Optimal control of a manufacturing system based on a novel continuous-flow model with minimal WIP requirement

This work aims to establish alternative continuous approximations to discrete event dynamic systems (DEDS) so as to mitigate some of the problems with the conventional fluid models. Conventional continuous-flow (fluid) models do not accurately represent the transient behavior of the discrete event systems that they represent, Furthermore, the approximation error can increase with such factors as the magnitude of operation times and the number of operations. In addition, they impose certain state variable constraints which lead to nonlinear dynamics for which the theory is not as developed as for linear systems. Some notions from continuous Petri net theory are used to establish an alternative fluid model for production systems. The effectiveness of the new formulation is illustrated through an application to the linear optimal control of a two-machine, single-part-type manufacturing system operating under a fixed demand rate. The control constraints imposed by the new formulation are interpreted as imposing a minimum nonzero WIP requirement on the system.