Models to estimate average route lengths in different geographical environments

This paper investigates how average route lengths for travelling salesman-type journeys are influenced by the pattern and number of points visited. Two mathematical functions to estimate average route lengths are presented. The first function relates to average route lengths when n points are randomly located and the second to average route lengths when certain areas are more likely to be visited than the others, as defined by ‘demand surfaces’. Estimation of route lengths in this way can be a useful tool in the analysis of strategic and operational distribution problems, particularly in public services such as health and social services.