Fewer Trains for Better Timetables: The Price of Fixed Line Frequencies in the Passenger-Oriented Timetabling Problem

This paper introduces the Passenger-Oriented Timetabling problem with flexible frequencies (POTflex) in the context of railway planning problems. POT-flex aims at creating feasible railway timetables minimising total perceived passenger travel time. The contribution of the POT-flex lies in its relaxation of the generally adopted assumption that line frequencies should be a fixed part of the input. Instead, we consider flexible line frequencies, encompassing a minimum and maximum frequency per line, allowing the timetabling model to decide on optimal line frequencies to obtain better solutions using fewer train services per line. We develop a mixed-integer programming formulation for POT-flex based on the Passenger-Oriented Timetabling (POT) formulation of [13] and compare the performance of the new formulation against the POT formulation on three instances. We find that POT-flex allows to find feasible timetables in instances containing bottlenecks, and show improvements of up to 2% on the largest instance tested. These improvements highlight the cost that fixed line frequencies can have on timetabling.