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The P-Hub maximal covering problem and extensions for gradual decay functions

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  • Peker, Meltem
  • Kara, Bahar Y.

Abstract

The p-hub maximal covering problem aims to find the best locations for hubs so as to maximize demands within a coverage distance with a predetermined number of hubs. Classically, the problem is defined in the framework of binary coverage only; an origin–destination pair is covered if the cost (time, etc.) is lower than the critical value, and not covered at all if the cost is greater than the critical value. In this paper, we extend the definition of coverage, introducing “partial coverage”, which changes with distance. We present new and efficient mixed-integer programming models that are also valid for partial coverage for single and multiple allocations. We present and discuss the computational results with different data sets.

Suggested Citation

  • Peker, Meltem & Kara, Bahar Y., 2015. "The P-Hub maximal covering problem and extensions for gradual decay functions," Omega, Elsevier, vol. 54(C), pages 158-172.
    • Handle: RePEc:eee:jomega:v:54:y:2015:i:c:p:158-172
    DOI: 10.1016/j.omega.2015.01.009
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    2. Paul, Nicholas R. & Lunday, Brian J. & Nurre, Sarah G., 2017. "A multiobjective, maximal conditional covering location problem applied to the relocation of hierarchical emergency response facilities," Omega, Elsevier, vol. 66(PA), pages 147-158.
    3. Taherkhani, Gita & Alumur, Sibel A., 2019. "Profit maximizing hub location problems," Omega, Elsevier, vol. 86(C), pages 1-15.
    4. Madani, Seyed Reza & Shahandeh Nookabadi, Ali & Hejazi, Seyed Reza, 2018. "A bi-objective, reliable single allocation p-hub maximal covering location problem: Mathematical formulation and solution approach," Journal of Air Transport Management, Elsevier, vol. 68(C), pages 118-136.
    5. Sudtachat, Kanchala & Mayorga, Maria E. & Mclay, Laura A., 2016. "A nested-compliance table policy for emergency medical service systems under relocation," Omega, Elsevier, vol. 58(C), pages 154-168.
    6. Ghaffarinasab, Nader & Motallebzadeh, Alireza, 2018. "Hub interdiction problem variants: Models and metaheuristic solution algorithms," European Journal of Operational Research, Elsevier, vol. 267(2), pages 496-512.
    7. Gusev, Vasily V., 2023. "Set-weighted games and their application to the cover problem," European Journal of Operational Research, Elsevier, vol. 305(1), pages 438-450.
    8. Silva, Marcos Roberto & Cunha, Claudio B., 2017. "A tabu search heuristic for the uncapacitated single allocation p-hub maximal covering problem," European Journal of Operational Research, Elsevier, vol. 262(3), pages 954-965.
    9. Yang, Lingxiao & Zheng, Jianfeng & Wang, Jian & Hu, Xiaowei, 2023. "The maximal detour liner shipping hub location problem: Improving the applicability of the p-hub center problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 179(C).
    10. Delle Donne, Diego & Alfandari, Laurent & Archetti, Claudia & Ljubić, Ivana, 2023. "Freight-on-Transit for urban last-mile deliveries: A strategic planning approach," Transportation Research Part B: Methodological, Elsevier, vol. 169(C), pages 53-81.
    11. Olivera Janković & Stefan Mišković & Zorica Stanimirović & Raca Todosijević, 2017. "Novel formulations and VNS-based heuristics for single and multiple allocation p-hub maximal covering problems," Annals of Operations Research, Springer, vol. 259(1), pages 191-216, December.
    12. Aijun Liu & Xiaohui Ji & Sang-Bing Tsai & Hui Lu & Gang Du & Feng Li & Guodong Li & Jiangtao Wang, 2018. "An Empirical Study on the Innovation Sharing Express Box: Collaborative Consumption and the Overlay Network Design," Sustainability, MDPI, vol. 10(7), pages 1-19, June.
    13. Rahmati, Reza & Neghabi, Hossein & Bashiri, Mahdi & Salari, Majid, 2023. "Stochastic regional-based profit-maximizing hub location problem: A sustainable overview," Omega, Elsevier, vol. 121(C).
    14. Ghaffarinasab, Nader & Kara, Bahar Y. & Campbell, James F., 2022. "The stratified p-hub center and p-hub maximal covering problems," Transportation Research Part B: Methodological, Elsevier, vol. 157(C), pages 120-148.
    15. Vasily V. Gusev, 2021. "Set-weighted games and their application to the cover problem," HSE Working papers WP BRP 247/EC/2021, National Research University Higher School of Economics.
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