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

Zhizhu Lai (), Qun Yue, Zheng Wang (), Dongmei Ge, Yulong Chen and Zhihong Zhou
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Zhizhu Lai: Gannan Normal University
Qun Yue: East China Normal University
Zheng Wang: East China Normal University
Dongmei Ge: Guizhou University of Engineering Science
Yulong Chen: Henan University
Zhihong Zhou: Guizhou University of Engineering Science

Journal of Combinatorial Optimization, 2022, vol. 44, issue 2, No 13, 1134-1160

Abstract: 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.

Keywords: Robust optimization; Facility location problem; p-robustness; Vertex substitution heuristic (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10878-022-00868-9

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