Managers of projects and multi-project programs often face considerable uncertainty in the duration and outcomes of specific tasks, as well as in the overall level of resources required by tasks. They must decide, in these uncertain conditions, how to allocate and manage scarce resources across many projects that have competing needs. This paper develops a nonlinear mixed-integer programming model for optimizing the resource allocations to individual tasks to minimize the completion times of a collection of projects. The model contains a very flexible representation of the effects of changing resource allocations on the probability distribution of task duration, so it can accommodate a wide variety of practical situations. A heuristic solution procedure is proposed that works quite effectively. An illustration involving a collection of bridge construction projects is provided.
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