Approximated Dynamic Programming for Production and Inventory Planning Problem in Cold Rolling Process of Steel Production
We study a multi-product production and inventory planning problem with uncertain demand in the cold rolling stage of steel production processes. The problem is to determine the production amount of each product in each planning period so that the sum of production, inventory holding, and backorder...
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2024-12-01
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| author | Jing Wu Lijie Su Gongshu Wang Yang Yang |
| author_facet | Jing Wu Lijie Su Gongshu Wang Yang Yang |
| author_sort | Jing Wu |
| collection | DOAJ |
| description | We study a multi-product production and inventory planning problem with uncertain demand in the cold rolling stage of steel production processes. The problem is to determine the production amount of each product in each planning period so that the sum of production, inventory holding, and backorder costs is minimized. We first formulate it into a Markov decision process (MDP) model, considering dynamic demand. Aiming at the proposed large-scale MDP model, we develop the improved Approximated Dynamic Programming (ADP) algorithms, which are composed of the reformulation and the approximation functions for the value function in MDP. Linear and two quadratic approximate functions are proposed to approximate the value function. Numerical experiments show the optimal gaps of the different approximation methods and illustrate the efficiency of the proposed ADP methods. |
| format | Article |
| id | doaj-art-cdc3bd16cae34017bd6bde64a31ae090 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-cdc3bd16cae34017bd6bde64a31ae0902024-12-27T14:38:01ZengMDPI AGMathematics2227-73902024-12-011224392210.3390/math12243922Approximated Dynamic Programming for Production and Inventory Planning Problem in Cold Rolling Process of Steel ProductionJing Wu0Lijie Su1Gongshu Wang2Yang Yang3School of Economics and Management, Shandong Huayu University of Technology, Dezhou 253034, ChinaKey Laboratory of Data Analytics and Optimization for Smart Industry (Northeastern University), Ministry of Education, Shenyang 110819, ChinaLiaoning Engineering Laboratory of Data Analytics and Optimization for Smart Industry, Shenyang 110819, ChinaLiaoning Key Laboratory of Manufacturing System and Logistics Optimization, Shenyang 110819, ChinaWe study a multi-product production and inventory planning problem with uncertain demand in the cold rolling stage of steel production processes. The problem is to determine the production amount of each product in each planning period so that the sum of production, inventory holding, and backorder costs is minimized. We first formulate it into a Markov decision process (MDP) model, considering dynamic demand. Aiming at the proposed large-scale MDP model, we develop the improved Approximated Dynamic Programming (ADP) algorithms, which are composed of the reformulation and the approximation functions for the value function in MDP. Linear and two quadratic approximate functions are proposed to approximate the value function. Numerical experiments show the optimal gaps of the different approximation methods and illustrate the efficiency of the proposed ADP methods.https://www.mdpi.com/2227-7390/12/24/3922steel productionproduction and inventory planninguncertain demandMarkov decision processapproximated dynamic programming |
| spellingShingle | Jing Wu Lijie Su Gongshu Wang Yang Yang Approximated Dynamic Programming for Production and Inventory Planning Problem in Cold Rolling Process of Steel Production Mathematics steel production production and inventory planning uncertain demand Markov decision process approximated dynamic programming |
| title | Approximated Dynamic Programming for Production and Inventory Planning Problem in Cold Rolling Process of Steel Production |
| title_full | Approximated Dynamic Programming for Production and Inventory Planning Problem in Cold Rolling Process of Steel Production |
| title_fullStr | Approximated Dynamic Programming for Production and Inventory Planning Problem in Cold Rolling Process of Steel Production |
| title_full_unstemmed | Approximated Dynamic Programming for Production and Inventory Planning Problem in Cold Rolling Process of Steel Production |
| title_short | Approximated Dynamic Programming for Production and Inventory Planning Problem in Cold Rolling Process of Steel Production |
| title_sort | approximated dynamic programming for production and inventory planning problem in cold rolling process of steel production |
| topic | steel production production and inventory planning uncertain demand Markov decision process approximated dynamic programming |
| url | https://www.mdpi.com/2227-7390/12/24/3922 |
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