The exponential increase in space activities has highlighted a growing demand for in-orbit services, which are essential to ensure the sustainability of space operations. In-Orbit Servicing (IOS) represents a true paradigm shift, introducing unprecedented scalability and system flexibility. It provides opportu-nities for in-orbit maintenance, inspection, refueling, and upgrades, and will potentially change the en-tire approach to satellite design. However, planning efficient and safe trajectories for IOS missions pos-es a complex challenge due to the non-convexity of trajectory generation problems and the multiple op-erational constraints involved. In this thesis, developed at the Mission Analysis & Operations unit of Thales Alenia Space in Turin, a di-rect numerical optimization method is presented to determine the optimal trajectories for IOS missions, with a specific focus on inspection and docking-type operations involving two spacecraft, a Servicer and a Target.