Dynamic optimization in the age of big data

This thesis revisits a fundamental class of dynamic optimization problems introduced by Dantzig (1955). These decision problems remain widely studied in many applications domains (e.g., inventory management, finance, energy planning) but require access to probability distributions that are rarely known in practice. First, we propose a new data-driven approach for addressing multi-stage stochastic linear optimization problems with unknown probability distributions. The approach consists of solving a robust optimization problem that is constructed from sample paths of the underlying stochastic process. As more sample paths are obtained, we prove that the optimal cost of the robust problem converges to that of the underlying stochastic problem. To the best of our knowledge, this is the first data-driven approach for multi-stage stochastic linear optimization problems which is asymptotically optimal when uncertainty is arbitrarily correlated across time.

Name thesis:degree_name

Doctoral

Department dc:contributor.department

Massachusetts Institute of Technology. Operations Research Center

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2020

Author dc:creator

• Sturt, Bradley Eli.

Advisor dc:contributor.advisor

• Dimitris Bertsimas.

• Operations Research Center.

Statement dc:rights

• MIT theses may be protected by copyright. Please reuse MIT thesis content according to the MIT Libraries Permissions Policy, which is available through the URL provided.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

https://hdl.handle.net/1721.1/127292

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/127292