Estimation of average TSP distance considering zone length-width ratio: implications for territory design

In vehicle routing, estimating route lengths using continuous approximation models can be valuable for delivery planning, particularly for tour cost estimation and territory design, because it eliminates the computational costs associated with solving TSP and VRP directly. In this study, we propose a route-length estimation formula based on rectilinear distances by considering the shape of the area. We calibrate the parameters through numerical experiments and apply them to a territorial decision problem. Thus, our proposed formula can estimate the average tour length over a rectilinear distance with high accuracy. As the number of points increases, the influence of the shape decreases.