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The min-p robust optimization approach for facility location problem under uncertainty

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Abstract

Improper value of the parameter p in robust constraints will result in no feasible solutions while applying stochastic p-robustness optimization approach (p-SRO) to solving facility location problems under uncertainty. Aiming at finding the lowest critical p-value of parameter p and corresponding robust optimal solution, we developed a novel robust optimization approach named as min-p robust optimization approach (min-pRO) for P-median problem (PMP) and fixed cost P-median problem (FPMP). Combined with the nearest allocation strategy, the vertex substitution heuristic algorithm is improved and the influencing factors of the lowest critical p-value are analyzed. The effectiveness and performance of the proposed approach are verified by numerical examples. The results show that the fluctuation range of data is positively correlated with the lowest critical p-value with given number of new facilities. However, the number of new facilities has a different impact on lowest critical p-value with the given fluctuation range of data. As the number of new facilities increases, the lowest critical p-value for PMP and FPMP increases and decreases, respectively.

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Availability of data and materials

The datasets used and analyzed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

This research was supported by National Natural Science Foundation of China (41671396), Scientific Research Foundation for PhD of GNNU (BSJJ202116) and Guizhou Theoretical Innovation Joint Project of China (GZLCLH-2020-331, GZLCLH-2021-86).

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Authors and Affiliations

  1. School of Geography and Environmental Engineering, Gannan Normal University, Ganzhou, 341000, China

    Zhizhu Lai

  2. Key Laboratory of Geographic Information Science, Ministry of Education, East China Normal University, Shanghai, 200241, China

    Zhizhu Lai, Qun Yue & Zheng Wang

  3. Guizhou University of Engineering Science, Bijie, 551700, Guizhou, China

    Dongmei Ge & Zhihong Zhou

  4. Key Research Institute of Yellow River Civilization and Sustainable Development and Collaborative Innovation Center On Yellow River Civilization of Henan Province, Henan University, Kaifeng, 475001, China

    Yulong Chen

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  1. Zhizhu Lai
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Lai, Z., Yue, Q., Wang, Z. et al. The min-p robust optimization approach for facility location problem under uncertainty. J Comb Optim 44, 1134–1160 (2022). https://doi.org/10.1007/s10878-022-00868-9

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