Robust MPL scheduling considering the number of in-process jobs

A robust scheduling method for max-plus linear systems is proposed. A principal concern in scheduling problems is how to accomplish robustness against external disturbances. To accomplish this, methods based on model predictive control (MPC) have been put forward to control system parameters or control inputs. In this context, we recently proposed a method for indirectly controlling the state variables by utilizing the idea of dead time. The idea imposes constraints for upper bounds of in-processing jobs between facilities, whereas several practical systems also consider the lower bounds. This paper, therefore, considers a modeling and robust scheduling method that takes into account both constraints. A numerical simulation for a transportation system is also presented in order of the method's effectiveness.