We propose a new method, based on semidefinite optimization, to find tight upper bounds on the expected project completion time and expected project tardiness in a stochastic project scheduling environment, when only limited information in the form of first and second (joint) moments of the durations of individual activities in the project is available. Our computational experiments suggest that the bounds provided by the new method are stronger and often significant compared to the bounds found by alternative methods.Singapore-MIT Alliance (SMA)