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In this work we present efficient solution strategies for the task of designing supply chains with theexplicit consideration of the detailed plant performance of the embedded facilities. Taking as a basisa mixed- integer linear programming (MILP) model introduced in a previous work, we propose threesolution strategies that exploit the underlying mathematical structure: A bi-level algorithm, a Lagrangeandecomposition method, and a hybrid approach that combines features from both of these two methods. Numerical results show that the bi-level method outperforms the others, leading to significant CPUsavings when compared to the full space MILP.