The N -1-1 contingency reliability criterion considers the consecutive loss of two components in a power system, with intervening time for system adjustments between the two losses. In this paper, we consider the problem of optimizing generation unit while ensuring the N -1-1 criterion. Due to the coupling of time pe- riods associated with consecutive component losses, the resulting problem yields a very large-scale mixed-integer linear optimization model. For efficient solution, we introduce a novel branch-and-cut algorithm using a temporally decomposed bilevel separation or- acle. The model and algorithm are assessed using multiple IEEE test systems, and a comprehensive analysis is performed to compare system performance across different contingency criteria. Compu- tational results demonstrate the value of considering intervening time for system adjustments in terms of total cost and system ro- bustness.