## 2 Reverse Logistics Facility Location Model
### Problem Description
#### 2.1.2 Model Parameters  
* Logistics facility  
\(I\) is the collection of recycling points, in the model, which is all the cities participating in product recycling, \(i\in I\); \(P\) is the set of established detection classification points, \(p\in P\); \(P_{\text{min}}\) and \(P_{\text{max}}\) are respectively the lower limit and upper limit of the number of detection classification points; \(D\) is the set of established collection processing points, \(d\in D\); \(D_{\text{min}}\) and \(D_{\text{max}}\) are respectively the lower limit and upper limit of the number of collection processing points. \(s_{i}\) is the amount of recycling at the recycling point \(i\); \(S_{p}\) is the amount of storage at the detection classification point \(P\); \(S_{d}\) is the amount of disposal at the recycling disposal point \(d\). \(l_{ip}\) is the route distance between recycling point \(i\) and detection classification point \(p\); \(l_{pd}\) is the route distance between detection classification point \(p\) and recycling processing point \(d\); \(M_{p}\) and \(M_{d}\) are respectively the volume limits of the detection classification point and the recycling processing point. Meanwhile, it is assumed that there is no volume limit when the product seller acts as the recycling point. \(X_{ip}\) and \(X_{pd}\) are respectively the transportation volume of waste products from the recycling point \(i\) to the detection classification point \(p\) and the transportation volume of waste products from the detection classification point \(p\) to the recycling and treatment point \(d\). * Classification of waste products According to the availability of waste products, the products are divided into dismountable type \(c_{1}\), recyclable parts type \(c_{2}\), and recyclable parts type \(c_{3}\), and the proportion of the three types in the total amount of recycled products is \(l_{1}\), \(l_{2}\) and \(l_{3}\). \(R_{1}\) and \(R_{2}\) are respectively the weight ratio of usable materials of dismountable products and usable parts and components of recyclable products. \(r_{1}\) is the unit value of disassembled products after material extraction, and the unit is CNY/kg; \(r_{2}\) is the market value of disassembled parts of recyclable parts, and the unit is CNY/kg; \(r_{3}\) is the second-hand market value of products that can be renovated and sold for a second time, and the unit is CNY/unit. \(W\) is the average weight of the product. * Cost of recycling \(F_{i}\), \(F_{p}\) and \(F_{d}\) represent the initial construction costs of the recycling point, detection classification point and recycling treatment point, respectively, in which the construction cost of the recycling point is zero or ignored. \(y\) represents the transportation cost of waste products per unit distance per unit quantity, and the unit is CNY/kg\(\cdot\)km. In the process of recycling, \(N_{p}\) refers to the cost generated by the processing unit product at the detection classification point, and the unit is CNY/part. The recycling cost generated by the recycling point is determined by the type of recycling. The recycling cost for the disassembled product, the recyclable part and the product sold for the second time that can be repaired are respectively \(N_{1}\), \(N_{2}\) and \(N_{3}\). The recycling price of waste products is \(q\), and the unit is CNY/part.