Average TSP Tour Length Approximations for Territory Design

In vehicle routing, estimating route lengths using continuous approximation models can be valuable for delivery planning, especially for tour cost estimation and territory design because it avoids the computational cost 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 calibrated the parameters through numerical experiments. Thus, our proposed formula can estimate the average tour length in rectilinear distance with high accuracy; and as the number of points increases, the influence of the shape decreases.