This paper addresses a key objective of the supply chain strategic design, i.e., the optimal selection of suppliers under uncertainty. A methodology integrating the cross-efficiency Data Envelopment Analysis and the Monte Carlo approach is proposed. Their combination allows overcoming the deterministic feature of the classical cross-efficiency DEA. Moreover, we define an indicator of the robustness of the determined supplier ranking. The resulting technique allows managing the supplier selection problem while considering nondeterministic input and output data, a significant circumstance for assessing potential suppliers, with which there are no previous commercial relationships. The approach helps buyers in choosing the right partners under uncertainty and ranking them upon a multiple sourcing strategy.