Optimal control for production inventory of uncertain random system with jump and deteriorating items

This paper explores an optimal control problem related to production inventory within an uncertain random system with jump. To address this issue effectively, we characterize an uncertain random optimal control problem with jump, incorporating subjective uncertainties from human factors and policy regulations, represented by a Liu process C(t) and a jump uncertain process V(t), respectively. Additionally, objective perturbations are modeled through random variables. By utilizing a hybrid framework of probability theory and uncertainty theory, this paper employs dynamic programming to establish the solution method for solving this optimal control problem. Furthermore, by applying the method to the production inventory problem, optimal strategies for joint pricing and dynamic production are obtained. Finally, we propose a numerical experiment to illustrate these findings.