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This paper proposes the Maximum Flow-Covering Location and service Start Time Problem (MFCLSTP). The problem seeks to determine locations and service start time of p facilities which provide a service for a given duration, so as to maximally cover flows. Each flow is specified by a pair of origin- destination (OD) nodes and the departure time of the origin node. We assume that a given commuter flow is covered when commuters can stop at a facility, fully consume that facility's service, and arrive at the destination node by a given time. Two models are considered for MFCLSTP: MFCLSTP1, in which the service start time of each facility can be independently determined; and MFCLSTP2, in which all facilities have the same service start time. We provide integer programming formulations and propose heuristic solution algorithms. The proposed models are applied to a case study of the Tokyo metropolitan railway network using census data for commuter traffic. The solutions obtained by the heuristic algorithms for both models are compared. Solutions of MFCLSTP2 show that selected locations are spatially dispersed to cover different types of flows, whereas solutions of MFCLSTP1 closely locates some facilities having different start times in the central area of Tokyo.

journal of the operations research society of japan

MAXIMUM FLOW-COVERING LOCATION AND SERVICE START TIME PROBLEM AND ITS APPLICATION TO TOKYO METROPOLITAN RAILWAY NETWORK(&lt;Special Issue&gt;SCOPE (Seminar on Computation and OPtimization for new Extensions))