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A Data-Driven Approach for Multi-Stage Linear Optimization

Banff International Research Station for Mathematical Innovation and Discovery

Multi-stage linear optimization is an integral modeling paradigm in supply chain, energy planning, and finance. However, these problems are computationally demanding, and identifying the correlation structure of the uncertainty across stages presents significant challenges. In this talk, we propose a novel data-driven framework for addressing multi-stage linear optimization based on a simple robustification of the data. For this framework, we report several results: 1) We present a general approximation algorithm for finding near-optimal solutions to the proposed framework via techniques from robust optimization. 2) We establish nonparametric convergence guarantees for the proposed framework which are, to the best of our knowledge, the first of their kind for data-driven multi-stage linear optimization with uncertainty that is arbitrarily correlated across stages. 3) We discuss differences and limitations of alternative multi-stage distributionally robust optimization approaches using Wasserstein ambiguity sets. Finally, we demonstrate the practical tractability and near-optimality of the proposed approach on several data-driven multi-stage inventory management problems. This is joint work with Dimitris Bertsimas and Shimrit Shtern.

Mathematics; Operations research, mathematical programming; Computer science; Applied computer science

video/mp4

Author affiliation: MIT

2019-07-16

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/71009

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/