Locations and service start time of flow-covering facilities with multiple coverage levels

This paper develops an extended version of MFCLSTP (Maximum Flow-Covering Location and service Start Time Problem, Tanaka 2011) by introducing multiple coverage levels based on the arrival time to a destination. The original MFCLSTP determines the locations of facilities and the start time of services of fixed duration to maximize coverage for flows on the way back home from work. In MFCLSTP, each flow is either fully covered if commuters can be back home by a given time (after consuming service from start to end at a facility), or not covered at all otherwise. In many situations, a service which ensures that commuters can be back home early is more desirable. To describe this situation, we introduce different levels of coverage and allow the value of coverage to vary depending on the arrival time to a destination (home). The model is applied to the railway network of Chukyo area in Japan by using commuter flow data for railway users in this area. By employing a model with two coverage levels, we obtain the optimal set of stations to site facilities and their service start times. The results show that the optimal time to start a service tends to be earlier when more importance is placed on covering flows that can return home early.