A continuum description for a DES control problem

In Perdaen et al [1] we developed a Discrete Event Simulation (DES) for a re-entrant semiconductor factory with a push dispatch policy at the beginning of the line and a pull dispatch policy at the end of the line. The simulation uses a heuristic to move the transition point between both policies, the push-pull point (PPP), along the production line. The paper showed that the heuristic PPP control together with a CONWIP policy as a starts policy reduces the mismatch between a fluctuating demand and a fluctuating production output. In this paper we develop a continuum model for the production line with dispatch policies using transport equation models. We analyze the resulting discontinuous partial differential equations and show that the movement of the PPPs generate shock waves that travel along the supply chain. The heuristic control approach of the DES is implemented in the continuum setting. We propose a project based on adjoint calculus to determine an optimal control policy for the PDE model.