Revisiting Continuous p-Hub Location Problems with the L1 Metric
Abstract
Motivated by emerging urban applications in commercial, public sector, and humanitarian logistics, we revisit continuous -hub location problems in which several facilities must be located in a continuous space such that the expected minimum Manhattan travel distance from a random service provider to a random customer through exactly one hub facility is minimized. In this paper, we begin by deriving closed-form results for a one-dimensional case and two-dimensional cases with up to two hubs. Subsequently, a simulation-based approximation method is proposed for more complex two-dimensional scenarios with more than two hubs. Moreover, an extended problem with multiple service providers is analyzed to reflect real-life service settings. Finally, we apply our model and approximation method using publicly available data as a case study to optimize the deployment of public-access automated external defibrillators in Virginia Beach.
Cite
@article{arxiv.2501.08439,
title = {Revisiting Continuous p-Hub Location Problems with the L1 Metric},
author = {Yifan Wu and Joseph Geunes and Xiaofeng Nie},
journal= {arXiv preprint arXiv:2501.08439},
year = {2025}
}