Production and inventory rationing in an unreliable Make-to-Stock System under preventive maintenance policy

Ting Jin; Yuting Yan; Houcai Shen; Ting Jin; Yuting Yan; Houcai Shen

doi:10.3934/jimo.2026032

Journal of Industrial and Management Optimization

2026, Volume 22, Issue 2: 880-910. doi: 10.3934/jimo.2026032

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Production and inventory rationing in an unreliable Make-to-Stock System under preventive maintenance policy

Ting Jin ^{1
,
,},
Yuting Yan ²,
Houcai Shen ^{3
,
,}

1.
School of Management Science and Engineering, Nanjing University of Information Science and Technology, Nanjing 210044, Jiangsu, China
2.
School of Mathematics, Nanjing University, Nanjing 210008, Jiangsu, China
3.
School of Management and Engineering, Nanjing University, Nanjing 210008, Jiangsu, China

Received: 28 September 2025 Revised: 28 November 2025 Accepted: 16 December 2025 Published: 13 January 2026
Primary: 90B30, 91-10; Secondary: 65-11

This paper proposes a joint optimization approach for the production decision-making and inventory allocation in a fault-prone machine Make-to-Stock System, considering both production-side uncertainties and demand-side uncertainties, these factors often cause operational inefficiencies, higher costs and lower customer satisfaction, thus highlighting the need to integrate maintenance strategies into production-inventory management. A model based on Markov decision theory is presented to more accurately reflect real-world production processes, utilizing a preventive repair maintenance strategy, which focuses on repairing the machine only when it fails, as opposed to traditional fixed-cycle or fixed-threshold maintenance strategies. To tackle the complex structure of the optimal control strategy, the paper employs a numerical algorithm for updating the optimal strategy. Computational experiments are conducted to explain the properties of the optimal control strategies and emphasize the importance of considering a maintenance factor in the system. The study highlights the significance of effective production inventory system management, with the conclusion that the optimal control strategy is a machine-state-dependent threshold strategy.
- preventive maintenance,
- optimal control strategy,
- fault-prone machine,
- Markov decision theory,
- stationary analysis
Citation: Ting Jin, Yuting Yan, Houcai Shen. Production and inventory rationing in an unreliable Make-to-Stock System under preventive maintenance policy[J]. Journal of Industrial and Management Optimization, 2026, 22(2): 880-910. doi: 10.3934/jimo.2026032

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Abstract

This paper proposes a joint optimization approach for the production decision-making and inventory allocation in a fault-prone machine Make-to-Stock System, considering both production-side uncertainties and demand-side uncertainties, these factors often cause operational inefficiencies, higher costs and lower customer satisfaction, thus highlighting the need to integrate maintenance strategies into production-inventory management. A model based on Markov decision theory is presented to more accurately reflect real-world production processes, utilizing a preventive repair maintenance strategy, which focuses on repairing the machine only when it fails, as opposed to traditional fixed-cycle or fixed-threshold maintenance strategies. To tackle the complex structure of the optimal control strategy, the paper employs a numerical algorithm for updating the optimal strategy. Computational experiments are conducted to explain the properties of the optimal control strategies and emphasize the importance of considering a maintenance factor in the system. The study highlights the significance of effective production inventory system management, with the conclusion that the optimal control strategy is a machine-state-dependent threshold strategy.

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