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

Authors: Daisuke Hasegawa; Naoshi Shiono

Addresses: Center for Real Estate Innovation, The University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo, 113-0033, Japan ' School of Business Administration, Senshu University, 2-1-1, Higashimita, Tama, Kawasaki, Kanagawa, 214-8580, Japan

Abstract: 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.

Keywords: travelling salesman problem; continuous approximation models; territory design; rectilinear metric.

DOI: 10.1504/AJMSA.2025.148897

Asian Journal of Management Science and Applications, 2025 Vol.8 No.2, pp.218 - 232

Received: 01 May 2024
Accepted: 20 Jul 2024
Published online: 01 Oct 2025 *