A pre-emptive goal programming model for locating obnoxious facilities

In this paper we present a multiobjective model for locating several obnoxious facilities that service a given set of customers. Each customer has a certain demand that must be satisfied. We consider a given set of candidate locations and a small number of different capacities for the facilities. Our objectives are to minimise the total cost of the facilities to be located, the total disutility imposed on all customers and the maximum disutility imposed on any individual customer. We introduce a mixed integer pre-emptive goal programming model for this problem and present an example to illustrate the trade-offs involved if one considers alternative priorities for the three objectives..