Centrally locate a facility that serves several customers or other facilities in
ID: 2746422 • Letter: C
Question
Centrally locate a facility that serves several customers or other facilities in order to minimize distance or miles traveled (d) between facility and customers.
Where:
(x,y) = coordinates of proposed facility
(xi,yi) = coordinates of customer or location facility i
Minimize total miles d = S diti
Where:
di = distance to town i
ti =annual trips to town i
Coordinates
Town
x
y
Annual Trips
Abbeville
Benton
Clayton
Dunnig
Eden
20
10
25
32
10
20
35
9
15
8
75
105
135
60
90
Which of the following statements is true?
Coordinates
Town
x
y
Annual Trips
Abbeville
Benton
Clayton
Dunnig
Eden
20
10
25
32
10
20
35
9
15
8
75
105
135
60
90
Explanation / Answer
c. The best solution is found by using the weighted center-of-gravity method.
In this with each node the weight of node is given in form of annual trips. By weighted center of gravity it will be easy to calculate the exact center point for the distribution network.
It can be calculated as:-
X= ( xi * wi ) /wi
X = (20*75) + (10*105) + (25*135) +(32*60)+ (10*90) / (75+105+135+60+90)
X= 18.80
Y= ( yi * wi ) /wi
y = (20*75) + (35*105) + (9*135) +(15*60)+ (8*90) / (75+105+135+60+90)
y= 17.22
(18.80, 17.22) are centrally located a facility that serves several customers or other facilities in order to minimize distance or miles traveled) between facility and customers.
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