Abstract
The flow-capturing location problem (FCLP), originally proposed by Hodgson (1990), identifies desirable facility locations on a network for flows traveling between various origins and destinations. The model aims to locate a given number of facilities on a network to maximize flows that have at least one facility along their travel route. Since the users cannot get off the train freely, it is easier for them to access a facility at the station where their train stops. For example, facilities at the express stations are easier to access when riding on an express train. To model this aspect, we proposed a model in which flows can only be covered at stations where the train stops, and it depends on the train types. FCLP and its variants assume that the number of facilities is a fixed input parameter. Often, however, a decision maker has a constraint on a total budget limit to locate facilities instead of the number of facilities. This paper introduces fixed costs of opening facilities into FCLP, making the number of facilities one of the decision variables. We present an integer programming formulation of the proposed model, and apply it to analyze optimal facility locations among stations of Keio Railway Network consisting of 6 railway lines and 69 stations. Commuter traffic flow data and the costs to post a billboard advertisement at each train station are used. Optimal solutions of Hodgson's FCLP and FCLP with fixed costs are obtained by a mathematical programming solver, IBM ILOG CPLEX. By comparing solutions of two models, it is shown that optimal solutions of the proposed FCLP tend to capture large volumes of flows within a relatively small facility location costs.
