Location of semi-obnoxious facilities

Facility location models in the literature usually consider the facility to be either purely attractive, and then seek the facility locations minimizing the overall transportation costs, or purely undesirable, and then seek the sites minimizing some social cost such as the environmental impact caused. When facilities, although necessary for the community, also have some negative impact on the population or the environment – pollution, noise, risk of accidents, etc. – these two contradicting aspects should be taken into account simultaneously. This leads to models which are more realistic, but are usually also much less tractable from a computational viewpoint. In this note we present a critical overview of the mathematical methods commonly used in this emerging field.