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

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 ro...

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Bibliographic Details
Published in:Journal of combinatorial optimization Vol. 44; no. 2; pp. 1134 - 1160
Main Authors: Lai, Zhizhu, Yue, Qun, Wang, Zheng, Ge, Dongmei, Chen, Yulong, Zhou, Zhihong
Format: Journal Article
Language:English
Published: New York Springer US 01.09.2022
Springer Nature B.V
Subjects:
Algorithms
Combinatorics
Convex and Discrete Geometry
Heuristic methods
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Operations research
Operations Research/Decision Theory
Optimization
Parameter robustness
Robustness (mathematics)
Site selection
Theory of Computation
Uncertainty
p-robustness
Robust optimization
Facility location problem
Vertex substitution heuristic
ISSN:1382-6905, 1573-2886
Online Access:Get full text
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Summary: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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ISSN:1382-6905
1573-2886
DOI:10.1007/s10878-022-00868-9