Uncertain dynamical system-based decision making with application to production-inventory problems

Abstract

• Firstly introduce uncertainty theory into constrained production-inventory problem. • A critical value model of uncertain optimal control is constructed for the problem. • A solving procedure for handling uncertain model is proposed. • The behavior of the value function is characterized. Uncertainty theory is a new methodology to describe subjective indeterminacy. This paper discusses an infinite-horizon production-inventory problem with constraints that the production rates shall be restricted to an appropriate interval, and the indeterminacy of the decision system is extracted and analyzed through uncertainty theory. To solve such a problem, an uncertain linear quadratic control model is investigated with a critical value criterion. Applying the equation of optimality, it is shown that an optimal feedback control exists. In addition, the behavior of the value function that is characterized benefits from numerical illustrations. Furthermore, we compare these optimal solutions with the solutions of an unconstrained problem. Then some economic interpretations are provided to reveal the significance of the model to practical applications.