Linear-Quadratic Optimal Control of Periodic-Review Perishable Inventory Systems

TLDR: This work applies formal methodology of discrete-time dynamical optimization to solve the optimal control problem analytically, and proposes a controller that outperforms the classical order-up-to policy in terms of higher service level, smaller holding costs, and smaller order-to-demand variance ratio.

Abstract: In this brief, the problem of inventory control in systems with perishable goods is addressed from the control-theoretic perspective. In the analyzed setting, the deteriorating stock used to fulfill unknown, time-varying demand is replenished with delay from a remote supply source. In order to eliminate the threat of the bullwhip effect (amplified demand variations translated to the ordering signal), we propose to use the benefits of linear-quadratic optimal control. In contrast to the earlier approaches to inventory management of perishable goods, mainly based on heuristics and static optimization, we apply formal methodology of discrete-time dynamical optimization, and solve the optimal control problem analytically. This allows us to formulate and strictly prove a number of advantageous properties of the designed controller, e.g., we demonstrate that it ensures full demand satisfaction in the system with arbitrary delay and any bounded demand pattern with unknown statistics. The proposed controller outperforms the classical order-up-to policy in terms of higher service level, smaller holding costs, and smaller order-to-demand variance ratio.