Planning Approximations to the Average Length of Vehicle Routing Problems with Varying Customer Demands and Routing Constraints

This paper studies approximations to the average length of vehicle routing problems (VRPs). The approximations are valuable for strategic and planning analysis of transportation and logistics problems. The focus is on VRPs with varying numbers of customers, demands, and locations. This modeling environment can be used in transport and logistics models that deal with a distribution center serving an area with daily variations in demand. The routes are calculated daily on the basis of what freight is available. New approximations and experimental settings are introduced. Average distance traveled is estimated as a function of the number of customers served and the number of routes needed. Approximations are tested in instances with different customer spatial distributions, demand levels, numbers of customers, and time windows. Regression results indicate that the proposed approximations can reasonably predict the average length of VRPs in randomly generated problems and real urban networks.