Firms can adopt several strategies to increase their robustness to potential supply chain (SC) disruptions. One promising strategy is the use of a cross-functional team with representatives from functional departments. Such a team may facilitate sharing relevant information, enabling the firm to respond effectively to SC disruption warnings. However, despite their potential, cross-functional teams also differ in their ability to respond to SC disruption warnings and to ensure firm robustness. Extending insights from information-processing theory and team research to the field of SC management, we propose that a cross-functional team’s ability to handle high numbers of SC disruption warnings depends on the extent to which the team adopts centralized decision-making, with one or two members orchestrating the decision-making process. We also introduce internal integration problems as a mediating mechanism explaining why a cross-functional team lacking centralized decision-making may be unable to handle high numbers of SC disruption warnings. In two independent studies, we use multi-source data on cross-functional teams’ performance in dealing with SC disruption warnings during a realistic SC management simulation; the results support our predictions.