Given Information:
Site 1: x1 = 360 , y1 = 180
Site 2: x2 = 420 , y2 = 450
Site 3: x3 = 250 , y3 = 400
Solution:
Xa = 200, Ya = 200, Wa = 75
Xb = 100, Yb = 500, Wb = 105
Xc = 250, Yc = 600, Wc = 135
Xd = 500, Yd = 300, Wd = 60
If centre of gravity is (x,y)
then x = (200*75+100*105+250*135+500*60)/(75+105+135+60)
x = 238
then y = (200*75+500*105+600*135+300*60)/(75+105+135+60)
y = 444
Using centre-of-gravity method, location of distribution centre = (238,444)
Using rectilinear distance,
Load distance score of Site 1: 75*(abs(360-200)+abs(180-200))+105*(abs(360-100)+abs(180-500))+135*(abs(360-250)+abs(180-600))+60*(abs(360-500)+abs(180-300)) = 161550
Load distance score of Site 2: 75*(abs(420-200)+abs(450-200))+105*(abs(420-100)+abs(450-500))+135*(abs(420-250)+abs(450-600))+60*(abs(420-500)+abs(450-300)) = 131100
Load distance score of Site 3: 75*(abs(250-200)+abs(400-200))+105*(abs(250-100)+abs(400-500))+135*(abs(250-250)+abs(400-600))+60*(abs(250-500)+abs(400-300)) = 93000
Site 3 tends to be optimal as it offers a lower distance ranking.
