IE 383
Assignment 3 solution
Some steps are omitted, but you should show your steps in your homework
solutions.
Problem 1.
a.)
This is a minisum problem that utilizes rectilinear distance w/ consideration of travel
frequency (weight). We can solve the problem by using median condition method.
Sum of W=
131
Sum of W/2 =
65.5
X
W
Cumulative W
100
35
35
210
24
59
250
15
74
300
19
93
400
38
131
Optimal X coordinate is 250.
Y
W
Cumulative W
150
19
19
180
24
43
200
38
81
300
35
116
400
15
131
Therefore the optimal point is at (250, 200)
b.)
This is a minisum problem that utilizes straightline distance w/ consideration of travel
frequency (weight). We can solve the problem by using center of gravity method.
Total weight=131
X*W
Y*W
Facility A
3500
10500
Facility B
5040
4320
Facility C
3750
6000
Facility D
5700
2850
Facility E
15200
7600
Sum
33190
31270
X* = Sum(Xi * Wi) / Sum (Wi)= 253.36
Y* = Sum(Yi * Wi) / Sum (Wi)= 238.7
The optimal location is at (253.36, 238.7)
c.)
This is a minimax per trip problem w/o consideration of travel frequency. Because we are
required to solve this problem graphically, we should use diamond method and we can
use the following formula to double check our graphical solution.
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 Spring '11
 Yi
 Distance, Harshad number, euclidean distance, FACILITY, Facility B Facility C Facility D Facility E

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