minimize distance

I have a national chain of 100 stores with 10 regional managers covering 10 stores each. Each manager travels 45 times a year (store 1 to 2...9 to 10). How do I group my managers so as to minimize total distance travelled? Bonus for p&oviding general solution ...

Operations Research homework?

Quote: mew3782

I have a national chain of 100 stores with 10 regional managers covering 10 stores each. Each manager travels 45 times a year (store 1 to 2...9 to 10). How do I group my managers so as to minimize total distance travelled? Bonus for p&oviding general solution ...

This is known as a "Traveling Salesman Problem". See a resource here.

Well, if the managers are assigned to 10 set stores and the managers' home locations are also set, then it is 10 independent TSPs. However, the phrase "how do I group my managers" makes me think that we can relocate the managers and reassign the stores. In that case, it's more like a multi-depot vehicle routing problem (VRP).

I don't see why a manager has to travel 45 times a year.
In the TSP, you have one circuit to find, passing through each town once.
Why should you want to do each town-to-town pair?

This is actually more like what I need, yes.

I don't actually own any stores. The real origin of my question, you can replace "me" with "the NCAA", my managers with "The Big Ten, the Pac-12", etc, and my stores with individual schools, who need to travel between each other. Basically, if the NCAA had to bucket all of its universities in such a way to minimize total travel, how would it do it...