An uncertain production-inventory problem with deteriorating items

• Published in: Advances in continuous and discrete models 2022-05, Vol.2022 (1), Article 42
• Main Authors: Shen, Jiayu, Jin, Yueqiang, Liu, Bing, Lu, Ziqiang, Chen, Xin
• Format: Article
• Language: English
• Subjects: Analysis; Confidence intervals; Difference and Functional Equations; Functional Analysis; Mathematics; Mathematics and Statistics; Nonlinear differential equations; Optimal control; Optimization; Ordinary Differential Equations; Partial Differential Equations; Uncertainty
• ISSN: 2731-4235; 1687-1839; 2731-4235; 1687-1847
• DOI: 10.1186/s13662-022-03714-8

The uncertain production-inventory problem with deteriorating items is investigated and an optimal control model is developed in the present paper. The uncertain production-inventory problem is perturbed by an uncertain canonical process. Based on uncertainty theory, an optimistic-value optimal-based control model is established. The present study aims to find the optimistic value of revenue at a certain confidence level. The uncertainty theory is used to obtain the equation of optimality. Using the Hamilton–Jacobi–Bellman principle, a nonlinear partial differential equation that has to be satisfied by a value function is obtained. Assuming a specific form of the solution, backsubstituting the partial differential equation to find functions of time is conducted, and the functions are then used to solve the partial differential equation. Numerical experiments with different demand functions are used to assess the feasibility of this model and this method.