Adaptive Multistage Stochastic Programming

TL;DR

This paper introduces adaptive multistage stochastic programming, balancing decision flexibility and commitment by optimally selecting revision times, supported by a new formulation, decomposition method, and computational validation.

Contribution

It presents a novel optimization framework that determines optimal decision revision points, along with a mathematical formulation and an adapted decomposition algorithm for mixed-integer problems.

Findings

Optimal revision times improve performance under limited flexibility.

The proposed method outperforms arbitrary revision strategies.

Computational experiments validate efficiency and effectiveness.

Abstract

Multistage stochastic programming is a powerful tool allowing decision-makers to revise their decisions at each stage based on the realized uncertainty. However, in practice, organizations are not able to be fully flexible, as decisions cannot be revised too frequently due to their high organizational impact. Consequently, decision commitment becomes crucial to ensure that initially made decisions remain unchanged for a certain period. This paper introduces adaptive multistage stochastic programming, a new optimization paradigm that strikes an optimal balance between decision flexibility and commitment by determining the best stages to revise decisions depending on the allowed level of flexibility. We introduce a novel mathematical formulation and theoretical properties eliminating certain constraint sets. Furthermore, we develop a decomposition method that effectively handles mixed-integer adaptive multistage programs by adapting the integer L-shaped method and Benders decomposition. Computational experiments on stochastic lot-sizing and generation expansion planning problems show substantial advantages attained through optimal selections of revision times when flexibility is limited, while demonstrating computational efficiency of the proposed properties and solution methodology. Optimizing revision times in a less flexible case can outperform arbitrary selection in a more flexible case. By adhering to these optimal revision times, organizations can achieve performance levels comparable to fully flexible settings.