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Article

Approximated Dynamic Programming for Production and Inventory Planning Problem in Cold Rolling Process of Steel Production

by
Jing Wu
1,2,
Lijie Su
3,
Gongshu Wang
4 and
Yang Yang
5,*
1
School of Economics and Management, Shandong Huayu University of Technology, Dezhou 253034, China
2
National Frontiers Science Center for Industrial Intelligence and Systems Optimization, Northeastern University, Shenyang 110819, China
3
Key Laboratory of Data Analytics and Optimization for Smart Industry (Northeastern University), Ministry of Education, Shenyang 110819, China
4
Liaoning Engineering Laboratory of Data Analytics and Optimization for Smart Industry, Shenyang 110819, China
5
Liaoning Key Laboratory of Manufacturing System and Logistics Optimization, Shenyang 110819, China
*
Author to whom correspondence should be addressed.
Mathematics 2024, 12(24), 3922; https://doi.org/10.3390/math12243922
Submission received: 12 November 2024 / Revised: 7 December 2024 / Accepted: 10 December 2024 / Published: 13 December 2024
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Abstract

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.
Keywords: steel production; production and inventory planning; uncertain demand; Markov decision process; approximated dynamic programming steel production; production and inventory planning; uncertain demand; Markov decision process; approximated dynamic programming

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MDPI and ACS Style

Wu, J.; Su, L.; Wang, G.; Yang, Y. Approximated Dynamic Programming for Production and Inventory Planning Problem in Cold Rolling Process of Steel Production. Mathematics 2024, 12, 3922. https://doi.org/10.3390/math12243922

AMA Style

Wu J, Su L, Wang G, Yang Y. Approximated Dynamic Programming for Production and Inventory Planning Problem in Cold Rolling Process of Steel Production. Mathematics. 2024; 12(24):3922. https://doi.org/10.3390/math12243922

Chicago/Turabian Style

Wu, Jing, Lijie Su, Gongshu Wang, and Yang Yang. 2024. "Approximated Dynamic Programming for Production and Inventory Planning Problem in Cold Rolling Process of Steel Production" Mathematics 12, no. 24: 3922. https://doi.org/10.3390/math12243922

APA Style

Wu, J., Su, L., Wang, G., & Yang, Y. (2024). Approximated Dynamic Programming for Production and Inventory Planning Problem in Cold Rolling Process of Steel Production. Mathematics, 12(24), 3922. https://doi.org/10.3390/math12243922

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