# An Analysis of Food Accessibility of Mountain Cities in China: A Case Study of Chongqing
## 4 Methodology
### Calculation of the Food Accessibility Indicator
#### 4.1.2 E2 SFCA for Calculating Food Accessibility  
The two-step mobile search method (2 SFCA model) considers both supply and demand factors, allowing for comprehensive and easy calculation of food store accessibility. E2 SFCA-based food accessibility assessment is influenced by a combination of three factors: food stores, community population, and road network. The E2 SFCA model avoids the potential dichotomy problem of 2 SFCA by constructing a Gaussian decay model G. Figure 7 shows the conceptual description of the two-step mobile search method.  
Figure 6: Distribution of house prices in Chongqing.  
Step 1: Given a food store POI location of type \(k\) as \(j\), the model searches for any community \(i\) within the time cost distance threshold \(d_{0}\) to form a region \(F_{j}\) centered on \(j\). The time cost value \(d_{ij}\) between community \(m_{i}\) and store \(S_{j}\) is calculated by the Gaussian function G for weighting; the contribution of \(C_{j}\) is accumulated for all communities \(i\) in the region \(F_{j}\); and finally, the ratio \(R_{j}\) between the population served (\(Sev_{j}\)) in store \(j\) and \(C_{j}\) is calculated.  
\[R_{j}=\frac{Sev_{j}}{\sum_{m\in\{d_{ij}\leq d_{0}\}}G\left(d_{ij},d_{0}\right) \ast D_{i}} \tag{1}\]  
Equation (1) assumes 2.45 people per household in Chongqing (\(D_{i}=2.45\times Households_{i}\)). The definition of \(Sev_{j}\) is given in Table 1.  
\[G(d_{i},d_{0})=f(x)=\left\{\begin{array}{cc}e^{-(\frac{1}{2})\times(\frac{d _{i}}{d_{0}})^{2}},&d_{i}\leq d_{0}\\ 0,&d_{i}>d_{0}\end{array}\right. \tag{2}\]  
Step 2: For any store \(j\) within \(d_{0}\) of distance from community \(i\), the value of R weighted by the Gaussian function G is accumulated to obtain the accessibility value of \(k\) type of food at community \(i\).  
\[A_{i}=\sum_{m\in\{d_{ij}\leq d_{0}\}}G\left(d_{ij},d_{0}\right)R_{j} \tag{3}\]  
\(A_{i}\) is a value that lies between 0 and 1. An \(A_{i}=0\) indicates that the community \(i\) is not reachable within a 20 min walk. The reachability of the community increases with increasing values of \(A_{i}\). The algorithms were written to implement an enhanced two-step approach to calculating the accessibility index in combination with the Rest service ([[http://api.map.baidu.com/route=matrix/v2/walking?output=json](http://api.map.baidu.com/route=matrix/v2/walking?output=json)]([http://api.map.baidu.com/route=matrix/v2/walking?output=json](http://api.map.baidu.com/route=matrix/v2/walking?output=json))). The accessibility indices were obtained under the same conditions by automatically obtaining the accessibility values of various types of food from 12:00 p.m. to 5:00 a.m. at night. Figure 8 shows the flow diagram of the algorithm. In this method, the first step uses the 1500 m range to filter out communities within 20 min for each store and then calculate the community's contribution (\(r\)) to the store. The second step uses the 1500 m range to filter the stores that can be reached within 20 min for each community and then calculates the comprehensive accessibility (\(Ai\)) by the r value for each community.  
Figure 7: Conceptual description of the two-step mobile search method (E2 SFCA).