An integer programming approach
was used to find the alignment that minimizes the
sum of intradivisional distances.
The locations of the cities and the distances between any two
of them can be found here.
Table 1:
Optimal alignment for the unrestricted problem. Value: 27957km.
See map.
Division |
Teams |
1 |
Atlanta |
Carolina |
Cincinnati |
Tennessee |
2 |
Baltimore |
Buffalo |
Pittsburgh |
Washington |
3 |
New England |
New York Giants |
New York Jets |
Philadelphia |
4 |
Chicago |
Cleveland |
Detroit |
Indianapolis |
5 |
Dallas |
Denver |
Arizona |
Houston |
6 |
Jacksonville |
Miami |
New Orleans |
Tampa Bay |
7 |
Kansas City |
Green Bay |
Minnesota |
St Louis |
8 |
Oakland |
San Diego |
San Francisco |
Seattle |
|
Table 2:
Realignment chosen by the NFL. Value: 50480km.
See maps of the
NFC
and
AFC.
NFC |
|
South |
Atlanta |
Carolina |
New Orleans |
Tampa Bay |
North |
Chicago |
Detroit |
Green Bay |
Minnesota |
West |
Arizona |
St Louis |
San Francisco |
Seattle |
East |
Dallas |
NY Giants |
Philadelphia |
Washington |
AFC |
|
East |
New England |
Buffalo |
Miami |
NY Jets |
North |
Baltimore |
Cincinnati |
Cleveland |
Pittsburgh |
West |
Denver |
Kansas City |
Oakland |
San Diego |
South |
Houston |
Indianapolis |
Jacksonville |
Tennessee |
|
The alignment chosen by the NFL
has a sum of intradivisional distances of 50480km, which is 80% greater
than the alignment given in Table 1.
In the alignment given in Table 1, no team is more than one time zone
from any other team in its division.
If the teams in the NFC are selected as in Table 2,
then San Francisco must be at least two time zones away from
at least one other team in its division.
The choice made by the NFL minimizes the sum of intradivisional distances,
given the composition of the AFC and NFC and subject to three additional
restrictions:
-
Dallas and Washington in the same division as each other,
- Chicago, Detroit, Green Bay and Minnesota in the same division,
- Buffalo, Miami, the New York Jets, and New England
in the same division.
A map of the solution in Table 1 is available.
If the AFC and NFC are optimized with no additional restrictions, the optimal
value is 41152km, as in Table 3.
Table 3:
Optimal realignment for the NFL's choice of AFC and NFC.
Value: 41152km
See maps of the
NFC
and
AFC.
NFC |
|
South |
Atlanta |
Carolina |
New Orleans |
Tampa Bay |
North |
Chicago |
Green Bay |
Minnesota |
St Louis |
West |
Arizona |
Dallas |
San Francisco |
Seattle |
East |
Detroit |
NY Giants |
Philadelphia |
Washington |
AFC |
|
East |
Baltimore |
New England |
Buffalo |
NY Jets |
North |
Cincinnati |
Cleveland |
Indianapolis |
Pittsburgh |
West |
Denver |
Kansas City |
Oakland |
San Diego |
South |
Houston |
Jacksonville |
Miami |
Tennessee |
|
Table 4:
Optimal realignment for the NFL's choice of NFC,
with Dallas and Washington in the same division.
Increase over the NFC distance in Table 3: 4208km.
This differs from the NFL's choice in the alignment
of Minnesota and St. Louis, and is 791km smaller
than their choice for the NFC.
NFC |
|
South |
Atlanta |
Carolina |
New Orleans |
Tampa Bay |
North |
Chicago |
Detroit |
Green Bay |
St Louis |
West |
Arizona |
Minnesota |
San Francisco |
Seattle |
East |
Dallas |
NY Giants |
Philadelphia |
Washington |
|
If the Houston Texans had been placed in the NFC then the optimal value,
with the additional conditions, is 48499km.
but the AFC alignment is quite different --
see Table 5.
Table 5:
Optimal NFC alignment
if Houston placed in NFC, with the following restrictions:
(1)
Dallas and Washington in the same division as each other,
(2) Chicago, Detroit, Green Bay and Minnesota in the same division,
(3) Buffalo, Miami, the New York Jets, and New England
in the same division.
Optimal value: 48499km
Division |
Teams |
South |
Atlanta |
Carolina |
New Orleans |
Tampa Bay |
North |
Chicago |
Detroit |
Green Bay |
Minnesota |
West |
Arizona |
St Louis |
San Francisco |
Houston |
East |
Dallas |
NY Giants |
Philadelphia |
Washington |
AFC 1 |
New England |
Buffalo |
Miami |
New York Jets |
AFC 2 |
Baltimore |
Cleveland |
Jacksonville |
Pittsburgh |
AFC 3 |
Denver |
Oakland |
San Diego |
Seattle |
AFC 4 |
Cincinnati |
Indianapolis |
Kansas City |
Tennessee |
|
A team other than Seattle could have been moved from the AFC to the NFC.
Given the three additional conditions imposed by the NFL, the best choice
is to move are the Kansas City Chiefs. The optimal solution exchanges these two
teams in Table 2, giving a value of 48296km.
This is 4.3% less than the chosen solution.
If all three restrictions are imposed without
assigning each team to a particular conference,
the optimal solution has value 37126km,
with the alignment given in Table 6.
Table 6:
Optimal alignment without preselecting conferences but
with three restrictions:
(1)
Dallas and Washington in the same division as each other,
(2) Chicago, Detroit, Green Bay and Minnesota in the same division,
(3) Buffalo, Miami, the New York Jets, and New England
in the same division.
Optimal value: 37126km.
Division |
Teams |
1 |
Atlanta |
Carolina |
Jacksonville |
Tampa Bay |
2 |
Chicago |
Detroit |
Green Bay |
Minnesota |
3 |
Arizona |
St Louis |
Denver |
Kansas City |
4 |
Dallas |
New Orleans |
Washington |
Houston |
5 |
New England |
Buffalo |
Miami |
New York Jets |
6 |
Baltimore |
New York Giants |
Philadelphia |
Pittsburgh |
7 |
Cincinnati |
Cleveland |
Indianapolis |
Tennessee |
8 |
Oakland |
San Diego |
San Francisco |
Seattle |
|