where is the dimension, is the number of existing facilities, are the coordinates of the existing facility (if ), and is the weight associated with the old-new facility. The model describes that one plans to build a new facility among existing facilities and chooses the location which minimizes the weights associated with the Euclidean distance between the new and existing locations. For simplicity, we consider . It is trivial to extend to higher dimensions. Let

for and

We then
introduce new linear constraints
for

Therefore, the problem becomes
(3-5) |

We denote

**Example 2.** The coordinates of the existing facilities and
the weight associated with each existing facility are both
generated by a uniform random number generator. We use
to create four problems.