Stock Control of Single Product Inventory System with Imperfect Delivery by Using Robust Linear Quadratic Regulator

In advanced inventory management problem, the received product will be not always entirely accepted due to the imperfect delivery process. The accepted delivered product volume can be represented by acceptance rate that is unknown/uncertain for the future delivery process. Then, a mathematical model and control method that can handle this problem is needed in order to control the product stock level in the warehouse. In this paper, we formulate a dynamical linear system with random parameter in the matrix coefficient to solve the inventory control problem with imperfect delivery proves and apply the robust linear quadratic regulator (RLQR) to find the optimal decision i.e. the optimal volume of the product that will be purchased at any review time period so that the inventory level will follow some set point decided by the decision maker with minimal effort (cost). To illustrate the model and its optimal decision, a computational experiment was performed with randomly generated inventory data. From the result, the optimal volume of the product for each review time period was determined where the product stock level was followed the desired set point.