Joint optimization of timetabling, vehicle scheduling, and ride-matching in a flexible multi-type shuttle bus system

Document Type

Journal Article

Publication Date


Subject Area

mode - bus, operations - scheduling, operations - performance, economics - operating costs, ridership - demand, planning - travel demand management, planning - methods


obility-on-demand shuttle bus, Timetabling, Vehicle scheduling, Ride-matching, Lagrangian relaxation, Rolling horizon optimization


Shuttle bus services play a vital role in public transit systems. However, conventional shuttle bus systems use the same type of buses and fixed departure timetables. They fail to meet the time-varying travel demand and do not consider the diversified characteristics of transit passengers. With the advent of the information era, communication among passengers, buses, and dispatching centers has become much easier. Accordingly, demand-responsive bus dispatching methods are expected to increase the flexibility of operation schemes to improve the performance of shuttle bus systems. To this end, this study proposes a mixed-integer linear programming model to incorporate ride-matching and shuttle bus dispatching in one framework. The bus trip schedules (including the number of used bus trips of different types, departure times, dwelling stops with dwelling times, and recommended travel speeds between adjacent stops of each trip) and passenger-to-vehicle matching schemes are optimized. The commonly used stop-skipping tactic, speed adjustment, and bus holding strategies are introduced to improve the flexibility and operational efficiency of shuttle bus systems. The objective is to minimize the weighted total passenger waiting times, passenger in-vehicle times, and operating costs. A modified Lagrangian relaxation algorithm is designed to improve computational efficiency for large-scale problems. A rolling horizon scheme is designed to implement the algorithm dynamically. It updates the dispatching scheme horizon by horizon according to newly collected requests, which can also improve the algorithm performance by reducing the problem scale. Numerical results show that the proposed flexible multi-type shuttle bus system outperforms a multi-type bus timetabling algorithm in all the considered cases, and it outperforms an on-demand ride-sharing algorithm in 80% of the cases.


Permission to publish the abstract has been given by Elsevier, copyright remains with them.


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