Optimal Design of a Conveyor-Based Automatic Sorting System

We consider a packaging optimization problem in a conveyor-based automatic sorting system. We first propose a probabilistic model of the entire system. Given the distribution of orders, the objective is to design the distribution of incoming products and the action policy of the robotic arm to maximize the efficiency defined as the discounted average number of completed orders over an infinite horizon. For the system without buffers, we obtain the deterministic optimal policy and provide an algorithm to calculate the optimal distribution of incoming products with polynomial time complexity. For the system with buffers, we formulate the problem as a Markov decision process (MDP) problem. It is proved that a deterministic and stationary optimal policy always exists and can be calculated by the value iteration algorithm. In addition, we postulate a conjecture about the relationship between the distributions of orders and incoming products under both the short-term and long-term considerations based on numerical simulations.