A Note on the Separability of Production and Location

The choice of a facility location and the design of the facility, including the choice of the quantity of each input to use, are intimately related. Consequently, one would expect facility location and facility design problems to be addressed as simultaneous problems in the theory of the firm. However, the traditional theory of the firm does not include spatial elements. Furthermore, the traditional theory of location, following Alfred Weber, does not include the choice of input mix. It is as if the developers of these traditional theories felt that a kind of separability was inherent in productionlocation problems. There are analytical advantages to the use of this separation, but it carries with it the possibility of suboptimization. A number of authors have taken the point of view that production and location problems should be treated simultaneously. These efforts include the classic paper by Leon Moses and more recent papers by Hurter and Richard Wendell, David Emerson, A. J. Goldman, M. Bradfield, Noboru Sakashita, Robert Woodward, and Amir Khalili, Vijay Mathur, and Diran Bodenhorn. In one way or another, each of these authors contributes something to the question of the conditions under which the location decision and input-mix decisions can be treated separately. Our purpose here is to address this question directly, to draw together the contribution of these various authors, and to extend them. I. Assumptions and Problem Formulation