How to design and scale sales territory?

My first naive approach is:

• Given N number of salesmen. Cluster an area to be N clusters with almost equal number of clients [1] with some kind of same-size clustering/facility location algorithm
• Assign 1 salesman to 1 territory (one-to-one assignment)

The question is:

• How should we divide the territory gracefully if the number of salesmen increase/decrease from N=10 to N=9, N=11, or N=20?
• Is one-to-one assignment is doomed to fail? What are the alternatives for designing and scaling sales territory?

Because:

• the location of centroids could be very different between N=9, N=10, N=11. It can make the territories very different.
• increase of salesman from N=10 to N=20 will shrink the area of previous territory

Out of scope for this question:

• Routing (TSP/VRP). TSP with Time Window would be done after sales territory, but it's out of this question scope. This question is more about designing/scaling the sales territory itself.

Notes:

[1] We could use equal expected sales amount, but for argument sake let's use number of clients.

• Welcome to OR.SE! I think you need to provide more information about your problem. What are you trying to do? Are you trying to assign N salesmen to M clients based on some constraints? If so, what are they? Do the salesmen need to start and end from the same location? Is there a time constraint? What's your objective? Your problem seems like a VRP. But provide more detail to get better answers. – EhsanK May 24 '20 at 18:23
• @rilut, if the problem you mentioned consists of different areas and you are willing to partition the problem based on the sales territory, one possible way is to decompose your model regarding this territory and then solve the model by using a variant of VRP models as EhsanK mentioned too. – A.Omidi May 24 '20 at 21:17