A Line Planning Approach for High-Speed Rail Networks with Time-Dependent Demand and Capacity Constraints

Table 1

The main notations used.

	the set of stations
,	stations
	the set of track sections
	track section
	a train
	a line traversed by train
	the station on line
	the number of stations on line
	the train stop pattern on line
	a 0-1 variable, the stop sign of train at station ,
	a set consisting of all possible train stop patterns on line
	a line plan
	the departure time of train at station
	the arrival time of train at station
	the sequence of departure times of train
	the sequence of arrival times of train
	the carriage composition of train
	the seat capacity of train
	the segment of train running between two neighborhood stop stations and ,
SPAM-TBP	a schedule-based passenger assignment method for high-speed rail networks considering the ticket-booking process
	the length of
	the horizon time
	the ticket pre-sale period
	set of passenger origin-destination pairs
	an O-D pair
	time-dependent demand of the O-D pair for and
	the set of time-dependent demand for all O-D pairs
	time deviation between the expected departure time and the actual boarding time
	time on trains
	transfer time
, ,	the value weights of , and respectively
	the minimum travel cost of passengers for O-D pair with expected departure time and ticket-booking time
	the time when there is no seat capacity for the passengers of O-D pair in the pre-sale period
	the train running time on track section
	the sum of dwell time and additional time for engine starting and stopping at station
	the number of passengers assigned on train segment
	the upper bound on the number of running trains per unit time for track section
	unit time
	a 0-1 variable, labeling whether train enters track section within the th time interval
	a 0-1 function telling if station is same as station
	The maximum gap between the number of starting trains and that of ending trains at a station
	weight of train in operational cost
	the operational cost of all trains
	travel cost for passengers who are served
	the penalty cost for passengers who are unserved
	the objective function
,	the weights in the objective function for trains and passengers respectively
	the load factor of train