## A BICRITERIA MODEL FOR LOCATING A SEMI-DESIRABLE FACILITY IN THE PLANE

## Abstract

We consider the problem of locating a facility in the plane. Customers
want the facility to be close to obtain cheaply the service offered
by it. But customers also want the facility to be far away to avoid the
pollution from it. We model the situation using two criteria: One is the
well-known minisum criterion; in the other we want to minimize the
weighted sum of Euclidean distances raised to a negative power. The
second criterion is analyzed in some detail, and we state some
properties of this part of the model. In the bicriteria model we
minimize the weighted sum of the two criteria, with weights adding to
one. We outline a method for determining the efficient frontier of
facility locations, and give several small computational examples.
## IMM Technical Report 9/95