A column generation algorithm for the demand-responsive feeder service with mandatory and optional, clustered bus-stops

With the rise of smart cities, relevant passenger data can be collected to improve the quality of transport services. In this article, a demand-responsive feeder service is presented. A feeder service transports passengers from a low-demand area, like a sub-urban area, to a transportation hub, like a city center. The feeder service modeled in this article 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. This gives the service both flexibility and some predictability. 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.