Design of production-inventory control systems incorporating fast-sampling control policies with implementation lead time

In this paper, singular perturbation methods are used to synthesize fast-sampling error-actuated control policies for two production-inventory system models in which there is a finite time delay of several sampling periods between the formulation and the implementation of the control policies. In the first model it is assumed that the demand for the product cannot be influenced by the management of the production-inventory system, and in the second model it is assumed that the demand for the product can be influenced by advertising and that the desired instantaneous demand rate is specified by management. In both cases, it is shown that the system will exhibit good transient and steady-state behaviour when controlled by such control policies. Furthermore, it is also shown that non-interacting control can be achieved when effective expenditure on advertising is introduced in order to influence the demand for the product, and that the provision of this extra flexibility thus leads to improved transient behaviour.