A demand-responsive feeder service with mandatory and optional, clustered bus-stops

With the rise of smart cities in the near future, it will be possible to collect relevant data from passengers in order to improve the quality of transport services. In this paper, a mathematical model and algorithm are developed to plan the trips of the buses in a demand-responsive feeder service. A feeder service transports passengers from a lowdemand area, like a sub-urban area, to a transportation hub, like a city center. The feeder service modeled in this paper considers two sets of bus stops: mandatory stops and optional stops. Mandatory stops are always visited by a bus, while optional stops are only visited when a client nearby makes a request for transportation. Passengers are assigned to a bus stop within walking distance. This in turn, gives the service both exibility through the changing timetables and routes of the buses and some predictability due to the mandatory stops. To optimize the performance of the service, mathematical modeling techniques to improve the model's runtime are developed. It is concluded that a combination of column generation and the separation of sub-tour elimination constraints decreases the computing time of small and midsize instances significantly.