Revisiting Continuous p-Hub Location Problems with the L1 Metric
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866915104256163840 |
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| author | Wu, Yifan Geunes, Joseph Nie, Xiaofeng |
| author_facet | Wu, Yifan Geunes, Joseph Nie, Xiaofeng |
| contents | Motivated by emerging urban applications in commercial, public sector, and humanitarian logistics, we revisit continuous $p$-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_08439 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Revisiting Continuous p-Hub Location Problems with the L1 Metric Wu, Yifan Geunes, Joseph Nie, Xiaofeng Optimization and Control Motivated by emerging urban applications in commercial, public sector, and humanitarian logistics, we revisit continuous $p$-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. |
| title | Revisiting Continuous p-Hub Location Problems with the L1 Metric |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2501.08439 |