Schedule risk analysis plays a key role in new product development. A typical project-schedule model using the Critical Path Method (CPM) and Program, Evaluation, and Review Technique (PERT) falls short in many practical situations. Instead, a graphical evaluation and review technique (GERT) has been recommended for its ability to address probability branches and loops. This paper introduces a GERT model based on a characteristic function and designs its numerical solution. First, an inversion formula is applied to derive the probability distribution of the completion time of a product development. Second, to address the implications of a due date, a novel measure of schedule risk is introduced to give a view of both loss and probability. Third, an elasticity analysis is used to identify the network parameters that facilitate the control of schedule risk. A case study of new product development in a high-technology enterprise is presented to demonstrate the proposed methods. The approach will be useful in schedule risk analysis across several problem domains including engineering, environment, management, economic development, etc.