Maximizing the expected net present value in a project with uncertain cash flows

This paper considers the problem of maximizing the expected net present value of a project under uncertain cash flows, which are described by a supporting set of discrete scenarios. While cash flows are often considered more or less stable in countries with a stable economy, they can be quite uncertain in countries with financial and/or political crisis. In these countries, cash flows may drastically rise after a certain political event or a financial crisis. Therefore, we assume that the price changes may well occur after a predictable time (e.g., an election or the date on which a deal is agreed or broken). Such an assumption has never been made in project scheduling under uncertainty. We propose two integer linear programming (ILP) formulations and develop two-stage stochastic programming approaches that use Benders decomposition to solve the problem efficiently. Since the number of generated scenarios may be large and thus intractable, we also employ a forward scenario reduction technique to construct a rather tractable set of scenarios. Computational results indicate that the developed Benders-based methods outperform the ILP formulations.