Mobility Data in Operations: The Facility Location Problem

TL;DR

This paper introduces a new variant of the facility location problem incorporating individual mobility data, providing a polynomial-time approximation algorithm with proven bounds and validating it through extensive experiments.

Contribution

The paper formulates a novel facility location problem using mobility data, develops a polynomial-time approximation algorithm, and extends the model to multiple locations with empirical validation.

Findings

Approximation ratio of the algorithm is at most 2.497.

No polynomial-time algorithm can achieve better than 2-psilon approximation.

Algorithm performs well on synthetic and real-world US census data.

Abstract

The recent large scale availability of mobility data, which captures individual mobility patterns, poses novel operational problems that are exciting and challenging. Motivated by this, we introduce and study a variant of the (cost-minimization) facility location problem where each individual is endowed with two locations (hereafter, her home and work locations), and the connection cost is the minimum distance between any of her locations and its closest facility. We design a polynomial-time algorithm whose approximation ratio is at most 2.497. We complement this positive result by showing that the proposed algorithm is at least a 2.428-approximation, and there exists no polynomial-time algorithm with approximation ratio $2-\epsilon$ under UG-hardness. We further extend our results and analysis to the model where each individual is endowed with K locations. Finally, we conduct numerical experiments over both synthetic data and US census data (for NYC, greater LA, greater DC, Research Triangle) and evaluate the performance of our algorithms.