In this paper, we offer a new network perspective on one of the central topics in Operations Management - demand variability and the bullwhip effect (BWE). The topic has both practical and scholarly implications. We start with a puzzling observation: while the traditional intra-firm measure of the BWE increases at upstream layers of the network, the demand variability experienced by upstream firms actually decreases. To reconcile these two facts, we hypothesize that firms manage their customer base to smooth out the aggregate demand. We test the hypothesis with a novel data set that tracks the evolution of supply relationships over time. By examining customer acquisition, drop, and swap decisions made by suppliers, we provide evidence that buyer-supplier relationship formation or dissolution is associated with smoothing of the aggregate demand experienced by suppliers. This provides a fresh insight into how firms may leverage their buyer- supplier relationships to mitigate the impact of the BWE.