In this work we present efficient solution strategies for the task of designing supply chains with the explicit consideration of the detailed plant performance of the embedded facilities. Taking as a basis a mixed-integer linear programming (MILP) model introduced in a previous work, we propose three solution strategies that exploit the underlying mathematical structure: A bi-level algorithm, a Lagrangean decomposition 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 CPU savings when compared to the full space MILP. (C) 2013 Elsevier Ltd. All rights reserved.