any other region by adjusting the relevant parameters in the model. For example, the importance of weighing containers in a certain place can be changed. This allows applying the model in practice across multiple scenarios.  
One direction for future research is to design a two-stage stochastic optimization problem with a stochastic demand for containers. Another direction involves determining the model's decisions with the actual historical demand data. Through this study, the model could be refined further, and the inefficiencies of the real maritime system could be diminished.  
Conceptualization, Z.Y., M.X., X.T. and S.W.; methodology, Z.Y., M.X., X.T., Y.J. and S.W.; software, Z.Y.; validation, Z.Y., X.T. and S.W.; formal analysis, Z.Y.; investigation, Z.Y.; resources, S.W.; data curation, S.W.; writing--original draft preparation, Z.Y., X.T. and S.W.; writing--review and editing, M.X., X.T. and S.W.; visualization, Z.Y.; supervision, M.X. and S.W.; project administration, Y.J.; funding acquisition, M.X. and Y.J. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. PolyU 15222822).  
Not applicable.  
The data presented in this study are available on request from the corresponding author. The data are not publicly available due to privacy.  
The authors declare no conflict of interest.