Tuesday 23 June 2015

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 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.

Picture

The following distances and two-way 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              


 
TWO-WAY 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 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.

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:

A-1
B-2
G-3
H-4
COURTYARD
E-5
F-6
C-7
D-8

c. What is the total flow-distance cost measure of this solution?

  Total flow-distance cost  


Explanation: