Recent industrial production paradigms have seen the promotion of the outsourcing of low-value-added operations to robotic cells as a service, particularly end-of-line packaging. As a result, various types of research have emerged, offering different approaches to the trajectory design optimization of robotic manipulators and their applications. Over time, numerous improvements and updates have been made to the proposed methodologies, addressing the limitations and restrictions of earlier work. This survey-type article compiles research articles published in recent years that focus on the main algorithms proposed for addressing placement and minimum-time path planning for a manipulator responsible for performing pick-and-place tasks. Specifically, the research examines the construction of an automated robotic cell for the palletizing of regular heterogeneous boxes on a collision-free mixed pallet. By reviewing and synthesizing the most recent research, this article sheds light on the state-of-the-art manipulator planning algorithms for pick-and-place tasks in palletizing applications.