Runway scheduling deals with the sequencing of arriving and departing aircraft at airports such that a predefined objective is optimized subject to several operational constraints. Different from the existing deterministic approaches in the literature, we consider a new approach to the stochastic version of this problem within the general context of machine scheduling problems. As part of our analysis, we first show that a restricted version of the stochastic runway-scheduling problem is equivalent to a machine-scheduling problem on a single machine with sequence-dependent setup times and stochastic due dates. We then extend this restricted model by considering characteristics specific to the runway-scheduling problem and present two different stochastic integer programming models. We derive some tight valid inequalities for these formulations and propose a solution methodology based on sample average approximation and Lagrangian-based scenario decomposition. Realistic data sets are then used to perform a...