Multi-depot vehicle scheduling with multiple vehicle types on overlapped bus routes

In China, overlapped routes from multiple bus lines are widespread. Some buses are overcrowded while others have few passengers. The goal of this study is to reduce onboard passenger crowding without wasting bus capacity. This paper examines an extended multiple-depot vehicle scheduling problem (VSP) with multiple vehicle types. First, a bi-objective integer programming model was created. The trade-off between operating cost and passenger travel cost was established and the crowding cost due to different vehicle sizes was especially considered. Then, the capacity restraint incremental assignment algorithm and a vehicle scheduling method with multiple vehicle types were developed to find Pareto-optimal solutions that considered vehicle capacity constraints. Finally, the proposed methodology was validated using a real-world transit network in Beijing, China. The optimization results from about 1.18 million bus card swiping records show that our model and solution algorithm can effectively reduce the passenger crowding cost and avoid the waste of transport capacity.