Finite Adaptability in Multistage Linear Optimization
Name
Bertsimas-2010-Finite Adaptability.pdf
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644 KB
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Adobe PDF
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Author(s)
Bertsimas, Dimitris J.
Caramanis, Constantine
Date Issued
May 2010
Journal
IEEE transactions on automatic control
Publisher
Institute of Electrical and Electronics Engineers / IEEE Control Systems Society
Citation
Bertsimas, D., and C. Caramanis. “Finite Adaptability in Multistage Linear Optimization.” Automatic Control, IEEE Transactions On 55.12 (2010) : 2751-2766. Copyright © 2010, IEEE
Version
Final published version
Abstract
In multistage problems, decisions are implemented sequentially, and thus may depend on past realizations of the uncertainty. Examples of such problems abound in applications of stochastic control and operations research; yet, where robust optimization has made great progress in providing a tractable formulation for a broad class of single-stage optimization problems with uncertainty, multistage problems present significant tractability challenges. In this paper we consider an adaptability model designed with discrete second stage variables in mind. We propose a hierarchy of increasing adaptability that bridges the gap between the static robust formulation, and the fully adaptable formulation. We study the geometry, complexity, formulations, algorithms, examples and computational results for finite adaptability. In contrast to the model of affine adaptability proposed in, our proposed framework can accommodate discrete variables. In terms of performance for continuous linear optimization, the two frameworks are complementary, in the sense that we provide examples that the proposed framework provides stronger solutions and vice versa. We prove a positive tractability result in the regime where we expect finite adaptability to perform well, and illustrate this claim with an application to Air Traffic Control.
MIT Department
Sloan School of Management
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1109/tac.2010.2049764
