Pharmaceutical companies have to face huge risks and enormous costs of production before they can produce a drug. Efficient allocation of resources is essential to help in maximizing profits. Chen [14] and Yu and Gittins [66] describe a stochastic optimisation model (the OPRRAa model) and associated software for determining efficient allocations for a pre-clinical research project. This is the starting point for this thesis. We first look for the nature of optimal policies for the selection o...