Towards integrating retiming in vehicle type scheduling problem

In this paper, we propose an integer linear programming (ILP) aiming at optimizing timetabling generation and the Vehicle Type Scheduling Problem (VTSP), based on a time-space network (TSN). The model was defined as Vehicle Type Scheduling Problem with Sequential Changes of timetable (VTSP- SCT). Additionally, we developed a new methodology to insert time window to the proposed problem based on small changes on the TSN structure, with easy computational implementation and optimal solution at low computation run-times. By including small changes to the timetable and/or including time windows for timetabling trips, we introduced flexibility levels in the departure times of trips, resulting in operational advantages for the service provider. Since we use a very short time window interval, the current timetable is only slightly modified, minimally changing the passenger routines. The developed approaches were tested using random instances based on a Brazilian city. The VTSP-SCT with and without time windows have resulted in relevant savings in the daily operations of the public transportation service,reducing the required number of scheduled vehicles to carry out the historic demand.