Production systems with limited repair capacity

Abstract

Optimizing manufacturing systems consists in generating large-quantity outputs to fulfill customers demands. But naturally machines may fail and the production process is either slowed down or completely interrupted. In order to keep production running, we are interested in assigning repair crews to currently broken-down machines. But due to the limited repair capacity and the dynamics involved in the production process, we propose a scheduling problem based on ordinary differential equations for the description of buffer levels and the actually available processing capacity. We discuss properties of the model and present a solution approach leading to a mixed-integer programming model.

Modeling and optimizing traffic light settings in road networks

“…The numerical solution obtained when finding an optimal traffic light setting follows the derivation of a linear mixed-integer programming model (MIP) [26,30]. We rigorously derive a discrete framework by the appropriate discretization of the car density along roads (i) and by the formulation of the coupling problem at intersections (ii).…”

“…Here, we combine this model based on partial differential equations with discrete decisions on switching times. The combination of optimization techniques for pde-based problems and integer restrictions on variables has been studied in the field of production in [24,26,29,30,63]. We proceed by transforming the model into a linear mixed-integer programming problem.…”