The Optimal Control of Inventory Systems

The science of Operational Research has traditionally dominated in the field of inventory theory. Yet there have been sporadic attempts to apply methods from control theory in this domain. We review these efforts, concentrating particularly on optimal control approaches. We also enumerate the generic benefits and limitations of operational research methods. Through these efforts we judge whether the supremacy of operational research techniques in the field of inventory systems is warranted. We apply a novel optimal control algorithm to a differential equation model of an inventory system. This enables us to mimic the cost structures implied by quantity discounts and approximate capacity constraints. Some examples illustrate how optimal responses to instantaneous jumps in demand are generated and how these are affected by quantity discounts.