## ON LOCATING A SEMI-DESIRABLE FACILITY ON THE CONTINUOUS PLANE

## Abstract

The paper considers a bicriteria model for locating a semi-desirable facility on
the plane. One criterion is that of minimizing the sum of weighted
distances between customers and facility, where distances are given by
an arbitrary norm. The other criterion is that of maximizing the
weighted Euclidean distance from the facility to the closest customer.
The objective is to generate the set of efficient points, from which the
decision maker must choose the preferred one.
Two reformulations are considered:
In one, the sum of weighted distances is minimized, subject to
constraints requiring that each customer must have a weighted Euclidean
distance to the
facility of at least a given parameter; varying the parameter yields the
efficient set.
In the other, both criteria are viewed as minization problems and a
convex combination of them is minimized.
Properties of the reformulations are given, and the reformulations are
compared.
Finally, a solution procedure is outlined.
## IMM Technical Report 11/95