Location problem in the plane:

In Kent, the council to respond to the people and government needs, it decided to establish 3 community care homes. The towns are recorded with their corresponding x and y coordinates as well as their population, see Table 1.

(i)Use Excel to solve this location problem in the plane. (Hint: As the problem is not convex and not linear, you cannot use the Simplex but the other 2 approaches shown in Solver (Evolutionary approach and GRG Non Linear)). Also you may need to use several starting points as poor local minima may be found instead, Try both approaches before you finalise your decision and comment on the way you attempted it.

(ii) What do you expect the solution quality will be if you had to solve the discrete version of the problem using all the town locations as potential sites? Which weaknesses you may be faced with when implementing the optimal solution of (i) if it exists.

(iii) Now consider that any facility built cannot serve more than 350000 in total. Use the locations found in (i) and determine the new allocation (This is now a TP which can be solved using Simplex LP in solver). Express in % the extra cost incurred due to such a restriction.

Table 1: Coordinates and population of Kent Towns