## 3 LRPTW Model
Equation (4) represents the cost of building a new warehouse during the distribution process, obtained by multiplying the number of new warehouses selected and the cost of building each new warehouse. Equation (5) represents part of the cost incurred along with mileage and fuel consumption during transportation, also known as the variable cost per vehicle kilometer, obtained by multiplying the mileage of the delivery vehicle and the transportation cost per kilometer of distance. Equation (6) represents fixed costs that do not depend on the distance traveled by the vehicle or the quantity of goods transported, including administrative expenses, repair and maintenance expenses, road maintenance fees, bridge fees, and other miscellaneous expenses. This part of the cost is only related to the number of vehicles. Equation (7) represents the carbon emissions caused by refrigeration during the vehicle's travel time, which is only related to the vehicle's travel time. Equation (8) represents the carbon emissions caused by fuel consumption related to the distance traveled by the vehicle, which is only related to the distance traveled by the vehicle. Equation (9) represents the loss caused by the distance traveled by the vehicle, where the loss is related to the vehicle load and loss coefficient. Equations (10) and (11) represent decisions made through 0-1 variables. Equation (12) indicates that all vehicles depart from the distribution center and return to it after completing all distribution tasks. Equation (13) indicates that the number of incoming and outgoing vehicles at each receiving point is equal. Equations (14) and (15) indicate that the load of each vehicle cannot exceed its maximum load limit. Equation (16) indicates that each receiving point only allows one delivery vehicle to serve it and visit it once. Equation (17) indicates that the maximum load of the vehicle must meet the demand at any receiving point. Equation (18) indicates that after completing a delivery task, the delivery vehicle must proceed to the next delivery point. Equation (19) represents time window constraints that must be satisfied for all receiving points. Equation (20) indicates that the time window constraints for all distribution centers must be satisfied. Equation (21) indicates that the driving distance of each vehicle cannot exceed its maximum driving distance. In summary, the multi-objective LRPTW model integrates equations designed to minimize distribution costs, carbon dioxide emissions, and product losses while complying with a variety of constraints. These equations account for factors such as the construction of new warehouses, variable transportation costs, fixed expenses, emissions from refrigeration and fuel consumption, and losses incurred during transit. Additionally, the model considers decision variables, vehicle departure and arrival conditions, load limits, and time window constraints to optimize distribution efficiency. The LRPTW model addresses three interrelated subproblems: coordinating objectives, optimizing vehicle routes, and ensuring adherence to constraints. The optimization of vehicle routes is crucial, as it directly affects the satisfaction of constraints and determines the viability of the routes. To address these subproblems effectively, a collaborative approach is essential, incorporating their characteristics into the MODRL-SIA framework to produce high-quality solutions. By collectively considering these subproblems and leveraging the MODRL-SIA framework, the model efficiently generates optimal solutions that balance cost, environmental sustainability, and operational efficiency in distribution logistics.