On the allocation of uncertainty-reduction effort to minimize total variability

Manufacturing processes and projects often consist of a series of activities with uncertain durations. The resulting uncertainty of the process or project impedes planning and disrupts the supply chain. Suppose that the uncertainty of the duration of individual activities can be reduced at a cost. We wish to minimize the variability of the sum of these durations, i.e., the variability of the projectʹs duration. Using mean-preserving transformations, we derive the optimal budget allocation among individual activities for separable and non-separable cost functions, and also explore the implications of statistical dependence on the allocation.