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Chapter 06 - Process Selection and Facility Layout
6-41
Education.
12. Arrange the departments into a 2 x 4 grid. Department 1 must be located in the shaded location.
First, we transfer the Muther grid information to a table as shown below:
A Links
X Links
E Links
I Links
1-3
1-6
1-2
4-6
1-7
2-6
1-4
2-3
3-6
1-5
2-4
3-7
2-5
2-7
3-8
6-7
3-5
5-6
4-7
4-8
6-8
7-8
Rather than drawing clusters, we can start with a blank layout and then try to satisfy the A
and X conditions above. After that, we can shift departments around to satisfy E conditions
followed by I conditions.
conditions above, we can see that Department. 6 should only be located by Departments 4, 7, or
8. We can shift departments more if needed using trial and error to meet E conditions and then I
conditions.
The layout below meets all conditions. The next page shows all of the possible layouts
that meet all conditions.
3
1
4
8
5
2
7
6
Chapter 06 - Process Selection and Facility Layout
6-42
Education.
All possible layouts for Problem 12:
3
1
4
8
Or
5
1
4
8
Or
5
1
4
6
5
2
7
6
3
2
7
6
3
2
7
8
5
1
7
8
Or
3
1
7
8
Or
3
1
4
6
3
2
4
6
5
2
4
6
5
2
7
8
3
1
7
6
Or
5
1
7
6
5
2
4
8
3
2
4
8
13. Given: We must arrange departments in a 3 x 3 grid, and Department 5 must be located in the
lower left corner (shown in the shaded area in the layout).
We start by placing the Muther grid information into a table.
A Links
X Links
E Links
I Links
1-3
1-2
1-4
2-4
1-7
1-6
1-9
1-8
2-3
2-9
2-5
3-4
3-7
2-6
3-6
4-8
2-7
3-8
6-7
3-9
4-5
4-6
4-9
4-7
5-6
5-7
5-8
5-9
6-9
7-8
8-9
7-9
Chapter 06 - Process Selection and Facility Layout
Looking at the A links, we can see that that Department 7 appears most frequently followed by
Departments 1, 2, 5, & 9, and then Departments 3, 4, 6, & 8.
Department 7 is a good candidate for a central location. Then, we satisfy the remaining A
conditions along with the X conditions. After that, we can use trial and error to move departments
Chapter 06 - Process Selection and Facility Layout
6-44
From this, we can see that Departments 2 and 4 have the greatest interdepartmental workflow, so
they should be close, perhaps at Locations C and B. Next, we can see that the workflows for
Departments 1 and 4, and Departments 3 and 4 are high. Therefore, Department 4 has to be
located at a central location (Location B), while Department 2 is in Location C, Department 1 is
in Location A, and Department 3 is in Location D as shown below.
A
#1
B
#4
C
#2
D
#3
Second, we must determine the cost for each department pair by multiplying Number of Trips
x Distance x $1.
Number of Trips x Distance x Cost ($1)
Department
1
2
3
4
1
10 x 80 x 1 = 800
20 x 70 x 1 = 1400
80 x 40 x 1 = 3200
2
40 x 60 x 1 = 2400
90 x 40 x 1 = 3600
3
55 x 50 x 1 = 2750
4
Total Cost = $14,150
b. Revised layout given the new number of trips between departments.
First, we rank or arrange the number of trips between departments from high to low.
Dept. Pair
# of Trips
3-4
60
2-4
50
1-4
40
1-2
20
1-3
20
2-3
10
Chapter 06 - Process Selection and Facility Layout
6-45
From this, we can see that Departments 3 and 4 have the greatest interdepartmental workflow, so
they should be close, perhaps at Locations C and B. Next, we can see that the workflows for
Departments 2 and 4, and Departments 1 and 4 are high. Therefore, Department 4 has to be
located at a central location (Location B), while Department 2 is in Location A, and Department 1
is in Location D.
Second, we must determine the cost for each department pair by multiplying Number of Trips
x Distance x $1.
Number of Trips x Distance x Cost ($1)
Department
1
2
3
4
1
20 x 70 x 1 = 1400
20 x 60 x 1 = 1200
40 x 50 x 1 = 2000
2
10 x 80 x 1 = 800
50 x 40 x 1 = 2000
3
60 x 40 x 1 = 2400
4
Total Cost = $9,800
A
#2
B
#4
C
#3
D
#1
6-46
Education.
15. Given: Work centers 1 & 3 must be positioned in the diagram below as shown in the shaded
areas. We have 8 work centers that we must arrange in the layout. Transportation costs are $1 per
load per meter. Assume that reverse distances are the same.
First, we will assign work center pairs based on ranking them by number of trips between them.
No. of Trips
Between
Order of
Assignment
1–2
10
1–3
5
1–4
90
11
1–5
370
1
1–6
135
6
1–7
125
7
1–8
0
2–3
360
2
2–4
120
8 (tie)
2–5
40
2–6
115
9
2–7
45
2–8
120
8 (tie)
3–4
350
3
3–5
110
10
3–6
40
3–7
20
3–8
200
4
4–5
190
5 (tie)
4–6
70
12
4–7
50
4–8
190
5 (tie)
5–6
10
5–7
40
5–8
10
6–7
50
6–8
20
7–8
20
A
#1
B
F
G
H
Chapter 06 - Process Selection and Facility Layout
Education.
From this, we can see that work centers 1-5 have the highest number of trips between them,
followed by work centers 2-3, 3-4, 3-8, 4-5, 4-8, 1-6, 1-7, 2-4, 2-8, etc.
A reasonable (intuitive) set of assignments is:
The distance (in meters) between work centers for this option is shown below:
From
To
1
2
3
4
5
6
7
8
1
100
120
60
40
80
40
110
2
50
40
120
40
70
40
3
40
60
90
85
40
4
40
50
45
45
5
140
60
130
6
40
60
7
90
8
Then, for each work center pair, we must multiply Number of Trips x Distance x $1.
Number of Trips x Distance x $1
From
To
1
2
3
4
5
6
7
8
1
1000
600
5400
14800
10800
5000
0
2
18000
4800
4800
4600
3150
4800
3
14000
6600
3600
1700
8000
4
7600
3500
2250
8550
5
1400
2400
1300
6
2000
1200
7
1800
8
A
#1
B
#5
F
#6
G
#2
H
#8
Chapter 06 - Process Selection and Facility Layout
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Education.
16. Given: Distance between the reception area and each potential location (A, B, C, D, E, & F) = 35
feet. The reception area must remain in the central location; therefore, we can omit the reception
area from our analysis.
First, we will list the department pairs and the number of trips between them.
No. of Trips
Between
Order of
Assignment
1–2
0
10
1–3
40
7 (tied)
1–4
110
3
1–5
80
5
1–6
50
6 (tied)
2–3
0
10 (tied)
2–4
50
6 (tied)
2–5
40
7 (tied)
2–6
120
2
3–4
10
9 (tied)
3–5
250
1
3–6
10
9 (tied)
4–5
40
7 (tied)
4–6
90
4
5–6
20
8
Second, we will assign departments based on ranking the number of trips between departments.
A reasonable set of assignments is:
3–A, 5–B, 1–C, 4–D, 6–E, 2–F.
An equivalent solution is the reverse order:
2–F, 6–B, 4–C, 1–D, 5–E, 3–F.
