Controllable, observable and stable state space representations of a generalized order-up-to policy

We outline a framework for developing state space representations of production and inventory control policies from their transfer functions. The particular replenishment rules that we consider are members of the inventory and order based production control system family that have previously been shown to be a generalization of the periodic review Order-Up-To policy. Traditionally, this model has been studied with transfer functions in the frequency domain. In this paper, we focus on the discrete time case and derive state space representations that are both controllable and observable. The state space approach is then used to determine the stability boundary of the production ordering system based on the eigenvalues of the state matrix.