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 (VRP). The approximations are valuable for strategic and planning analysis of transportation and logistics problems. The research focus is on VRP with varying number 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 the demand. The routes are calculated daily based on what freight is available. New approximations and experimental settings are introduced. Average distance travelled 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, number of customers, and time windows, Regression results indicate that the proposed approximations can reasonably predict the average length of VRP problems in randomly generated problems and real urban networks.