An approach based on robust optimization and decision rules for analyzing real options in engineering systems design

In this article, a novel approach to analyze flexibility and real options in engineering systems design is proposed based on robust optimization and decision rules. A semi-infinite robust counterpart is formulated for a worst-case non-flexible Generation Expansion Planning (GEP) problem taken as a demonstration application. An exact solution methodology is proven by converting the model into an explicit mixed-integer programming model. Strategic capacity expansion flexibility-also referred to as real options-is analyzed in the GEP problem formulation and a multi-stage finite adaptability decision rule is developed to solve the resulting model. Finite adaptability relies on uncertainty set partitions, and in order to avoid arbitrary choices of partitions, a novel heuristic partitioning methodology is developed based on upper-bound paths to guide the partitioning of uncertainty sets. The modeling approach and heuristic partitioning methodology are applied to analyze a realistic GEP problem using data from the Midwestern United States. The case study provides insights on the convergence rates of the proposed heuristic partitioning methodology, decision rule performances, and the value of flexibility compared with non-flexible solutions, showing that explicit considerations of flexibility through real options can yield significant cost savings and improved system performance in the face of uncertainty.