Formulas for Estimating Average Distance Traveled in Vehicle Routing Problems in Elliptic Zones

Abstract

This paper defines some compact expressions to evaluate the average distance traveled in VRP problems in circular and elliptic zones. These formulas have been carried out empirically from the results obtained by the application to a set of problems of heuristic algorithms (Clarke & Wright, Fisher & Jaikumar and Gillet & Miller) and Daganzo’s method based on continuous approximations of the demand spatial distribution. The problems are solved and designed automatically by a computer. Vehicle capacity has been the only constraint considered in the tour design. If N is the number of points and C is the vehicle capacity, it has been shown that the Clarke and Wright algorithm provides the best solutions especially when N<50 or N/C<14. On the other hand, solutions with Daganzo’s method are not adequate when N/C≤3.