Locating optimal timetables and vehicle schedules in a transit line

The Transit Network Timetabling and Scheduling Problem (TNTSP) aims at determining optimal timetables for each line in a transit network by establishing departure and arrival times at each station allocating a vehicle to each timetable. Customers could know departure times of the line runs offered by the system in a regular way. However, each user, traveling later or in advance than their desired travel time, will give raise to an inconvenience cost, or a penalization cost if that user cannot be served. This paper deals with the optimal timetable and vehicle schedules for a given number of vehicles in a public transit line. The provided formulation ensures that each user is allocated to the best possible timetable ensuring capacity constraints. The problem is formulated using a p-median based formulation and solved using a clustering technique. Computational results that show useful applications of this methodology are also included. Keywords— Timetabling; vehicle scheduling; schedule delay; location-allocation.