Supplement
K
Layout
PROBLEMS
Step 2: Develop a Block Plan
1. Baker Machine Company
Closeness
Department
Rating
Current Plan
Proposed Plan
Pair
wij
Distance (dij)
wijdij
Distance (dij)
wijdij
1–2
8
3
24
3
24
1–3
3
1
3
1
3
1–5
9
1
9
2
18
1–6
5
2
10
1
5
2–4
3
1
3
1
3
3–5
8
2
16
3
24
3–6
9
3
27
2
18
4–6
3
2
6
1
3
5–6
3
1
3
1
3
wd =
101
wd =
101
There is no change in the weighted-distance score. These layouts can be assessed
using the Layout Solver of OM Explorer, as shown following for the current plan.
2. Baker Machine Block Plan
The following Excel spreadsheet provides the weighted-distance score for the two
alternative layouts.
⚫
Supplement K
⚫
Layout
K-2
Closeness
Rating
Department
Pair
wij Distance (dij) wijdij Distance (dij) wijdij Distance (dij) wijdij
1–2 8 3 24 1 8 2 16
1–3 3 1 3 2 6 1 3
1–5 9 1 9 1 9 2 18
1–6 5 2 10 1 5 1 5
2–4 3 1 3 1 3 1 3
3–5 8 2 16 1 8 1 8
3–6 9 3 27 1 9 2 18
4–6 3 2 6 1 3 2 6
5–6 3 1 3 2 6 1 3
Total 101 Total 57 Total 80
Current Plan
Alternative Plan 1
Alternative Plan 2
While both alternative layouts are superior to the current layout, Alternative Plan
1 is the better of the two alternatives.
The Layout Solver of OM Explorer confirms its wijdij score.
Layout
⚫
SUPPLEMENT K
⚫
I-3
3. Conway Consulting
The following Excel spreadsheet provides the weighted-distance score for the two
alternative layouts.
Closeness
Rating
Analyst
Pairs wij Distance (dij) wijdij Distance (dij) wijdij Distance (dij) wijdij
A-C 6 2 12 1 6 1 6
B-D 12 224 112 112
C-D 2 1 2 2 4 2 4
C-E 7 1 7 3 21 1 7
D-F 4 1 4 2 8 2 8
Total 49 Total 51 Total 37
Alternative Plan 1
Alternative Plan 2
Alternative Plan 3
The Layout Solver of OM Explorer confirms its wijdij score.
624
135
Rating Matrix
Closeness Rating
Dept. Name 1 2 3 4 5 6
1 A — 6
2 B — 12
3 C — 2 7
4D — 4
5 E —
6 F —
Results
Solver – Layout
Department Closeness
Pair Factor Distance Score 6 2 4
2, 4 12 112 1 3 5
3, 5 7 1 7
1, 3 6 1 6
4, 6 4 2 8
3, 4 2 2 4
Total 37
Build Table
Rectilinear Distances
Euclidean Distances
⚫
Supplement K
⚫
Layout
K-4
4. Richard Garber’s designs
a. Departments (or Offices) A and F should be located most closely, all other
factors being equal.
b. The wd scores for the current plan are shown in the following table:
Closeness
Department
Rating (wij)
Distance (dij)
wijdij
A–F
185
1
185
C–F
125
1
125
C–E
125
2
250
B–E
105
1
105
E–F
105
1
105
A–C
90
2
180
A–B
25
3
75
D–E
25
1
25
wd =
1,050
c. The layout appears to be reasonably good, with most department pairs with high
wij values being only one unit of distance apart. The main exceptions involve
department C, because C–E and A–C are both pairings that are two units of
distance apart. One possible switch is departments C and D. Department C
would be closer to both A and E (but farther away from F). WD = 985, a 6%
reduction.
Due to the large number of possible swaps, the only way to be sure which swap
is best is to evaluate each one. The Layout modual of POM for Windows can
peform this analysis. The solution provided by POM for Windows follows
along with the calculation of weighted-distance scores. It’s explicit enumeration
Layout
⚫
SUPPLEMENT K
⚫
I-5
For additional insights, see Active Model K.1 in MyLab Operations
Management.
⚫
Supplement K
⚫
Layout
K-6
5. Four departments
a. The load-distance score is 84, as calculated in the left side of the following
table:
Closeness
Department
Rating
Current Plan
Proposed Plan
Pair
wij
Distance (dij)
wijdij
Distance (dij)
wijdij
A–B
12
1
12
1
12
A–C
10
1
10
2
20
A–D
8
2
16
1
8
B–C
20
2
40
1
20
B–D
6
1
6
2
12
wd =
84
wd =
72
b. A better layout is one that switches departments C and D, as shown by the
following block plan. The calculations on the right side of the preceding table
show that its weighted-distance score drops to 72. See the Layout Solver of OM
Explorer to facilitate this analysis.
A
B
D
C
6. Department of Engineering
a. The following heuristic process was used to construct the block plan shown
following. The faculty member pairing with the highest number of contacts is B
and D, which suggests B gets assigned to office 5. Putting E at office 4 responds
to the frequent contacts between C and E. Member F gets assigned to office 3,
the only one left.
b. The weighted-distance score is calculated below to be 45. Only two of the least
frequent contacts between C and D are not matched with the minimum distance
of one unit.
Faculty
Rating
Distance
Pair
wij
dij
wijdij
B–D
12
1
12
B–F
10
1
10
C–E
7
1
7
A–C
4
1
4
D–F
4
2
8
C–D
2
2
4
wd =
45
A
C
F
E
B
D