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Robust solutions to Euclidean facility location problems with uncertain data

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  • We consider uncertainty Euclidean facility location problems. Using the existing robust optimization methodology, we certainly obtain robust optimal solution of the Euclidean facility location problem with unknown-but-bounded uncertainty or with an ellipsoidal uncertainty by solving an SOCP or an SDP. In addition, we show that the robust counterpart of the Euclidean facility location problem with $\cap$-ellipsoidal uncertainty is NP-hard. We give an explicit SDP to approximate the NP-hard problem and estimate the quality of the approximation via the level of conservativeness.
    Mathematics Subject Classification: Primary: 90C08; Secondary: 90C25.


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