A combined distribution and assignment model for continuous facility location problem

Consider a general, heterogeneous geographical space with a set of competit ive facilities, where the customers' demand locations from each of the faci lities are continuously dispersed over the area. The total demand generated from a particular location in the space is fixed, but the demands from thi s location to the set of competitive facilities are subject to a distributi on function with respect to the relative transportation costs to these faci lities. Furthermore, we take into account congested transportation cost in characterizing customer choices. Congestion effect is explicitly built into our model by using a flow-dependent and location-dependent transportation cost function. The routing behavior of customers over the space and the use r equilibrium choices of facilities are modeled by constructing a spatial u ser equilibrium flow pattern. The problem is formulated as a combined distr ibution and assignment model. An iterative algorithm between the distributi on function for the choice of facilities and a mixed finite element method for route choices is proposed to solve the resulting continuous facility lo cation problem. A numerical example is given to demonstrate the effectivene ss of the proposed methodology.