We develop an actionable data-driven approach to a periodic-review dual sourcing inventory management system in the presence of purchase price and demand uncertainties. The two supply sources differ in their lead times and prices due to, e.g., different transportation modes. We adopt robust optimization because the limited historical data is insufficient to construct meaningful distributions to characterize purchase price and demand fluctuations. Specifically, we build a robust rolling-horizon model and, in particular, construct the uncertainty sets from data and business insights. Using a real four-year data set, we show that our approach can yield significant cost savings compared to the other popular methods. Our experiments echo the earlier theoretical finding that a firm may incur a lower cost under a more volatile purchase price process. However, we find that under data-driven decision-making, in comparison with the theoretical results that assume complete distributional information, some interesting results arise. For example, first, considering a longer planning horizon may backfire. Second, some feasible region-reducing business constraints such as limited inventory capacity may lead to unintended benefits. These are consequences of protecting model performance from sampling error and our practically limited forecast ability, as almost always, to characterize uncertainties. Our research therefore calls for prudence in extending theoretical insights to data-driven decision-making scenarios.