The Dorton University president has asked the OSCM department to assign eight blology professors (A, B, C, D, E, F, G, and H) to eight offices (numbered 1 to 8 In the diagram) In the new blology building. 1 46772235 ABCDEFGH North wing 1 Courtyard The following distances and two-way flows are given: DISTANCES BETWEEN OFFICES (FEET) 2 3 4 5 6 7 8 10 25 34 15 18 20 30 18 25 10 South wing 341 3 | 0 1,024 - O 40,320 O 64 oooo e e 5 e e e 18 20 10 30 Funeo I 88888 1 15 10 20 TWO-WAY FLOWS (UNITS PER PERIOD) A B с D E F G 0 10 20 18 New biology building ISODEO 3 0 I u 5 18. RUOOO0041 2654421 e 18 34 10 H 4 ++0003 4 e a. If there are no restrictions (constraints) on the assignment of professors to offices, how many alternative assignments are there to evaluate? e 25,600 O 64,000 O There are an infinite number of possibilities

Practical Management Science
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ISBN:9781337406659
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Chapter5: Network Models
Section5.3: Assignment Models
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Ch. 8 Q1
The Dorton University president has asked the OSCM department to assign eight blology professors (A, B, C, D, E, F, G, and H) to eight
offices (numbered 1 to 8 in the diagram) in the new blology building.
1
1
2
3
4
5
6
7
8
A
B
с
D
1
1-
E
F
North wing
The following distances and two-way flows are given:
DISTANCES BETWEEN OFFICES (FEET)
2 3 4 5
7
10
G
H
2
Courtyard
6
-
South wing
3
A B
- 4
7
25 34
18
-
0
e
-
O 40,320
O 64
4
25 18
10
20
-
30
8
-
6
15 18
15
10
15 18
20
18
15
10 25 34
-
18
TWO-WAY FLOWS (UNITS PER PERIOD)
C
F
G
New
biology
building
D E
e
5
0
e
e
3
e
e e
1
-
8
20 30
10 20
e
5
-
25
10
-
0
0
e
0
H
0
4
4
0
e
e
4 e
-
3
e. If there are no restrictions (constraints) on the assignment of professors to offices, how many alternative assignments are there to
evaluate?
1,024
O 25,600
O 64,000
O There are an infinite number of possibilities
H
OL
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1 of 8
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Transcribed Image Text:The Dorton University president has asked the OSCM department to assign eight blology professors (A, B, C, D, E, F, G, and H) to eight offices (numbered 1 to 8 in the diagram) in the new blology building. 1 1 2 3 4 5 6 7 8 A B с D 1 1- E F North wing The following distances and two-way flows are given: DISTANCES BETWEEN OFFICES (FEET) 2 3 4 5 7 10 G H 2 Courtyard 6 - South wing 3 A B - 4 7 25 34 18 - 0 e - O 40,320 O 64 4 25 18 10 20 - 30 8 - 6 15 18 15 10 15 18 20 18 15 10 25 34 - 18 TWO-WAY FLOWS (UNITS PER PERIOD) C F G New biology building D E e 5 0 e e 3 e e e 1 - 8 20 30 10 20 e 5 - 25 10 - 0 0 e 0 H 0 4 4 0 e e 4 e - 3 e. If there are no restrictions (constraints) on the assignment of professors to offices, how many alternative assignments are there to evaluate? 1,024 O 25,600 O 64,000 O There are an infinite number of possibilities H OL < Prev 1 of 8 www www Next X
. If there are no restrictions (constraints) on the assignment of professors to offices, how many alternative assignments are there to
evaluate?
O 40,320
O64
O 1,024
O 25,600
O 64,000
O There are an Infinite number of possibilities
b. The blology department has sent the following Information and requests to the OSCM department:
Offices 1, 4, 5, and 8 are the only offices with windows.
A must be assigned Office 1.
D and E, the blology department co-chairpeople, must have windows.
H must be directly across the courtyard from D.
A, G, and H must be in the same wing.
F must not be next to D or G or directly across from G.
How many possible solutions (assignments of faculty to offices) satisfy all of the stated constraints?
Number to possible solutions
c. Suppose the biology department has selected the following final layout:
A-1
E-5
B-2
G-3
COURTYARD
F-6
C-7
H-4
Total flow-distance cost
D-8
What is the total flow-distance cost measure of this solution?
OL
1
E
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Transcribed Image Text:. If there are no restrictions (constraints) on the assignment of professors to offices, how many alternative assignments are there to evaluate? O 40,320 O64 O 1,024 O 25,600 O 64,000 O There are an Infinite number of possibilities b. The blology department has sent the following Information and requests to the OSCM department: Offices 1, 4, 5, and 8 are the only offices with windows. A must be assigned Office 1. D and E, the blology department co-chairpeople, must have windows. H must be directly across the courtyard from D. A, G, and H must be in the same wing. F must not be next to D or G or directly across from G. How many possible solutions (assignments of faculty to offices) satisfy all of the stated constraints? Number to possible solutions c. Suppose the biology department has selected the following final layout: A-1 E-5 B-2 G-3 COURTYARD F-6 C-7 H-4 Total flow-distance cost D-8 What is the total flow-distance cost measure of this solution? OL 1 E Prev 1 of 8 www 00 Next
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