Most facilities in today's technological society may be classified as semi-desirable. That is, the facility provides a benefit or service to society, while adversely affecting the quality of life or social values in a number of possible ways. The paper proposes a location model for a new semi-desirable facility that accounts for the service costs by a standard minisum objective with arbitrary travel distance function. The social costs are imputed by specifying around each demand point or population center a convex forbidden region, also defined by an arbitrary distance metric, in which the new facility may not be located. A general solution algorithm is suggested, and the methodology is applied to circular forbidden regions and special travel distance functions.
Juel, H., & Brimberg, J. (1998). A minisum model with forbidden regions for locating a semi-desirable facility in the plane. Location Science, 6(1-4), 109-120. https://doi.org/10.1016/S0966-8349(98)00050-3