The Length of Tours in Zones of Different Shapes

The object of this paper is to explain how the expected length of traveling salesman tours changes with zone shape. To do this, a simple strategy that yields good traveling salesman tours is presented. The resulting tours are suboptimal but appear to be close to those that can be obtained by hand. Thus, the formulas that are provided may also be indicative of the length of tours built with better strategies. The results of this paper are useful for the design of distribution systems.