A methodology of multilevel organizational management is proposed for the design and implementation of complex projects at the national, regional, and municipal levels. Its main elements are described. At the top hierarchy level, under conditions of environmental uncertainty, goal-setting functions are performed as scenarios (sequences of expertly significant control events) for project implementation and search for its performers. At lower hierarchy levels, the problem of task scheduling with deadlines is considered for a set of resources with the quantity of which may vary over time. Interruptible and uninterruptible tasks are studied. In the former case, a polynomial algorithm is created by reducing the original problem to finding a flow in a special type of network; in the latter case, a pseudo-polynomial algorithm of an exhaustive search type is developed. A problem with a mixed set of tasks, which is reduced to the first two cases, has also been studied