A hydrodynamic modelling framework for production networks

This paper is concerned with a fluid approach towards modelling of production networks. It focuses on developing a macroscopic modelling framework that is able to describe the average dynamics of the manufactured items' movement in a production network taking under consideration possible non-linearities that occur due to the operation and interaction of workcells. The notion of clearing functions is used in a similar manner as the fundamental diagram of traffic engineering is used for modelling vehicular traffic flow. The system dynamics are represented by the macroscopic variables of items' density, flow, speed and queue length, which are associated through the use of a conservation law. These variables are further differentiated with respect to the customer order they belong to, providing this way a more detailed description of system dynamics. The suggested approach is a computationally efficient scheme that can be used for modelling and control purposes in a manner similar to macroscopic freeway traffic flow models.