We address the dynamic design of supply chain networks in which the moments of demand distribution function are uncertain and facilities’ availability is stochastic because of possible disruptions. To incorporate the existing stochasticity in our dynamic problem, we develop a multi-stage stochastic program to specify the optimal location, capacity, inventory, and allocation decisions. Further, a data-driven rolling horizon approach is developed to use observations of the random parameters in the stochastic optimization problem. In contrast to traditional stochastic programming approaches that are valid only for a limited number of scenarios, the rolling horizon approach makes the determined decisions by the stochastic program implementable in practice and evaluates them. The stochastic program is presented as a quadratic conic optimization, and to generate an efficient scenario tree, a forward scenario tree construction technique is employed. An extensive numerical study is carried out to investigate the applicability of the presented model and rolling horizon procedure, the efficiency of risk-measurement policies, and the performance of the scenario tree construction technique. Several key practical and managerial insights related to the dynamic supply chain network design under uncertainty are gained based on the computational results.