Discrete Control Theory


Using block diagrams, z-transforms and Tsypkin’s relation I show how to obtain the variances of the orders and inventory levels maintained by the proportional order-up-to policy. Assuming demand is uncorrelated and normally distributed, a proportional feedback controller equal to the golden ratio minimizes a weighted sum of the variances. One may also minimize the inventory and capacity costs maintained by this replenishment policy.

Cardiff, United Kingdom