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

Table 3

Decision variables.

symbol	description
	departure time of train service in the up direction at the origin
	departure time of train service in the up direction at the destination
	departure time of train service in the down direction at the origin
	departure time of train service in the down direction at the destination
	0-1 binary variables, if =1, then train service is a short turning train service
	0-1 binary variables, if =1, then train service is a short turning train service
	0-1 binary variables, if =1, then train service is the connection train of train service i at the destination station
	0-1 binary variables, if =1, then train service is the connection train of train service l at the destination station
	0-1 binary variables, if train in the up direction comes out from the depot, =0, otherwise, =1
	0-1 binary variables, if train in the down direction comes out from the depot, =0, otherwise, =1
	0-1 binary variables, if train in the up direction goes back to the depot, =0, otherwise, =1
	0-1 binary variables, if train in the down direction goes back to the depot, =0, otherwise, =1