So in this case the final and concentrator locations coincide. So in this case the final and concentrator locations are near to each other. So in this case the final and concentrator locations are not particularly close to each other. Technically the approach used above for location, where any point is a potential location for a new facility, is called the infinite set approach. More commonly nowadays location studies are done using a feasible set approach.
Location models based upon the feasible set approach typically use integer programming .
More about such models can be found here . One example of a facility location problem that I have worked on was to do with church location for Church of England churches. The idea here was to investigate which churches could best be closed. For the purposes of this study a 100 kilometre square to the north-east of London was chosen. Alas the organisation did not seem too sure of the answers to this question.