Adaptive Two-Stage Stochastic Programming with an Analysis on Capacity Expansion Planning Problem.

This article introduces adaptive two-stage stochastic programming, a novel framework for sequential decision-making under uncertainty that optimally determines revision points for decisions requiring limited flexibility. Unlike traditional two-stage models with fixed first-stage decisions or fully flexible multistage models, this approach allows each decision variable to be revised once at an optimally chosen time, balancing flexibility and commitment constraints. The authors develop a mixed-integer linear programming formulation, prove its NP-hardness, and analyze its value relative to two-stage and multistage approaches, focusing on capacity expansion planning problems under uncertainty. They propose heuristic algorithms with approximation guarantees to identify revision times and demonstrate through extensive computational experiments on generation capacity expansion that the adaptive two-stage approach achieves significant cost reductions compared to two-stage models, with solution quality close to multistage models, while offering computational advantages. The study highlights practical implications for energy systems planning and suggests future research directions including decomposition methods and extensions to other limited-flexibility settings.