R&D project scheduling when activities may fail

An R&D project typically consists of several stages. Due to technological risks, the project may have to be terminated before completion, each stage having a specific likelihood of success. In the project planning and scheduling literature, this technological uncertainty has typically been ignored and project plans are developed only for scenarios in which the project succeeds. In this paper we examine how to schedule projects in order to maximize their expected net present value when the project activities have a probability of failure and when an activity's failure leads to overall project termination. We formulate the problem, show that it is NP-hard, develop a branch-and-bound algorithm that allows us to obtain optimal solutions and provide extensive computational results. In the process, we establish a complexity result for an open problem in single-machine scheduling, namely for the discounted weighted-completion-time objective with general precedence constraints.