Stability and Robustness: Reliability in the World of Uncertainty
Stability and Robustness: Reliability in the World of Uncertainty
Stability and Robustness: Reliability in the World of Uncertainty
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Exact algorithms•Kouvelis <strong>and</strong> Yu 1997 – first formulation for f<strong>in</strong>ite set <strong>of</strong> scenarios. Ithas been proven that <strong>the</strong> problem is NP-hard for bounded set S <strong>and</strong>strongly NP-hard for unbounde set S.•Yaman, Karasan <strong>and</strong> P<strong>in</strong>ar (2001) – basic <strong>the</strong>oretical backgrounds for<strong>the</strong> problem•Aron <strong>and</strong> Hentenryck (2002) – one more evidence <strong>of</strong> NP-hardness: <strong>the</strong>RST problem is related to <strong>the</strong> well-known central tree problem. Twocases when <strong>the</strong> RST problem is easily solvable:a) no edge <strong>in</strong>tervals have <strong>in</strong>tersectionsb) graph is complete <strong>and</strong> all edge costs take <strong>the</strong>ir value from <strong>the</strong> same<strong>in</strong>terval•Montemanni <strong>and</strong> Gambardella (2003) – branch <strong>and</strong> bound procedurewhich outperforms all exact algorithms known before16/04/2009 Yury Nikul<strong>in</strong>, Sensitivity analysis 17
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