Approximating the Length of Vehicle Routing Problem Solutions Using Complementary Spatial Information

Accurately estimating the length of Vehicle Routing Problem (VRP) distances can inform transportation planning in a wide variety of delivery and service provision contexts. This study extends the work of previous research where multiple linear regression models were used to estimate the average distance of VRP solutions with various customer demands and capacity constraints. This research expands on that approach in two ways: first, the point patterns used in estimation have a wider range of customer clustering or dispersion values as measured by the Average Nearest Neighbor Index (ANNI) as opposed to just using a Poisson or random point process; second, the tour coefficient adjusted by this complementary spatial information is shown to exhibit statistically more accurate estimations. To generate a full range of ANNI values, point patterns were simulated using a Poisson process, a Matern clustering process, and a simple sequential inhibition process to obtain random, clustered, and dispersed point patterns, respectively. The coefficients of independent variables in the models were used to explain how the spatial distributions of customers influence the VRP distances. These results demonstrate that complementary spatial data can be used to improve operational results, a concept that could be applied more broadly.