We investigate a project scheduling problem in which cash flows are periodically variable, and we aim to maximize the net present value (NPV). For each activity, a set of cash flows is considered where each one pertains to a particular period. This setting is compatible with inflation rates that may well occur in some countries with unstable economic situations where the occurrence times of inflation are sometimes known in advance. In this case, the project can be scheduled more suitably to abate probable pitfalls. In this paper, we investigate the problem in two settings: deterministic and stochastic cash flows. In the deterministic case, in each period we consider the expected value of cash flows of each activity as a constant and develop an integer linear programming model in conjunction with a branch-and-bound algorithm to solve the problem optimally. Moreover, we develop a multi-stage stochastic programming (MSSP) model to formulate the stochastic version of the problem. Using a set of randomly generated test instances and extensive computational results, we analyze the performance of our developed solution approaches. In addition, we compare the deterministic and stochastic models and analyze the sensitivity of the most important parameters.

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