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.
TOWN/CITY
X
Y
POPULATION
Ashford
600985
142805
58,178
Broadstairs
639320
167760
24,370
Canterbury
614880
157830
42,249
Chatham
575785
167920
70,540
Dartford
554200
174325
50,000
Deal
637510
152745
29,248
Dover
631650
141835
39,078
Faversham
601530
161425
18,000
Folkestone
622765
135915
53,411
Gillingham
577350
168385
99,773
Gravesend
564730
174170
51,150
Herne Bay
617900
167945
31,000
Maidstone
576150
155705
75,000
Margate
635460
170580
58,465
Northfleet
562235
174310
13,590
Ramsgate
638365
165180
37,967
Rochester
574375
168475
25,000
Royal Tunbridge Wells
558360
139265
45,000
Sevenoaks
552375
155295
18,588
Sheerness
591955
174725
20,000
Sittingbourne
590740
163660
55,000
Tonbridge
559080
146600
31,600
Table 1: Coordinates and population of Kent Towns