A Fast Approach for Reoptimization of Railway Train Platforming in Case of Train Delays

Table 2

Sets, parameters, and variables.

Symbol	Definition
Sets
	Set of trains, indexed by
	Set of delayed trains,
	Set of platform tracks, indexed by
	Set of platform tracks that train can utilize,
	Set of time intervals in the planning horizon, indexed by
Parameters
	Cost of assigning train to platform track
	0-1 parameter is equal to 1 if train is running in the downstream direction; 0, otherwise
	0-1 parameter is equal to 1 if train was initially assigned to platform track before a delay occurs; 0, otherwise
	The time when the information of train delays is updated
	Scheduled arrival time of train
	Scheduled departure time of train
	Estimated arrival time of train when a delay occurs
	Estimated departure time of train when a delay occurs
	Dwell time of train
	Priority of train
	Safety time interval for platform track operation
	Sum of the length of the planning horizon and the safety time interval for platform track operation
	Maximum value of dwell times of all trains
	Headway between two arrival trains running in the same direction
	Headway between two departure trains running in the same direction
	Objective function weighting factor
	A sufficiently large number
Variables
	0-1 platform track assignment variable = 1 if train is assigned to platform track ; = 0 otherwise
	0-1 same platform track choice variable = 1 if train and train choose the same platform track; = 0 otherwise
	0-1 platform track occupancy state variable = 1 if train occupies platform track at moment ; = 0 otherwise
	0-1 platform track utilization state variable = 1 if train has not yet arrived at platform track at moment ; = 0 otherwise
	0-1 platform track clearance state variable = 1 if train has left platform track at moment ; = 0 otherwise
	0-1 train arrival sequence variable = 1 if train arrives at the station before train ; = 0 otherwise
	0-1 train departure sequence variable = 1 if train departs from the station before train ; = 0 otherwise
	Actual arrival time of train at the station
	Actual departure time of train at the station