A Generalized Model for Locating Facilities on a Network with Flow-Based Demand

Flow-interception location problems identify good facility locations on a network with flow-based demand. Since the early 1990s, over 30 different flow-interception location models have appeared. In these publications, location researchers have developed new models by introducing changes in the objectives functions, constraints, and/or assumptions. These changes have led to many disparate models, each requiring a somewhat different solution method, and they have challenged the development of standardized software that would encourage widespread use in real-world, strategic decision-making processes. In this article, we formulate a generalized flow-interception location–allocation model (GFIM) which, with few exceptions, requires only simple modifications to its input data to effectively solve all current deterministic flow-interception problems. Additional flow-interception problems can be solved by simple model manipulation or the addition of constraints. Moreover, several critical considerations in flow-interception models—such as deviation from predetermined journeys, locational and proximity preferences, and capacity issues—can be handled within the proposed single framework. Two real-world examples reported in the literature (1989 morning and 2001 afternoon peak traffic for the city of Edmonton in Canada) show that a standard optimization engine such as ILOG-CPLEX optimally solves GFIM much more efficiently than it does the classic flow-interception location model.