How to: solve the sales man problem

The sales man problem is a famous problem in applied mathematics.

The task is easy to define:
A salesman shall visit all the customers in his territory, using the shortest travel path.

With only a few customers, this is not such a big problem, but with more than 30, it gets already difficulty and with much more, it may  not be solvable with the most powerful computers.

But for practical applications, one can use the following simple method, to find an acceptable solution:

• Look at your territory and mark the center of the distribution of your customers
• Around this center draw circles with radiuses, which increase.
• Divide all circles in 6 sections.
• Start in the center and cover all customers in one section, when you reach the customer  at the last circle,  go to the next section and then go backwards to the center.
• Repeat this procedure for all sections.

That procedure will not give the shortest possible travel path, but a reasonable short one.

The same method can be applied to similar problems, at which some points have to be connected, using the shortest connection path like:

• electrical cabling
• location of production facilities or distibution centers
• emergency centers