We address the maximization of a project’s expected net present value when the activity durations and cash flows are described by a discrete set of alternative scenarios with associated occurrence probabilities. In this setting, the choice of scenario-independent activity start times frequently leads to infeasible schedules or severe losses in revenues. We suggest to determine an optimal target processing time policy for the project activities instead. Such a policy prescribes an activity to be started as early as possible in the realized scenario, but never before its (scenario-independent) target processing time. We formulate the resulting model as a global optimization problem and present a branch-and-bound algorithm for its solution. Extensive numerical results illustrate the suitability of the proposed policy class and the runtime behavior of the algorithm.