Facility location in a user-optimizing environment with market externalities: Analysis of customer equilibria and optimal public facility locations

In many location models, the customers’ choice of which facility to patronize is independent of the action of all other customers, except to the extent of capacity restrictions. This paper introduces a class of location problems where customers select a facility based not only on travel time or distance to the facility, but also on externalities associated with the market share of the facility. It characterizes the user-choice equilibrium given J fixed facility locations and any locational topology. It shows that when the externality costs are purely negative, the user-optimizing equilibrium utilization of facilities is unique. It then considers the strategic decision of facility locations, given the equilibrium behaviour of the users. The analysis is specialized to a tree network with two facilities and negative externalities. The paper considers public facilities that locate to minimize social cost. It shows how to find an optimal solution in O(n³) steps, where n is the number of network nodes (customers).