LQ Optimal and Robust Control of Perishable Inventory Systems With Multiple Supply Options

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.