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

Abstract

Problem definition: Multistage stochastic programming is a well-established framework for sequential decision making under uncertainty by seeking policies that can be dynamically adjusted as uncertainty is realized. Often, for example, because of contractual constraints, such flexible policies are not desirable, and the decision maker may need to commit to a set of actions for a certain number of periods. Two-stage stochastic programming might be better suited to such settings, where first-stage decisions do not adapt to the uncertainty realized. In this paper, we propose a novel alternative approach, named as adaptive two-stage stochastic programming, where each component of the decision policy requiring limited flexibility has its own revision point, a period prior to which the decisions are determined at the beginning of the planning until this revision point, and after which they are revised for adjusting to the uncertainty realized thus far until the end of the planning. We then analyze this approach over the capacity expansion planning problem, that may require limited flexibility over expansion decisions. Methodology/results: We provide a generic mixed-integer programming formulation for the adaptive two-stage stochastic programming problem with finite support, in particular, for scenario trees, and show that this problem is NP-hard in general. Next, we focus on the capacity expansion planning problem and derive bounds on the value of adaptive two-stage programming in comparison with the two-stage and multistage approaches in terms of revision points. We propose several heuristic solution algorithms based on this bound analysis. These algorithms either provide approximation guarantees or computational advantages in solving the resulting adaptive two-stage stochastic problem. Managerial implications: We provide insights on the choice of the revision times based on our analytical analysis. We further present an extensive computational study on a generation capacity expansion planning problem with different generation resources including renewable energy. We demonstrate the value of adopting adaptive two-stage approach against the existing policies under limited flexibility and highlight the efficiency of the proposed heuristics along with practical implications on the studied problem. Funding: This work was supported by the National Science Foundation [Grant 1633196] and the Office of Naval Research [Grant N00014-18-1-2075]. Supplemental Material: The online appendices are available at https://doi.org/10.1287/msom.2023.0157 .