Adaptive Multistage Stochastic Programming

Sezen Ece Kayacık; Beste Basciftci; Albert H Schrotenboer; Evrim Ursavas

doi:10.48550/arxiv.2401.07701

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Adaptive Multistage Stochastic Programming

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Adaptive Multistage Stochastic Programming

Sezen Ece Kayacık, Beste Basciftci, Albert H Schrotenboer and Evrim Ursavas

ArXiv.org

Cornell University

01/15/2024

DOI: 10.48550/arxiv.2401.07701

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https://doi.org/10.48550/arxiv.2401.07701View

Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

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.

Mathematics - Optimization and Control

Details

Title: Subtitle: Adaptive Multistage Stochastic Programming
Creators: Sezen Ece Kayacık
Beste Basciftci
Albert H Schrotenboer
Evrim Ursavas
Resource Type: Preprint
Publication Details: ArXiv.org
DOI: 10.48550/arxiv.2401.07701
ISSN: 2331-8422
Publisher: Cornell University
Language: English
Date posted: 01/15/2024
Academic Unit: Business Analytics
Record Identifier: 9984548375502771

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