Quadratic Control Model for Shuttle Dispatching in Automated Overhead Rail Systems

Automated Overhead Rail Systems (AORs) have a key role in warehouse and in-house industry, as well as in the modern hospital, where efficient shuttle dispatching directly impacts throughput and reliability. This paper presents a quadratic control model formulated in symmetric quadratic matrix form to capture balanced interactions between shuttles, tasks, and priorities. A Genetic Algorithm (GA) is employed to solve the optimization problem, with operators adapted to exploit quadratic symmetry, for faster convergence and stable performance. Simulation results on a microcontroller-based testbed demonstrated that the proposed model achieved shorter dispatching times, reduced waiting costs, and more symmetrically distributed workloads compared with conventional heuristic approaches. The study shows that symmetry is not only a modeling feature, but also a design principle, supporting future extensions such as emergency handling and multi-priority dispatching.