Maximizing the net present value of a project under uncertainty: Activity delays and dynamic policies

We study a project with stochastic activity durations and cash flows; we model the uncertainty using discrete scenarios. The project entails precedence-related activities, each of which incurs a cash flow that may be positive (inflow) or negative (outflow). The problem is to find a scheduling policy that maximizes the expected net present value of the project. A scheduling policy decides the starting time of each activity under every possible realization of the unknown parameters. Ideally, one wants to expedite the inflows (e.g., incoming payments), while delaying the outflows (e.g., costs) as much as possible, without violating the project deadline. In this article, we devise an exact and a heuristic method to define policies within two new classes of scheduling policies. The first policy class generalizes all existing static policies in the literature and further illustrates the importance of intentional activity delays from both a theoretical as well as an empirical point of view. Whereas the literature on project scheduling has mainly focused on static policies, we also propose a second class of dynamic policies. We show that dynamic policies outperform static policies by means of extensive computational experiments.