Uncertain optimal control problem of production and inventory under time-varying customer demand

In the dynamic landscape of global trade and logistics, the optimization of inventory control has risen as a crucial topic of academic discourse. Acknowledging that inventory management functions as the intersection of production and sales, these domains often manifest significant uncertainty, which consequently poses formidable challenges to the inventory management optimization. This paper leverages uncertainty theory in a novel approach to articulate the optimal production strategy for navigating time-varying demand with inherent fluctuations. And the inventory state equation, characterized by fluctuations, is proposed as a constraint condition. By factoring in the residual value of terminal inventory, a production inventory model catering to time-varying demand is devised, and the optimal production strategy is ascertained. Simultaneously, solutions along the $ \alpha $-Path are introduced to procure more intuitive numerical results. Finally, a case study of Chinese clothing sales was used to substantiate the reliability of the model conclusion. This research amplifies the application of uncertainty theory to the optimization of production strategies, offering a novel perspective on inventory control in the ambit of uncertain factors. It provides a theoretical paradigm for companies with uncertain customer needs to orchestrate production, thereby bolstering the operational efficiency and profitability of the company.