Variational Analysis of Directional Minimal Time Functions and Applications to Location Problems

TL;DR

This paper analyzes directional minimal time functions using variational analysis, providing new insights into their properties and applying these to develop a novel facility location model involving sets.

Contribution

It introduces a new variational analysis framework for directional minimal time functions and applies it to a set-based facility location problem.

Findings

Derived differentiation properties of directional minimal time functions

Developed a new facility location model involving sets

Extended variational analysis techniques to location problems

Abstract

This paper is devoted to the study of directional minimal time functions that specify the minimal time for a vector to reach an object following its given direction. We provide a careful analysis of general and generalized differentiation properties of this class of functions. The analysis allows us to study a new model of facility location that involves sets. This is a continuation of our effort in applying variational analysis to facility location problems.