Stochastic optimization in supply chain networks: averaging robust solutions
Abstract We propose a novel robust optimization approach to analyze and optimize the expected performance of supply chain networks. We model uncertainty in the demand at the sink nodes via polyhedral sets which are inspired from the limit laws of probability. We characterize the uncertainty sets by...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Springer Berlin Heidelberg
2021
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| Online Access: | https://hdl.handle.net/1721.1/131385 |
| _version_ | 1826214467390668800 |
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| author | Bertsimas, Dimitris Youssef, Nataly |
| author2 | Massachusetts Institute of Technology. Operations Research Center |
| author_facet | Massachusetts Institute of Technology. Operations Research Center Bertsimas, Dimitris Youssef, Nataly |
| author_sort | Bertsimas, Dimitris |
| collection | MIT |
| description | Abstract
We propose a novel robust optimization approach to analyze and optimize the expected performance of supply chain networks. We model uncertainty in the demand at the sink nodes via polyhedral sets which are inspired from the limit laws of probability. We characterize the uncertainty sets by variability parameters which control the degree of conservatism of the model, and thus the level of probabilistic protection. At each level, and following the steps of the traditional robust optimization approach, we obtain worst case values which directly depend on the values of the variability parameters. We go beyond the traditional robust approach and treat the variability parameters as random variables. This allows us to devise a methodology to approximate and optimize the expected behavior via averaging the worst case values over the possible realizations of the variability parameters. Unlike stochastic analysis and optimization, our approach replaces the high-dimensional problem of evaluating expectations with a low-dimensional approximation that is inspired by probabilistic limit laws. We illustrate our approach by finding optimal base-stock and affine policies for fairly complex supply chain networks. Our computations suggest that our methodology (a) generates optimal base-stock levels that match the optimal solutions obtained via stochastic optimization within no more than 4 iterations, (b) yields optimal affine policies which often times exhibit better results compared to optimal base-stock policies, and (c) provides optimal policies that consistently outperform the solutions obtained via the traditional robust optimization approach. |
| first_indexed | 2024-09-23T16:06:11Z |
| format | Article |
| id | mit-1721.1/131385 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T16:06:11Z |
| publishDate | 2021 |
| publisher | Springer Berlin Heidelberg |
| record_format | dspace |
| spelling | mit-1721.1/1313852023-03-24T19:11:30Z Stochastic optimization in supply chain networks: averaging robust solutions Bertsimas, Dimitris Youssef, Nataly Massachusetts Institute of Technology. Operations Research Center Abstract We propose a novel robust optimization approach to analyze and optimize the expected performance of supply chain networks. We model uncertainty in the demand at the sink nodes via polyhedral sets which are inspired from the limit laws of probability. We characterize the uncertainty sets by variability parameters which control the degree of conservatism of the model, and thus the level of probabilistic protection. At each level, and following the steps of the traditional robust optimization approach, we obtain worst case values which directly depend on the values of the variability parameters. We go beyond the traditional robust approach and treat the variability parameters as random variables. This allows us to devise a methodology to approximate and optimize the expected behavior via averaging the worst case values over the possible realizations of the variability parameters. Unlike stochastic analysis and optimization, our approach replaces the high-dimensional problem of evaluating expectations with a low-dimensional approximation that is inspired by probabilistic limit laws. We illustrate our approach by finding optimal base-stock and affine policies for fairly complex supply chain networks. Our computations suggest that our methodology (a) generates optimal base-stock levels that match the optimal solutions obtained via stochastic optimization within no more than 4 iterations, (b) yields optimal affine policies which often times exhibit better results compared to optimal base-stock policies, and (c) provides optimal policies that consistently outperform the solutions obtained via the traditional robust optimization approach. 2021-09-20T17:16:52Z 2021-09-20T17:16:52Z 2019-02-25 2020-09-24T21:05:34Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/131385 en https://doi.org/10.1007/s11590-019-01405-0 Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ Springer-Verlag GmbH Germany, part of Springer Nature application/pdf Springer Berlin Heidelberg Springer Berlin Heidelberg |
| spellingShingle | Bertsimas, Dimitris Youssef, Nataly Stochastic optimization in supply chain networks: averaging robust solutions |
| title | Stochastic optimization in supply chain networks: averaging robust solutions |
| title_full | Stochastic optimization in supply chain networks: averaging robust solutions |
| title_fullStr | Stochastic optimization in supply chain networks: averaging robust solutions |
| title_full_unstemmed | Stochastic optimization in supply chain networks: averaging robust solutions |
| title_short | Stochastic optimization in supply chain networks: averaging robust solutions |
| title_sort | stochastic optimization in supply chain networks averaging robust solutions |
| url | https://hdl.handle.net/1721.1/131385 |
| work_keys_str_mv | AT bertsimasdimitris stochasticoptimizationinsupplychainnetworksaveragingrobustsolutions AT youssefnataly stochasticoptimizationinsupplychainnetworksaveragingrobustsolutions |