Metro Timetabling for Time-Varying Passenger Demand and Congestion at Stations

Table 1

Summary of publications related to the TTP.

Work	Model	Objectives	Decision variable	Solution approach
Caprara et al. [6]	ILP	Maximize profit	Arrival/departure times	Lagrangian-based heuristic
Cacchiani et al. [12]	ILP	Maximize profit	A full timetable of a train	Column generation, decomposition, and heuristic
Dollevoet et al. [13]	IP	Minimize total passenger delay	If a connection is maintained/used	Modified Dijkstra
Niu and Zhou [10]	IP	Minimize passenger wait time	Arrival/departure times	GA
Barrena et al. [7]	LP	Minimize passenger wait time	Arrival/departure times	Branch and bound
Dollevoet et al. [14]	IP	Minimize passenger arrival times, maximize consecutive delay	Connection and arrival/departure times	Iterative optimization approach
Kroon et al. [15]	MIP	Minimize the number of trains, passenger transfer time, and total travel time	Arrival/departure times	CPLEX
Niu et al. [11]	MIP	Minimize passenger wait time	Arrival/departure times	GAMS
Wang et al. [3]	NSNCP	Minimize passenger travel time and energy	Arrival/departure times	Rolling horizon with SQP and GA
Robenek et al. [2]	MILP	Maximize operating profit while maintaining passenger satisfaction	Departure times at first station	CPLEX
Robenek et al. [5]	MILP	Maximize passenger satisfaction	Departure times at first station	Simulated Annealing (SA) heuristic
Schöbel [8]	Eigenmodel	Passenger- and operator-oriented objectives in all three planning stages	Frequency, A/D times, trip assignment	Iterating algorithm
Luan et al. [16]	MILP	Minimize absolute arrival time deviations	A/D times, route selection	Lagrangian relaxation
Yin et al. [4]	MILP	Minimize passenger wait time and energy	A/D times, train control	Lagrangian-based heuristic
This paper	MIP	Minimize passenger wait and travel time, energy, and train cost	Segment travel times and arrival times at the first station	Branch and bound, Rolling optimization