This thesis focuses on the modeling and solution methods for facility location and network design problems under uncertainty, with a particular emphasis on robust optimization with integer recourse. The application studied concerns the blood supply chain in the context of disasters, where demand is uncertain, infrastructures may be damaged, and an emergency response must be implemented.
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This thesis focuses on the modeling and solution methods for facility location and network design problems under uncertainty, with a particular emphasis on robust optimization with integer recourse. The application studied concerns the blood supply chain in the context of disasters, where demand is uncertain, infrastructures may be damaged, and an emergency response must be implemented.
In this work, we developed several mathematical formulations based on discrete uncertainty sets, incorporating different risk measures: the expectation, the Conditional Value-at-Risk (CVaR), and the worst-case approach. To solve these models, we implemented decomposition techniques, including Benders decomposition (in its multi-cut and stabilized variants) and the Column-and-Constraint Generation (CCG) algorithm. To improve solution quality, especially for large-scale instances, we also proposed an adjustable robust model based on continuous uncertainty sets. Using different types of sets, we applied affine decision rules as well as a static approach for recourse decisions in order to ensure tractability.
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This project aims at proposing theoretical and practical results for hard combinatorial optimization problems in an uncertain environment. These problems have in common the fact that the parameters needed to assess the validity of the solution and compute its cost are unknown. Uncertainty in decision making can be caused by several external factors. The most common are related to stochastic parameters (service demand, time needed for a task, prices, …). Incomplete information can also come from the presence of competitors whose policies are not known to the decision maker.
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