Problem $8-3($Algo$)$

The Dorton University president has asked the OSCM 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.

An illustration shows layout of different offices allocation in the new biology building. The layout shows the new biology building with four offices each on both the sides of the courtyard. North wing has offices numbered from $1$ to $4$ and south wing has offices numbered from $5$ to $8.$

The following distances and two$-$way flows are given:

DISTANCES BETWEEN OFFICES $($FEET$)$

$12345678$

$110203015182534$

$20102018151825$

$3001025181518$

$400034251815$

$50000102030$

$6000001020$

$700000010$

$80000000$

TWO$-$WAY FLOWS $($UNITS PER PERIOD$)$

A B C D E F G H

A $2006000$

B $0000202$

C $0000004$

D $0003000$

E $0000300$

F $0000020$

G $0000002$

H $0000000$

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

multiple choice

$40,320$

$64$

$1,024$

$25,600$

$64,000$

There are an infinite number of possibilities

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$.$

How many possible solutions $($assignments of faculty to offices$)$ satisfy all of the stated constraints?

Suppose the biology department has selected the following final layout:

An illustration shows layout of final allocation in the new biology building. The layout shows the new biology building with four offices each on both the sides of the courtyard. North wing has offices numbered A $-1,$ B $-2,$ G $-3,$ and H $-4$ and south wing has offices numbered E $-5,$ F $-6,$ C $-7,$ and D $-8.$

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