Methods for optimizing project schedules for the criterion of minimizing the weighted average time of their execution are considered. In the case when the durations of the jobs are given deterministically, an exact and approximate method for solving the problem of choosing the optimal schedule is proposed. If changes in the durations of the jobs are possible, an analytical tool for estimating the stability of the schedules is created both for the situation of interval setting of the durations of the jobs and for the situation of changes in the durations of the jobs under possible disturbances in the external environment. In the event that the durations of the jobs are given stochastically, a mechanism for evaluating the effectiveness of the schedule by two criteria is proposed, and a procedure for the quantitative assessment of the risk of the schedule is proposed.