Modeling and design of an optimal line manager of a packaging system with MILP

The present paper addresses the design of an optimal online scheduler for a robotized packaging system. The task of the plant is to pick randomly incoming products from a conveyor belt which can never be stopped, and pack them into boxes with multiple capacity, with the goal to lose as less products as possible. Through a special mathematical representation, the control problem is formulated as a MILP optimization problem to be solved whenever a product is moved by a robot or enters the conveyor. The result is the assignment of products to robots and box places, which defines current and future missions for all the robots. In addition, the optimal scheduler decides also the speeds of the conveyors, to maximize the throughput. The proposed approach is independent of the layout (same belt directions, opposite belt directions, cross directions) and deals seamlessly with the steady state condition and transient behaviors. Numerical results confirm the superiority of the proposed approach with respect to the simpler solutions adopted in industrial applications.