A multicriteria approach to the location of public facilities

We argue that practical problems involving the location of public facilities are really multicriteria problems, and ought to be modeled as much. The general criteria are those of cost and service, but there exist several distinct criteria in each of those two categories. For the first category, fixed investment cost, fixed operating cost, variable operating cost, total operating cost, and total discounted cost are all reasonable criteria to consider. In terms of service, both demand served and response time (or distance traveled) are appropriate criteria, either agglomerated or considered on the basis of the individual clients. In this paper we treat such multicriteria questions in the framework of a model for selecting a subset of M sites at which to establish public facilities in order to serve client groups located at N distinct points. We show that for some combinations of specific criteria, parametric solutions of a generalized assignment problem (GAP) will yield all efficient solution. In most other cases the efficient solutions can be found through parametric solution of a GAP with additional constraints of a type which can be incorporated into an existing algorithm for the GAP. Rather than attempting to find all efficient solutions, however, we advocate an interactive approach to the resolution of multicriteria location problems and elaborate on a specific interactive algorithm for multicriteria optimization which for the present model solves a finite sequence of GAP's or GAP-type problems. Finally, some similar aspects of private sector location problems are discussed.