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Increasing penetration of variable loads and renewable resources in smart distribution networks brings about great challenges to the conventional scheduling and operation due to the uncertain nature. This paper presents a novel uncertainty handling framework, based on the underlying idea of robust optimization approach, to portray the uncertainties of load demands and wind power productions over uncertainty sets. Accordingly, a tractable min–max–min cost model is proposed to find a robust optimal day-ahead scheduling of smart distribution network immunizing against the worst-case realization of uncertain variables. In addition, considering demand response programs as one of the important resources in the smart distribution network, participation of customers in both energy and reserve scheduling is explicitly formulated. As the proposed min–max–min cost model cannot be solved directly by commercial optimization packages, a decomposition algorithm is presented based on dual cutting planes to decouple the problem into a master problem and a sub-problem. The master problem finds the day-ahead scheduling, while the sub-problem determines the worst-case realization of uncertain variables within uncertainty sets. Computational results for the modified version of IEEE 33-bus distribution test network demonstrate the effectiveness and efficiency of the proposed model.