A Short Turning Strategy for Train Scheduling Optimization in an Urban Rail Transit Line: The Case of Beijing Subway Line 4

Table 1

Summary of the relevant studies with short turning train scheduling.

Publication	Objective	Decision variables	Solution approach
Wang [26]	minimize the number of trains	short turning service headway and cycles	fuzzy optimization
Wang and Ni [23]	minimize the passenger travel cost and enterprise operation cost	short turning offsets, turn back station	ideal point method
Canca et al. [21]	reduce the passenger waiting time	turn back points location, departure and arrival times, short turning offsets	MILP
Bai et al. [24]	minimize the number of trains	turn back point location, headway, turning times	enumeration method
Ghaemi et al. [22]	minimize the delays and canceled services after blockage	short turning stations routes and platform tracks	MILP