# A Tailored Pricing Strategy for Different Types of Users in Hybrid Carsharing Systems
## 3 Model Formulation
### User Clusters and Price Elasticity  
In this study, differential prices are given to different user clusters based on the unique characteristics of each one. In our previous study [36], the using frequency monthly and duration (equal to the time of the last use minus the time of the first use) are proposed to be indicators. Then, users can be clustered into three types by the K-means clustering method. Details about the indicators and the clustering results are all shown in Table 1. The first cluster is called the loyal users, i.e., the number of daily trips remains constant. The second cluster is named the losing users, i.e., the number of trips keeps fading until it reaches 0. The last cluster is called the potential users since the number of trips keeps increasing from the middle of the study period. Each cluster of users have unique characteristics, e.g., travel potential \(G^{h}\), consumption potential \(B^{h}\), travel efficiency \(\kappa^{h}\), and average revenue \(R^{h}\). Travel potential is defined as the number of carsharing trips of each user cluster. Consumption potential is the revenue that each user cluster can contribute to the operator. Travel efficiency is equal to the total travel time divided by the total travel distance, which means the average travel time per unit travel distance. The bigger the value, the lower the travel efficiency for the corresponding cluster. The average revenue means the average profit per trip each cluster can bring to the operator. As shown in Table 1, the loyal users have the highest travel potential and consumption potential with the lowest average revenue. The average revenue of the losing users is the highest, while the other two indicators are the lowest. Based on the analysis mentioned above, the penalty coefficient \(\beta^{h}\) is defined to describe the differences of all user clusters in the model. Since CSCs or SAVs might not serve all travel demands. The operator would pay extra penalty costs for unmet demands. The penalty coefficient \(\beta^{h}\) is used to evaluate the potential effect of the unsatisfied demands for user cluster \(h\) on the operator's profit. It combines the average revenue, travel potential, and consumption potential, given as Equation (1). The second term and last term mean the proportion of consumption potential and travel potential of user clusters \(h\) among all user clusters, respectively. The higher the coefficient of user cluster \(h\), the more important the corresponding user cluster. Since the penalty coefficient for loyal users is the highest, it is apparent that losing them would significantly reduce the operator's profit. \[\beta^{h}=R^{h}\times\frac{B^{h}}{\sum_{h\in\mathbf{H}}B^{h}}\times\frac{G^{h}}{ \sum_{h\in\mathbf{H}}G^{h}},\forall\,h\in\mathbf{H} \tag{1}\]  
Given the circumstances that different user clusters have different features, the TPS is used to set different prices for different clusters and then exploit the potential of all user clusters. In this study, user clusters are distinguished by the price elasticity \(E^{h}\). The formulation is as shown in Equation (2), which connects the price variations and demand variations. The price elasticity of each user cluster is also given in Table 2. When jointly \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Indicators** & **Cluster 1** & **Cluster 2** & **Cluster 3** \\ \hline Proportion (\%) & 36.63 & 34.55 & 28.82 \\ Using frequency monthly & 6.41 & 1.01 & 3.38 \\ Time of the first use & 181.58 & 169.95 & 51.81 \\ Time of the last use & 19.95 & 147.93 & 31.71 \\ Using duration & 161.63 & 22.02 & 20.1 \\ Consumption potential \(B^{h}\)(\(\mathsf{V/day}\)) & 921.87 & 206.5 & 223.16 \\ Travel potential \(G^{h}\) & 42.53 & 6.5 & 7.46 \\ Travel efficiency \(\kappa^{h}\) (min/\(\mathsf{km}\)) & 4.90 & 5.29 & 5.92 \\ Average revenue \(R^{h}\)(\(\mathsf{V/trip}\)) & 21.67 & 31.75 & 29.89 \\ Penalty coefficient \(\beta^{h}\) & 11.113 & 0.554 & 0.651 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Details about the indicators for different user clusters.