The
Dorton University president has asked the OM department to assign eight
biology professors (A, B, C, D, E, F, G, and H) to eight offices
(numbered 1 to 8 in the diagram) in the new biology building.
The following distances and twoway flows are given:
DISTANCES BETWEEN OFFICES (FEET)
 
1

2

3

4

5

6

7

8
 
1  —  10  20  30  15  18  25  34 
2  —  10  20  18  15  18  25  
3  —  10  25  18  15  18  
4  —  34  25  18  15  
5  —  10  20  30  
6  —  10  20  
7  —  10  
8  —  

TWOWAY FLOWS (UNITS PER PERIOD)
 
A

B

C

D

E

F

G

H
 
A  —  4  0  0  6  0  0  0 
B  —  0  0  0  5  0  5  
C  —  0  0  0  0  6  
D  —  1  0  0  0  
E  —  3  0  0  
F  —  2  0  
G  —  1  
H  —  

a. 
If
there are no restrictions (constraints) on the assignment of professors
to offices, how many alternative assignments are there to evaluate?

40,320 
The biology 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 biology department cochairpeople, 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. 
b.  How many possible solutions (assignments of faculty to offices) satisfy all of the stated constraints? 
Number to possible solutions 
Assume the solution is as follows: 
A1

B2

G3

H4

COURTYARD
 
E5

F6

C7

D8

c.  What is the total flowdistance cost measure of this solution? 
Total flowdistance cost 
a.
b.
c.
For
any problem with an equal number of assignees and slots (call this
“n”), the number of possible assignments is n! = n × n − 1 × n − 2 × n −
3 × … × 1.Therefore, in this problem, the number of possible
assignments is 8! = 40,320.

b.
There are two solutions that satisfy the constraints: 
A1

C2

G3

H4

COURTYARD
 
E5

F6

B7

D8

A1

B2

G3

H4

COURTYARD
 
E5

F6

C7

D8

c.
Generally
speaking, for all 28 pairs of offices, multiply the distance between
the offices times the twoway flows between the faculty that occupy
those offices. Then sum up the results to get the total flowdistance
measure. Here you only need to worry about those office pairs where
there is travel between the assigned faculty members (nonzero flow),
significantly reducing your computational work.
