# Integrated Framework for Bus Timetabling and Scheduling in Multi-Line Operation Mode
## 1 Introduction  
With urban development, travel demand has grown considerably. The ground bus system is considered a feasible solution to provide a green and efficient travel service. As for the transit operational enterprise, the fundamental problem is how to provide efficient and feasible services. A bus operation mode includes the single-line operation mode and the multi-line operation mode. The single-line operation mode means that each vehicle only serves a particular line and does not allow the vehicle to be assigned to other lines. The single-line operation mode is widely used in daily operations because it is easy to manage. But this mode has made transportation resource-scar [1]. Unlike the single-line mode, the multi-line operation model plans multiple lines at the same depot in a unified manner to realize the sharing of timetables and vehicles. Figure 1 shows a typical multi-line scenario where all three lines have a joint depot. Vehicles obey centralized management in the joint depot and can be flexibly assigned to all the lines. Based on this characteristic, some scholars have studied the vehicle scheduling problem in the multi-line mode. [PERSON] et al. [1] demonstrated through experiments that vehicle resources are saved due to the improvement of vehicle turnover efficiency in the multi-line operation model. Recently, [PERSON] et al. [2] proposed a dynamic bus substitution strategy in the multi-line operation model to enhance system reliability. Thus, the existing resources show a significant benefit by centralized management in the multi-line operation mode. Timetabling in multi-line operation mode is also a research hotspot. [PERSON], [PERSON] et al. [3] proposed the Synchronization BusTimetabling Problem (SBTP) that favors passenger transfers and avoids the congestion of buses at common stops. [PERSON], [PERSON] et al. [4] proposed a headway control strategy in bus transit corridors served by multiple lines. Although bus operating systems are integrated, there are few studies that consider bus timetabling and vehicle scheduling together, especially in multi-line operation mode. Therefore, we will review the methods of bus operation planning considering the research in single-line mode. Public transit resource management involves two fundamental processes: timetabling (TT) and vehicle scheduling (VS). TT defines departure times of trips at all depots, and VS determines the trips-vehicles assignment to cover all the planned trips [5; 6]. Traditionally, TT and VS are solved independently as they have different decision objects [1; 2; 7; 8]. However, systemically, TT and VS are interdependent because the output of TT becomes the input for VS [6]. Indeed, a slight change in TT output could render an initial VS output infeasible or create options for less costly VS output [9]. Therefore, sequential optimizing possibly produces suboptimal solutions [10]. Compared with solving these problems sequentially, integrated optimization often achieves superior performance [11]. Thus, this study is devoted to proposing an optimization framework for integrated TT and VS problems in multi-line operation mode (M-TT/VS). It should be noted that bus route design [12] and driver shift [13] are part of the bus operation planning processes, but they are beyond the scope of this study. They will be included in further research. Some recent research focuses on methods for integrated TT and VS problems to construct the optimal scheme systematically. Some of these methods are used to solve integrated TT and VS problems in single-line operation mode (S-TT&VS) [10; 14; 15]. [PERSON] et al. [14] developed a multi-objective particle swarm optimization algorithm to get the Pareto optimal solution set for an electric bus line. [PERSON] et al. [15] proposed a multi-objective optimization approach for the S-TT&VS problem with uncertainty. Some research applies to the multi-line operation mode [16; 17; 18; 19; 20]. [PERSON] et al.