Optimal packing of material flow on conveyor belts

We are interested in an optimal packing density problem for material flows on conveyor belts in two spatial dimensions. The control problem is concerned with the initial configuration of parts on the belt to ensure a high overall flow rate and to further reduce congestion. An adjoint approach is used to compare the optimization results from the microscopic model based on a system of ordinary differential equations with the corresponding macroscopic model relying on a hyperbolic conservation law. Computational results highlight similarities and differences of both optimization models and emphasize the benefits of the macroscopic approach.