No abstract

In this technical note, an analytical framework for studying the dynamics of perishable inventory systems is developed using control-theoretic approach. In the considered systems, the deteriorating stock at a goods distribution center is used to fulfill unknown, time-varying demand. The stock is replenished using multiple supply options characterized by different lead-time delay. In contrast to the classical stochastic, or heuristic approaches, a formal design procedure based on discrete-time linear-quadratic (LQ) optimal control is employed. The analytically derived suboptimal controller satisfies positivity constraints and ensures full demand satisfaction for any bounded demand pattern. Moreover, a methodology for analysis of parametric uncertainties is elaborated, and another, nonlinear controller that guarantees robustness to uncertain delay variations is designed.

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.

No abstract