@conference{Disney2019,
  author       = {S.M. Disney},
  title        = {Discrete Control Theory},
  booktitle    = {14th International Society for Inventory Research Summer School},
  year         = {2019},
  address      = {Leuven, Belgium},
  month        = {26th-30th August},
  doi          = {10.13140/RG.2.2.33616.87048},
  abstract     = {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.}}