On allocating R&D budgets among and within projects

Choosing how to allocate resources to R&D projects is challenging, due to their uncertain success rates and achievement levels. We address the issue of allocating a given R&D budget among projects, and to parallel teams within each project. The achievement level of each team is assumed to be stochastically increasing in its funding level. We consider the objectives of maximizing: 1. the weighted sum of the probabilities that best team in each project achieves a threshold; 2. the weighted sum of expected achievement levels; and 3. the weighted sum of the expected number of teams attaining their threshold. Numerical results for a particular family of distributions are provided. The nature of the objective is seen to have a substantial impact on the optimal allocation.