Long transfer times often add unnecessary inconvenience to journeys in public transport systems. Synchronizing relevant arrival and departure times through small timetable modifications could reduce excess transfer times, but may also directly affect the operational costs, as the timetable defines the set of feasible vehicle schedules. Therefore better results in terms of passenger service, operational costs, or both, could be obtained by solving these problems simultaneously. This paper addresses the tactical level of the integrated timetabling and vehicle scheduling problem as a bi-objective mixed integer programming problem that minimizes transfer costs and operational costs. Given an initial non-cyclical timetable, and time-dependent service times and passenger demand, the weighted sum of transfer time cost and operational costs is minimized by allowing modifications to the timetable that respect a set of headway constraints. Timetable modifications consist of shifts in departure time and addition of dwell time at intermediate stops with transfer opportunities. A matheuristic is proposed that iteratively solves the mathematical formulation of the integrated timetabling and vehicle scheduling problem allowing timetable modifications for a subset of timetabled trips only, while solving the full vehicle scheduling problem. We compare different selection strategies for defining the sub-problems. Results for a realistic case study of the Greater Copenhagen area indicate that the matheuristic is able to find better feasible solutions faster than a commercial solver and that allowing the addition of dwell time creates a larger potential for reducing transfer costs.
- Bus timetabling
- Mixed integer linear programming
- Public transport
- Vehicle scheduling