Paper:

# Expected Value Model of an Uncertain Production Inventory Problem with Deteriorating Items

## Jiayu Shen^{†}, Yueqiang Jin, and Bing Liu

Department of Public Basic Courses, Nanjing Vocational University of Industry Technology

No.1 Yangshan North Road, Nanjing 210023, China

^{†}Corresponding author

In this study, we present an optimal control model for an uncertain production inventory problem with deteriorating items. The dynamics of the model includes perturbation by an uncertain canonical process. An expected value optimal control model is established based on the uncertainty theory. The aim of this study is to apply the optimal control theory to solve a production inventory problem with deteriorating items and derive an optimal inventory level and production rate that would maximize the expected revenue. The uncertainty theory is used to obtain the equation of optimality. The Hamilton–Jacobi–Bellman (HJB) principle is used to solve the equation of optimality. The results are discussed using numerical experiments for different demand functions.

*J. Adv. Comput. Intell. Intell. Inform.*, Vol.26, No.5, pp. 684-690, 2022.

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