The control of inventory systems incorporating quantity discounts

A novel optimal control algorithm incorporating a cost structure implied by quantity discounts is applied to a differential equation model of an inventory system. Rather than using a demand forecast, this approach is intended to regulate the system in real time in response to inventory variations. Some examples illustrate how the system response is generated and how it is affected by quantity discounts. The contribution of quantity discounts to the well-known demand amplification effect is also demonstrated.