Optimal location problems with routing cost

TL;DR

This paper introduces a new model for optimal location problems that incorporates routing costs, analyzing the limit as the number of points grows large and applying it to airfreight systems.

Contribution

It extends traditional location models by including routing costs and characterizes the limit problem as the number of points approaches infinity.

Findings

Limit problem characterized for large N

Application to airfreight system optimization

Routing costs significantly impact location decisions

Abstract

In the paper a model problem for the location of a given number $N$ of points in a given region $\Omega$ and with a given resources density $\rho(x)$ is considered. The main difference between the usual location problems and the present one is that in addition to the location cost an extra {\it routing cost} is considered, that takes into account the fact that the resources have to travel between the locations on a point-to-point basis. The limit problem as $N\to\infty$ is characterized and some applications to airfreight systems are shown.