A time-consistent Benders decomposition method for multistage distributionally robust stochastic optimization with a scenario tree structure
A computational method is developed for solving time consistent distributionally robust multistage stochastic linear programs with discrete distribution. The stochastic structure of the uncertain parameters is described by a scenario tree. At each node of this tree, an ambiguity set is defined by co...
| Main Authors: | , , |
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| Format: | Journal Article |
| Language: | English |
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SPRINGER
2021
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| Subjects: | |
| Online Access: | http://hdl.handle.net/20.500.11937/91429 |
| _version_ | 1848765518191788032 |
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| author | Yu, H. Sun, Jie Wang, Y. |
| author_facet | Yu, H. Sun, Jie Wang, Y. |
| author_sort | Yu, H. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | A computational method is developed for solving time consistent distributionally robust multistage stochastic linear programs with discrete distribution. The stochastic structure of the uncertain parameters is described by a scenario tree. At each node of this tree, an ambiguity set is defined by conditional moment constraints to guarantee time consistency. This method employs the idea of nested Benders decomposition that incorporates forward and backward steps. The backward steps solve some conic programming problems to approximate the cost-to-go function at each node, while the forward steps are used to generate additional trial points. A new framework of convergence analysis is developed to establish the global convergence of the approximation procedure, which does not depend on the assumption of polyhedral structure of the original problem. Numerical results of a practical inventory model are reported to demonstrate the effectiveness of the proposed method. |
| first_indexed | 2025-11-14T11:36:31Z |
| format | Journal Article |
| id | curtin-20.500.11937-91429 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T11:36:31Z |
| publishDate | 2021 |
| publisher | SPRINGER |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-914292023-05-03T07:25:23Z A time-consistent Benders decomposition method for multistage distributionally robust stochastic optimization with a scenario tree structure Yu, H. Sun, Jie Wang, Y. Science & Technology Technology Physical Sciences Operations Research & Management Science Mathematics, Applied Mathematics Multistage stochastic programming Distributionally robust Scenario tree model Decomposition method LINEAR-PROGRAMS CONVERGENCE ALGORITHM SELECTION A computational method is developed for solving time consistent distributionally robust multistage stochastic linear programs with discrete distribution. The stochastic structure of the uncertain parameters is described by a scenario tree. At each node of this tree, an ambiguity set is defined by conditional moment constraints to guarantee time consistency. This method employs the idea of nested Benders decomposition that incorporates forward and backward steps. The backward steps solve some conic programming problems to approximate the cost-to-go function at each node, while the forward steps are used to generate additional trial points. A new framework of convergence analysis is developed to establish the global convergence of the approximation procedure, which does not depend on the assumption of polyhedral structure of the original problem. Numerical results of a practical inventory model are reported to demonstrate the effectiveness of the proposed method. 2021 Journal Article http://hdl.handle.net/20.500.11937/91429 10.1007/s10589-021-00266-7 English SPRINGER fulltext |
| spellingShingle | Science & Technology Technology Physical Sciences Operations Research & Management Science Mathematics, Applied Mathematics Multistage stochastic programming Distributionally robust Scenario tree model Decomposition method LINEAR-PROGRAMS CONVERGENCE ALGORITHM SELECTION Yu, H. Sun, Jie Wang, Y. A time-consistent Benders decomposition method for multistage distributionally robust stochastic optimization with a scenario tree structure |
| title | A time-consistent Benders decomposition method for multistage distributionally robust stochastic optimization with a scenario tree structure |
| title_full | A time-consistent Benders decomposition method for multistage distributionally robust stochastic optimization with a scenario tree structure |
| title_fullStr | A time-consistent Benders decomposition method for multistage distributionally robust stochastic optimization with a scenario tree structure |
| title_full_unstemmed | A time-consistent Benders decomposition method for multistage distributionally robust stochastic optimization with a scenario tree structure |
| title_short | A time-consistent Benders decomposition method for multistage distributionally robust stochastic optimization with a scenario tree structure |
| title_sort | time-consistent benders decomposition method for multistage distributionally robust stochastic optimization with a scenario tree structure |
| topic | Science & Technology Technology Physical Sciences Operations Research & Management Science Mathematics, Applied Mathematics Multistage stochastic programming Distributionally robust Scenario tree model Decomposition method LINEAR-PROGRAMS CONVERGENCE ALGORITHM SELECTION |
| url | http://hdl.handle.net/20.500.11937/91429 |