Three new facilities are to be located among five possible sites. The new facilities interact with four existing facilities. The (X,Y) coordinates for the possible sites and the existing facilities are given in the following table:
(X,Y) coord. 1 2 3 4 5
possible sites (0,0) (10,5) (0,10) (10,0) (20,5)
existing fac. (5,5) (10,10) (0,5) (20,0)
The flow between new facility i and existing facility k is given by:
k=1 k=2 k=3 k=4
i=1 5 0 5 0
i=2 0 10 5 0
i=3 10 0 0 10
Euclidean distances are to be used.
a) Determine the locations of the new facilities that minimize total distance traveled.
b) Suppose it is required that one of the new facilities be located at Site 1 and space limitations prohibit locating new facility 1 at Site 1. Determine the locations of the new facilities that minimize total distance traveled, subject to the restrictions.