You are asked to determine a location for a recycling depot serving three urban
ID: 356455 • Letter: Y
Question
You are asked to determine a location for a recycling depot serving three urban area's They are:
Smallville, population 1,200, at grid location (8.8, 2.8);
Bigburg, population 1,400, at grid location (3.5, 8.1); and
Middleton, population 900, at grid location (7.8, 6.2).
a) Determine the center of gravity of the three locations.
b) It is determined that planners would prefer to have the depot in either Bigburg or Middleton (although it will serve all three places). Using metropolitan distances, determine the load- distance scores for both Bigburg and Middleton and make a recommendation as to which town should have the depot.
c) You are asked to provide input on a layout for a new office. The old layout is thought of as being inefficient. You are asked to redesign the layout and evaluate your redesign using load distance scores. The current layout is shown below. The overall shape cannot change; you can merely move the individual departments around. (8 marks)
Trips between the different departments are as follows: A B-4 trips per day, A-C-5, A-D-7,A-E-9 B A 5, B-C-2, B-D-4,B-»E-2 C A - 4, C-»B - 5, C-D-1,C-»E-8 D-»A - 8, D-»B - 4, D->C -3, D- E - 4 E-A - 8, E-B- 3, E-»C- 5, E-»D- 3Explanation / Answer
(A)
Center of Gravity method
To identify the location for housing Center of Gravity method is used.
The x and y coordinates of center of gravity (CG) gives appropriate site location with respect to the travel frequency and service point locations.
Calculate X and Y coordinates for CG as:
CX = [?(w)(Xi)]/[?wi]
CY = [?(wi)(Yi)]/[?wi]
Coordinates-
Market-
Xi
Yi
Demand (wi)
(wi)(Xi)
(wi)(Yi)
Smallville
8.8
2.8
1200
10560
3360
Bigburg
3.5
8.1
1400
4900
11340
Middleton
7.8
6.2
900
7020
5580
Total
?(wi)
= 3500
?(wi)(Xi)
= 22480
?(wi)(Yi)
= 20280
Center of Gravity
CX = [?(w)(Xi)]/[?wi]
= 65.48
CY = [?(wi)(Yi)]/[?wi]
= 30.23
(B)
Apply load-Distance Model is used for comparing various locations.
Relative locations are compared by computing the load–distance, or LD, score for each location. The LD score for a particular location is obtained by multiplying the load (denoted by L) for each location by the distance traveled (denoted by D) and then summing over all the locations. Our goal is to make the LD score as low as possible by reducing the distance the large loads have to travel.
Step 1 Identify rectilinear Distances (dij): Select one particular location for warehouse, say A. Calculate rectilinear distance from location A to B as shown below:
dAB = |XB ? XA| + |YB ? YA| = |32 ? 12| + |18 ? 48| = 20 + 30 = 50
Calculate dij from location A to other locations also.
Step 2 Calculate the Load–Distance Score for Each Location: Calculate the load–distance score for each location by multiplying the load, wj, by the distance, Dij. Then compute the sum of widijto get the wD score. Finally, select the site with the lowest load–distance score.
Coordinates-
Location Bigburg
Market-
X
Y
Demand (L)
|XB - Xi|
|YB - Yi|
D(Bi)
L x D(Bi)
Smallville
8.8
2.8
1200
5.3
5.3
10.6
12720
Bigburg
3.5
8.1
1400
0
0
0
0
Middleton
7.8
6.2
900
4.3
1.9
6.2
5580
Total
5580
Load distance score from Bigburg location = 5580
Coordinates-
Location Middleton
Market-
X
Y
Demand (L)
|XM - Xi|
= |3.5 - Xi|
|YM - Yi|
= |8.1 - Yi|
D(Mi)
L x D(Mi)
Smallville
8.8
2.8
1200
|3.5-8.8|
= 1
|8.1-2.8|
= 3.4
1+3.4
= 4.4
4.4 x 1200
= 5280
Bigburg
3.5
8.1
1400
4.3
1.9
6.2
8680
Middleton
7.8
6.2
900
0
0
0
0
Total
8680
Load distance score from Middleton location = 8680
Thus, the best location is Bigburg which gives lowest load-distance.
Coordinates-
Market-
Xi
Yi
Demand (wi)
(wi)(Xi)
(wi)(Yi)
Smallville
8.8
2.8
1200
10560
3360
Bigburg
3.5
8.1
1400
4900
11340
Middleton
7.8
6.2
900
7020
5580
Total
?(wi)
= 3500
?(wi)(Xi)
= 22480
?(wi)(Yi)
= 20280
Center of Gravity
CX = [?(w)(Xi)]/[?wi]
= 65.48
CY = [?(wi)(Yi)]/[?wi]
= 30.23
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