Government acquisitions requiring research and development (R&D) efforts are fraught with uncertainty. The risks are often mitigated by employing a multi-stage competition, with multiple projects funded initially until a single successful project is selected. While decision-makers recognize they are using a real options approach, analytical tools are often unavailable to evaluate optimal decisions. The use of these techniques for R&D project selection to reduce the uncertainties has been shown to increase overall project value.

This dissertation first presents an efficient stochastic dynamic programming (SDP) approach that managers can use to determine optimal project selection strategies and apply the proposed approach on illustrative numerical examples. While the SDP approach produces optimal solutions for many applications, this approach does not easily accommodate the inclusion of a budget-optimal allocation or side constraints, since its formulation is scenario specific. Thus, we then formulate an integer program (IP), whose solution set is equivalent to the SDP model, but facilitates the incorporation of these features and can be solved using available commercial IP solvers. The one-level IP formulation can solve what is otherwise a nested two-level problem when solved as an SDP. We then compare the performance of both models on differently sized problems. For larger problems, where the IP approach appears to be untenable, we provide heuristics for the two-level SDP formulation to solve problems efficiently.

Finally, we apply these methods to carbon capture and storage (CCS) projects in the European Union currently under development that may be subject to public funding. Taking the perspective of a funding agency, we employ the real options models presented in this dissertation for determining optimal funding strategies for CCS project selection. The models demonstrate the improved risk reduction by employing a multi-stage competition and explicitly consider the benefits of knowledge spillover generated by competing projects. We then extend the model to consider two sensitivities: 1) the flexibility to spend the budget among the time periods and 2) optimizing the budget, but specifying each time period's allocation a priori. State size, scenario reduction heuristics and run-times of the models are provided.