<p>Spraying applications occur multiple times a year and are a key task in agricultural production. Robotic spray vehicles are increasingly used in orchards to apply agrochemicals such as fertilisers and pesticides. This study formulates the NP-hard Orchard Spraying Routing Problem (OSRP) as a mixed-integer programming (MIP) model within the Split-Delivery Capacitated Arc Routing Problem (SDCARP) framework. We propose a basic model and an extended version for large-demand scenarios, and develop both exact and heuristic methods, incorporating lazy constraints, symmetry elimination, and a repair heuristic to obtain high-quality solutions. The proposed algorithms are evaluated on datasets derived from real-world orchard applications as well as classical SDCARP benchmark instances. This work contributes to the advancement of agricultural robotics for autonomous spraying tasks and offers valuable insights into mobile routing challenges. Furthermore, we highlight the structural differences between classical SDCARP instances and realistic orchard scenarios. New benchmark instances are introduced to support future research in this domain.</p>