# Optimal Model for Carsharing Station Location Based on Multi-Factor Constraints
## 4 Case Study
### Parameter Calibration  
Lanzhou is a strip-shaped city. This research selects a rectangular research area of 30 km \(\times\) 12 km in Lanzhou and divides the research area into small areas of 2 km \(\times\) 1 km. A total of 15 \(\times\) 12 area is obtained. The specific division is shown in Figure 4.  
Figure 3: Spatial layout of the study area. The demand for electric carsharing \(D\) is obtained according to the survey done by the carsharing company. Seven types of land use, namely, transportation hubs, ordinary interchange point, business districts, college campuses, jobs, residential areas, and tourist attractions, have significant effects on the demand for electric carsharing. Using Equation (2), the final carsharing demand matrix is obtained. We divide the area by a grid of 12 rows and 15 columns and set the fixed station placement plan \(B\) as a matrix of 12 rows and 15 columns. \(K\) is the free station placement plan. In this research, the location of the free station is preset. Therefore, the capacity of the free station needs to be optimized. \[K=\left[ \begin{array}{cccccccccccccccc}0&0&0&0&0&0&0&0&0&0&0&0&0&0\\ 0&0&0&0&0&0&0&0&0&0&0&0&0&0\\ 0&0&0&k_{2,4}&0&0&0&0&0&0&0&0&0&0\\ k_{3,0}&k_{3,1}&0&0&0&0&0&0&0&0&0&0&0&0\\ k_{4,0}&k_{4,1}&k_{4,2}&0&0&0&0&0&0&0&0&0&0&0\\ 0&0&0&0&0&0&0&0&0&0&0&0&0&0\\ 0&0&0&0&0&0&0&0&0&0&0&0&0&0\\ 0&0&0&0&0&0&k_{7,7}&0&k_{7,9}&0&0&0&0&0\\ 0&0&0&0&0&0&0&k_{8,8}&k_{8,9}&k_{8,10}&0&k_{8,12}&0&0\\ 0&0&0&0&0&0&0&k_{9,8}&k_{9,9}&0&k_{9,11}&0&k_{9,13}&k_{9,14}\\ 0&0&0&0&0&0&0&0&k_{10,9}&k_{10,10}&k_{10,11}&k_{10,12}&0&0\\ 0&0&0&0&0&0&0&0&0&0&0&0&k_{11,12}&0&0\end{array} \right]\]  
The service capacity \(R_{uv}\) and demand \(P_{uv}\) of a single car rental station are generally closely related to the location and capacity of the electric carsharing at the station. It is given by the electric carsharing company based on its own investment level and development strategy. Service intensity usually decreases as the distance to the center of the carsharing station increases. Thus, this research divides the district into core, secondary, and marginal districts. Then, the service matrix of each station can be constructed. This study supposes that a single station has same service capabilities \(A\). Figure 4: Diagram of area division. \(V\) is the average monthly rent matrix per square meter in each small grid. \[V=\left[ \begin{array}{cccccccccccccccc}2&3&1&2&2&2&2&2&4&3&3&3&3&2&2\\ 2&2&3&7&5&5&5&2&8&3&4&5&7&4&2\\ 15&10&8&7&5&5&5&2&8&3&4&5&7&4&2\\ 25&26&15&13&8&6&14&12&11&11&8&8&5&10\\ 24&24&18&12&12&10&10&10&10&7&14&12&11&10&8\\ 11&12&10&10&10&10&8&7&7&4&5&7&10&10\\ 4&4&3&6&5&5&8&8&8&9&16&7&7&9&9\\ 4&4&3&6&5&9&10&10&10&30&20&20&15&15&15\\ 8&5&5&8&6&9&10&10&10&30&30&20&20&20&20\\ 2&3&3&5&8&8&8&10&25&25&30&20&19&17\\ 3&2&2&3&4&4&6&8&8&15&20&24&20&15&15\\ 2&2&3&3&3&3&5&7&5&3&8&10&25&20&10\\ \end{array} \right]\]  
\(J\) is the parking price per hour in the free parking area. \[J=\left[ \begin{array}{cccccccccccccccc}0&0&0&0&0&0&0&0&0&0&0&0&0&0&0\\ 0&0&0&0&0&0&0&0&0&0&0&0&0&0&0\\ 0&0&0&0&6&0&0&0&0&0&0&0&0&0\\ 8&8&0&0&0&0&0&0&0&0&0&0&0&0\\ 3&7&3&0&0&0&0&0&0&0&0&0&0&0&0\\ 0&0&0&0&0&0&0&0&0&0&0&0&0&0\\ 0&0&0&0&0&0&0&0&0&0&0&0&0&0\\ 0&0&0&0&0&0&0&3&0&7&0&0&0&0&0\\ 0&0&0&0&0&0&0&3&8&6&0&6&0&0\\ 0&0&0&0&0&0&0&0&3&3&0&5&0&6&6\\ 0&0&0&0&0&0&0&0&0&2&3&5&2&0&0\\ 0&0&0&0&0&0&0&0&0&0&0&5&0&0\\ \end{array} \right]\]  
The company intends to invest \(W=50\) million in these costs. The cost of buying each car is \(b=100\),000 yuan. The construction cost of each charger is \(e\)= 2000 yuan. The average parking time for each car in the free parking area is \(t=1440\) h a year. The corresponding coefficient \(\mu=20\) of the area of the stations and the size of the stations. The corresponding coefficient \(\lambda=0.5\) between the scale of the stations and the required number of chargers. The maximum number of cars dropped at each station is 100. We design a genetic optimization algorithm to solve the model.