Optimal Control for Inventory System Under Uncertainty on Demand and Delivery Using Robust Linear Quadratic Control Approach

Document Type : Research Paper


Department of Mathematics, Faculty of Science and Mathematics, Universitas Diponegoro, Semarang, Indonesia


The supply chain management comprises many uncertain parameters such as the demand value and delivered product rate as the result of an imperfect delivery process. In this article, therefore, a mathematical model in a linear dynamical state-space equation is formulated for an inventory system with uncertain demand value and imperfect delivery process developed from the existing classical model. The new model is used to determine the optimal decision for this inventory system i.e. to calculate the optimal amount of product that should be ordered from the supplier. Moreover, the optimal decision is calculated for the purpose to control the inventory level as the decision-maker wanted to, in this paper, the inventory level is brought to a set point. The robust linear quadratic control, which is an existing model, is employed to this system with a numerical experiment performed to illustrate the controlling responses. From the obtained results, it achieved the optimal decision with the proper control of the inventory level based on the performed set-point control problem. In addition, the performed computational experiment is compared to some related existing works. The analysis showed that the achieved optimal decision is well enough and is not worse than the other results. In conclusion, the proposed model and the method performed in this research are implementable and therefore can be used by practitioners especially in the supply chain management field.


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