Discrete control theory

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.

Publication
The spectrum of systems approaches to problem solving - from systems engineering to systems dynamics to systems thinking. A workshop hosted by the UK Chapter of the Systems Dynamics Society and the EPSRC ReRun project, Cardiff Business School, 22nd March, Cardiff, UK.