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 of successive candidate drugs using two restricted versions of the OPRRAa model, and investigate how these depend on the model parameters. To some extent these results are likely to be applicable to the OPRRAa model. We then extend the OPRRAa model by introducing further modelling for stages and incorporating feedback from clinical trials to update the success probabilities for the corresponding stages using a hierarchical Bayes setting. Computer software has been written to implement the optimisation calculations. We show that very large improvements in profitability are possible in realistic cases.