In this paper, both the duration and the cost of an activity are modeled as random variables, and accordingly, the cumulative cost at each time point also becomes a random variable along a project’s progress. We first present the new concept of an ‘alphorn of uncertainty’ (AoU) to describe the domain of cumulative cost variation throughout the life of a project and subsequently apply it to assess the project’s financial status over time. The shape of the alphorn was obtained by mixing Monte Carlo sampling with Gantt chart analysis, which enabled us to determine a project’s financial status related to specific payment modes. To validate the AoU, we designed and conducted an extensive numerical experiment using a randomly generated data set of activity networks. The results indicate that the AoU may be a promising method for the financial management of projects under uncertainty. Furthermore, financial status under uncertain conditions is not sensitive to an activity’s choice of duration distributions or to the form of cost functions. However, payment rules can greatly affect financial status over the duration of a project.
