Minimal budget for activities chain with chance constrained lead-time

An activities chain is considered with FV activities, in which only the expected duration is affected by speeding performance with additional budget, and FCV activities, in which the speeded performance affects both the expected activity duration and its standard deviation. We assume deterministic activity costs for each performance speed. We introduce an analytic solution for minimizing the budget required for attaining a pre-given chance constrained lead-time, or for maximizing the confidence probability for a pre-given lead-time under a constrained budget. We show that the inclusion of FCV activities dictates an iterative procedure for optimizing the budget allocation among the activities.