Budget allocation among R&D teams with interdependent uncertain achievement levels and a common goal

How should a firm allocate a budget among projects with different uncertain potentials and interdependent achievement levels? Parallel teams pursuing different R&D approaches towards a particular objective, whose uncertain achievement levels improve with funding, are to be allocated a fixed budget. Clearly, the optimal allocation depends on the exact objective. We consider three objectives: maximizing the probability that the most successful activity achieves some pre-specified threshold; maximizing the expected achievement of the most successful activity; and maximizing the expected number of activities reaching some threshold(s). To model achievement levels, we use the Marshall and Olkin and a Gumbel's bivariate exponential distributions. The achievement levels in the individual activities are set to be stochastically increasing in the respective budget allocations. We analyze the models resulting from the three objectives and provide supportive numerical results. Some of the qualitative conclusions are intuitive, while others are not.