# Integrated Framework for Bus Timetabling and Scheduling in Multi-Line Operation Mode
## 2 Problem Description
### Description of Input Data  
Passenger flow data, trip runtime data, and operational parameters are known information for the M-TT/VS problem. They are key inputs for subsequent model solving. It should be noted that our research focuses on bus operation planning. We expect to find the rules of passenger flow and trip run time through historical data and design an operation scheme set with the rules. Therefore, we use the statistical and estimated data as input and evaluate the planning results based on the same data. The accuracy of subsequent implementation effect evaluation and data prediction is beyond the scope of this paper.  
A brief introduction to them is given below.  
* Passenger flow data is obtained from historical IC card data. The IC card data enumerates passengers' boarding times and trip numbers. At the same time, according to the operation data of vehicles, we can obtain the departure time and the line number of this trip. Therefore, we can count the total number of passengers carried on each trip. We assume that passengers are evenly distributed within the interval of two departure times. For example, suppose there is a trip carrying 100 passengers, and the departure time of this trip is 10 min apart from the previous trip. In this case, the arrival rate of passenger flow is 10 passengers/min. We have calculated the arrival rate of passenger flow \(fnp_{t}^{l}\) of each line \(l\) at time \(t\). In addition, we restore the passenger's alighting station data from IC card data through an alight inference method. Based on the complete passenger on-and-off action, we can calculate the highest section flow of the trips. The highest section flow of each line \(l\) at time \(t\) is represented as \(fnnp_{t}^{l}\).
* Trip run time data is obtained from historical GPS data. For each line, we calculate the mean run time \(frt_{t}^{l}\) of the trips whose departure time is \(t\) in a historical period. We also smooth the data and supplement the missing values, as shown in Equation (1). \[frt_{t}^{l\prime}=\frac{1}{2\eta}\cdot\sum_{x=t-\eta+1}^{t+\eta}frt_{x}^{l}\] (1)
* The operational parameters are determined based on actual operation scenarios. Part of these come from labor laws or regulations, and others from the experience of bus operators. The known operational parameters in this study include the set of all depots, set of all lines, number of standby vehicles, range of departure time, vehicle's total operating time daily, minimum idle time between trips, and maximum departure time interval. These are listed in Table 1.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Meaning** \\ \hline \(D\) & Set of all depots \\ \(L\) & Set of all lines \\ \(nc\) & Number of vehicles \\ \([st_{min},st_{max}]\) & Range of departure time \\ \([str_{min},str_{max}]\) & Range of total operating time \\ \(itta_{min}\) & Minimum idle time between trips \\ \(et_{max}\) & Maximum departure time interval \\ \hline \hline \end{tabular}
\end{table}
Table 1: Operational parameters.  
Figure 2: A schematic diagram of different operation modes.