Joint Facility and Demand Location Problem

TL;DR

This paper introduces a new optimization framework for jointly locating facilities and demand nodes, extending classic problems like k-median and k-center, with applications demonstrated in hurricane evacuation scenarios.

Contribution

It formulates joint facility and demand location problems as integer programs and proposes a local search heuristic for solving them.

Findings

Heuristic performs well with many potential locations.

Joint location problems are more challenging than traditional fixed-demand models.

Application to hurricane evacuation shows practical relevance.

Abstract

In typical applications of facility location problems, the location of demand is assumed to be an input to the problem. The demand may be fixed or dynamic, but ultimately outside the optimizers control. In contrast, there are settings, especially in humanitarian contexts, in which the optimizer decides where to locate a demand node. In this work, we introduce an optimization framework for joint facility and demand location. As examples of our general framework, we extend the well-known k-median and k-center problems into joint facility and demand location problems (JFDLP) and formulate them as integer programs. We propose a local search heuristic based on network flow. We apply our heuristic to a hurricane evacuation response case study. Our results demonstrate the challenging nature of these simultaneous optimization problems, especially when there are many potential locations. The local search heuristic is most promising when the the number of potential locations is large, while the number of facility and demand nodes to be located is small.