A novel variational inequality approach for modeling the optimal equilibrium in multi-tiered supply chain networks
We present a novel variational inequality model (VIM) to capture the complex real decision-making process in multi-tiered supply chain networks (MSCN) without strictly limiting the features of related functions. The VIM is formulated with the equilibrium conditions on links as the optimization goal...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Elsevier
2023-12-01
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| Series: | Supply Chain Analytics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2949863523000389 |
| _version_ | 1797237774002159616 |
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| author | Sheng-Xue He Yun-Ting Cui |
| author_facet | Sheng-Xue He Yun-Ting Cui |
| author_sort | Sheng-Xue He |
| collection | DOAJ |
| description | We present a novel variational inequality model (VIM) to capture the complex real decision-making process in multi-tiered supply chain networks (MSCN) without strictly limiting the features of related functions. The VIM is formulated with the equilibrium conditions on links as the optimization goal and the flow conservation condition as the main constraints. We transform the VIM into a series of equivalent Non-Linear Programming Models (NLPMs) to solve. To address this challenge, we propose a novel population-based heuristic algorithm called the Multiscale Model Learning Algorithm (MMLA). The MMLA is inspired by the learning behavior of individuals in a group and can converge to an optimal equilibrium state of the MSCN. The MMLA has two key operations: zooming in on the search field and learning search in a learning stage. The excellent performers, called medalists, are imitated by other learners. With the increase in learning stages, the learning efficiency is improved, and the searching energy is concentrated in a more promising area. We employ sixteen benchmark optimization problems and two supply chain networks to demonstrate the effectiveness of the MMLA and the rationality of the equilibrium models. The results obtained by MMLA for the NLPM show that the MMLA can solve the equilibrium model effectively, and multiple optimal equilibrium states may exist for an MSCN. The flexibility of the NLPM makes it possible to consider more complicated decision-making mechanisms in the model. |
| first_indexed | 2024-04-24T17:25:05Z |
| format | Article |
| id | doaj.art-a018b13eb2b640c38e3ce33827096d89 |
| institution | Directory Open Access Journal |
| issn | 2949-8635 |
| language | English |
| last_indexed | 2024-04-24T17:25:05Z |
| publishDate | 2023-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Supply Chain Analytics |
| spelling | doaj.art-a018b13eb2b640c38e3ce33827096d892024-03-28T06:41:27ZengElsevierSupply Chain Analytics2949-86352023-12-014100039A novel variational inequality approach for modeling the optimal equilibrium in multi-tiered supply chain networksSheng-Xue He0Yun-Ting Cui1Correspondence to: Department of Transportation, Business School, University of Shanghai for Science and Technology, Jun Gong Road No. 334, 200093 Shanghai, China.; Department of Transportation, Business School, University of Shanghai for Science and Technology, Shanghai, ChinaDepartment of Transportation, Business School, University of Shanghai for Science and Technology, Shanghai, ChinaWe present a novel variational inequality model (VIM) to capture the complex real decision-making process in multi-tiered supply chain networks (MSCN) without strictly limiting the features of related functions. The VIM is formulated with the equilibrium conditions on links as the optimization goal and the flow conservation condition as the main constraints. We transform the VIM into a series of equivalent Non-Linear Programming Models (NLPMs) to solve. To address this challenge, we propose a novel population-based heuristic algorithm called the Multiscale Model Learning Algorithm (MMLA). The MMLA is inspired by the learning behavior of individuals in a group and can converge to an optimal equilibrium state of the MSCN. The MMLA has two key operations: zooming in on the search field and learning search in a learning stage. The excellent performers, called medalists, are imitated by other learners. With the increase in learning stages, the learning efficiency is improved, and the searching energy is concentrated in a more promising area. We employ sixteen benchmark optimization problems and two supply chain networks to demonstrate the effectiveness of the MMLA and the rationality of the equilibrium models. The results obtained by MMLA for the NLPM show that the MMLA can solve the equilibrium model effectively, and multiple optimal equilibrium states may exist for an MSCN. The flexibility of the NLPM makes it possible to consider more complicated decision-making mechanisms in the model.http://www.sciencedirect.com/science/article/pii/S2949863523000389Supply chainLearning algorithmNonlinear programmingNetwork equilibriumVariational inequalities |
| spellingShingle | Sheng-Xue He Yun-Ting Cui A novel variational inequality approach for modeling the optimal equilibrium in multi-tiered supply chain networks Supply Chain Analytics Supply chain Learning algorithm Nonlinear programming Network equilibrium Variational inequalities |
| title | A novel variational inequality approach for modeling the optimal equilibrium in multi-tiered supply chain networks |
| title_full | A novel variational inequality approach for modeling the optimal equilibrium in multi-tiered supply chain networks |
| title_fullStr | A novel variational inequality approach for modeling the optimal equilibrium in multi-tiered supply chain networks |
| title_full_unstemmed | A novel variational inequality approach for modeling the optimal equilibrium in multi-tiered supply chain networks |
| title_short | A novel variational inequality approach for modeling the optimal equilibrium in multi-tiered supply chain networks |
| title_sort | novel variational inequality approach for modeling the optimal equilibrium in multi tiered supply chain networks |
| topic | Supply chain Learning algorithm Nonlinear programming Network equilibrium Variational inequalities |
| url | http://www.sciencedirect.com/science/article/pii/S2949863523000389 |
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