## 3 Mathematical Model  
### Problem Description  
The hazardous waste recycling network within shipyards comprises a four-level network structure, encompassing production line edges, hazardous waste collection points, hazardous waste treatment centers, and hazardous waste temporary storage centers, as illustrated in Figure 4. Reverse materials, including hazardous waste and incompletely used production materials, are generated by the production line. The collection point, built in proximity to the production line, serves as a recycling facility with a specific storage capacity. The reverse materials produced by the production line are initially gathered at the collection point, resulting in a small-scale and multi-batch in-plant transportation. The reprocessing center is responsible for processing hazardous waste, including classification, redox, and compression, among other processes. The hazardous waste temporary storage center, on the other hand, is intended for storing hazardous waste during processing. Once hazardous waste materials have been treated, such as waste paint ash, waste paint sludge, and waste paint drums, they are placed in the hazardous waste temporary storage center. Once the upper limit of storage capacity is reached, a professional treatment company is invited to the plant to transport the hazardous waste to a specific environmentally friendly treatment enterprise for further processing.  
In the conventional recycling process, each production department employs its own departmental vehicles to transport hazardous waste from the collection point to the treatment point. However, such multiple round-trip transport poses a greater risk of exposure, increases the burden on the plant's green management, scheduling of carrier tools, and places more pressure on the treatment center to carry out multiple reception processes, among other issues. Overall, this approach fails to facilitate cost savings, green transport, and safe HSE management. Consequently, we propose to manage the recycling and transport of hazardous waste through centralized vehicle scheduling. Adhering to the principles of economic efficiency, ecological coordination, health, and safety, our vehicle scheduling model for hazardous waste materials in the plant seeks to identify the most cost-efficient, safety-conscious, and environmentally friendly recycling path. The main factors considered in the model include the following:  
Figure 4: Diagrammatic map of hazardous waste reverse logistics network.  
Effective cost management is crucial in the reverse flow of hazardous waste, as it not only impacts financial expenditures but also directly influences the overall efficiency and sustainability of hazardous waste management practices. Centralized vehicle scheduling solutions can lead to significant reductions in transportation costs by minimizing redundant routes and optimizing transport pathways. This centralized approach not only decreases the necessity for multiple round trips, but also effectively lowers the vehicle empty rate, thereby enhancing the efficient use of resources.  
For this purpose, selecting the most appropriate hazardous waste transport vehicle is essential for balancing operating costs with safety and environmental considerations. Different types of transport vehicles exhibit significant variations in load capacity, fuel efficiency, and maintenance expenses. By strategically deploying and selecting suitable vehicles, organizations can reduce unit transport costs while ensuring compliance with safety regulations and environmental standards during transit.