Finite-Time Bounded Control for Multitime-Scale Production-Inventory Systems Under Inventory Inaccuracy

The production-inventory system is a fundamental component of the supply chain, and inconsistencies in production rates arise from the flow of products from suppliers to retailers within the supply chain network. This article investigates the problem of dynamic control of inventory levels in a multitime-scale production-inventory system, the basic unit in a supply chain. First, the dynamic behavior of the production-inventory quantity of two different level factories is modeled by the ordinary differential equations. Second, the issue of inconsistent production rates among different factories is considered, and the singular perturbation theory is introduced to describe the phenomenon. In addition, to deal with the bullwhip effect caused by the variation of order demand and the phenomenon of inaccurate inventory levels caused by misplacing and theft, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathscr{H}_{\infty}$</tex-math></inline-formula> control strategy is considered to improve the system's robustness. Then, the finite-time boundedness of the production-inventory system is analyzed by combining it with the Lyapunov control theory, and the theorem is given to ensure that the dynamic change of the factory inventory is bounded and controllable. Finally, the effectiveness of the proposed method is verified by a simulation example of the potassium carbonate production process in a chemical plant.