This paper analyzes a simple project with two activities. The activities can be executed in a serial mode (separately), in a parallel mode (overlapping), or in a mixed mode (partly in a serial mode and partly in a parallel mode). There is interdependence between the activities and the duration-budget tradeoffs functions of the activities are defined differently for each execution strategy. The paper presents a deterministic duration-budget tradeoff model that takes into account the interdependence between the activities in order to determine the optimal execution-mode and the budget distributions among the project activities. A stochastic extension of the proposed model is also considered. The presented analysis can help project managers and practitioners in choosing the optimal overlapping strategy for different objective functions and constraints.