On closed-form solutions of a resource allocation problem in parallel funding of R&D projects

In order to reduce the risk of complete failure, research managers often adopt a parallel strategy by simultaneously funding several R&D activities and several research teams within each activity. The parallel strategy requires the allocation of an available budget to a number of R&D activities, the determination of the number of research teams within each activity and the amount of funding they receive. We consider a formulation of this problem as a nonlinear resource allocation problem by Gerchak and Kilgour, and present a sufficient condition as a function of problem parameters, under which closed-form solutions to the problem are obtained.