A novel viewpoint for the analysis of the production control of FMS

The authors present the partial differential equations (PDEs) describing the transients of the probability density function characterizing the statistical evolution of a flexible manufacturing system producing a single product under hedging-point control policies. A second and more important aim is to bring forth the Markov renewal nature of the dynamics of the controlled process, and subsequently use the authors´s system of PDEs to compute the transition kernel of that renewal process. The authors characterize the evolution of the product-level probability density functions under hedging-point policies. They present a new approach based on the Markov renewal viewpoint. A simple numeral example is used to illustrate the ideas in the paper