The 1-Center and 1-Highway problem

TL;DR

This paper investigates an extension of the 1-center problem by adding a highway to optimize transportation time, analyzing different highway types and length constraints to improve facility placement strategies.

Contribution

It introduces a novel variation of the 1-center problem incorporating highways, analyzing fixed and adjustable highway lengths for optimal facility and highway placement.

Findings

Optimal placement strategies for facilities and highways identified.

Comparison between freeways and turnpikes in minimizing travel time.

Impact of highway length constraints on solution quality.

Abstract

We study a variation of the 1-center problem in which, in addition to a single supply facility, we are allowed to locate a highway. This highway increases the transportation speed between any demand point and the facility. That is, given a set $S$ of points and $v>1$, we are interested in locating the facility point $f$ and the highway $h$ that minimize the expression $\max_{p\in S}d_{h}(p,f)$, where $d_h$ is the time needed to travel between $p$ and $f$. We consider two types of highways ({\em freeways} and {\em turnpikes}) and study the cases in which the highway's length is fixed by the user (or can be modified to further decrease the transportation time).