# Performance Analysis of a Forecasting Relocation Model for One-Way Carsharing
## 3 Methodology
### Forecasting Relocation Model  
This paper used forecasting relocation to solve the imbalanced distribution of cars at each station. Thus, the performance of the forecasting model, multilayer perceptron (MLP), must be evaluated first. The MLP consisted of input, hidden, and output layers. Inputs were fed forward from the input layer through the hidden layer(s), ultimately providing the output. For an untrained network, the output differs from the known targets. The training process consisted of estimating weights to minimize deviations between the network outputs and actual data. The deviations were then propagated backwards through the network and weights were adjusted to reduce error. Detailed explanations of MLP are described elsewhere, e.g., [29].  
MLP was used to predict the daily number of trips for each station, which allows prediction of the number of cars needed at each station. In our study, the daily demand is considered as an input to be used by MLP for prediction. The demand based on the time (i.e., different demand between morning, afternoon, and night) is not considered in this study as we only focus on the static relocation (relocation is done at the end of the day). Thus, predicting the total number of cars needed by each station for the next day and relocating the cars at midnight are the main tasks in order to maximize the customer demand. The MLP was trained for a particular month using data from the previous 3 months, where the oldest 2 months comprised the training set and the most recent month comprised the validation set (28 days). For a particular station, the output layer was the daily total trips made by customers to particular stations and the input layer included the day type and number of trips in the previous week. Day types are defined by eight binary digits: Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, or Sunday, and holiday, where 0 was \"no\" and 1 was \"yes\". The number of trips in the previous week was the total reservations by customers in the previous week for that particular station. The training and testing process was implemented in the Weka 3.6 data mining tool (University of Waikato, Hamilton, New Zealand). Figure 4 shows the trip predictions for 28 days in the Seongbuk-gu area.  
MLP captured the daily number of reservation patterns for 28 days in Seongbuk-gu area quite well. The mean absolute error and root mean squared error of the forecasting model were 2.9003 and 3.5166 trips, respectively. Daily reservation forecasting was also applied to the other stations (details not shown), and overall the MLP model predicted the daily reservations made by the customer in each station accurately, i.e., with low errors.  
The relocation model proposed in this study was based on periodical relocation, i.e., relocation was triggered at the end of the day (midnight), with the total number of cars required at each station for the next day predicted by the forecasting model. That is, this relocation was not triggered by customer demand (as per dynamic relocation). Consequently, the total number of relocations is expected to be lower than dynamic relocation, i.e., lower relocation cost.  
Predicting the total number of cars based on customer reservation demands is also expected to increase the system utilization. To implement vehicle relocations, the operator sets the vehicle inventory threshold at each station. The vehicle inventory threshold is defined as present cars (number of present or parked cars)--predicted cars (number of predicted cars for the next day). The predicted cars are calculated based on the predicted customer demand (trips) using the MLP model, thus the high demand stations will have a high number of predicted cars. The system relocates the number of cars from an overstocked station (exceeding the inventory threshold) to the nearest understocked station (below the threshold) in terms of the lowest travel cost at the time of relocation.  
Figure 4: Predicted total number of reservations using MLP (multilayer perceptron) in the Seongbuk-gu area.