## 1 Introduction  
In robotic applications, it is crucial to reduce the overall operational cost and increase productivity, which usually results in the need to reduce the necessary cycle time of robotic tasks. Particular attention must be paid to the optimization of the robot end effector motion considering various criteria such as minimum execution time and/or energy consumption, smoothness, as well as robot constraints such as maximum joint velocity and acceleration, accuracy, workspace constraints such as obstacles and/or process constraints such as time window or end effector velocity and acceleration limits. Among the most common methods to optimize robotic operations is the placement of the task to be executed at an optimal location with respect to the robot's base or vice versa. In most cases, the proposed methods comprise three key aspects: (a) the introduction of a performance measure, (b) an optimization method and (c) an optimal search method. Performance measures are at the core of such optimization methods. Their use allows for the quantification of different aspects of the manipulator's operation targeted to be optimized. A wide range of different kinematic indices, either local, task based or global have been proposed in the relevant literature. Local indices are configuration dependent, i.e., dependent on the current posture of the manipulator at a given point. Task-based indices are usually formed by the algebraic manipulation of local indices along the given kinematic task, as such being dependent on the manipulator's configurations during task execution. Global indices are configuration independent, since they represent the overall measure of a performance aspect across the whole manipulator's workspace. Among the well-established indices in the relevant literature is [PERSON]'s manipulability index [1], providing a measure of the manipulator's ability to move in any given direction from a given configuration. However, it presents a number of inherit limitations, such as scale, order and dimensional dependency as well as the fact that in its general form is an unbounded index. Moreover, it does not take into account the direction of motion,since it examines all possible directions of motion from a given configuration. However, various improvements have been proposed to overcome its limitations [2]. Other well-established indices include the Minimum Singular Value [3] and the Jacobian condition number [4]. The first examines the \"most difficult\" direction of motion of the end effector, providing a concise means to determine the manipulator's posture distance from a singularity as well as a measure of the upper bound of the velocity the manipulator may move in all directions. The latter examines both the \"most difficult\" and the \"easiest\" motion directions from a given posture, providing a concise measure of accuracy of the transmission of joint speeds to end effector velocity. Similar indices of the latter are the Local Condition Number and the Reciprocal Local Condition Number [2]. However, these indices retain the limitations of the manipulability index, due to being dependent on the manipulator's Jacobian. In the case of the determination of the effectiveness of the transmission of joint speeds to the end effector velocity, [PERSON] and [PERSON] proposed the Manipulator Velocity Ratio (MVR) [5]. The measure examines the transmission in a given direction of motion of the end effector, providing a more concise view of the manipulator's ability to move in a specific direction. Moreover, it also provides a measure of the required values of the latter in order to achieve a specified end effector velocity. A thorough and comprehensive review of performance indices may be found in [2]. Optimal kinematic task placement methods utilize some of the above-mentioned indices depending on the manipulator's performance aspect considered for optimization to formulate the optimization problem's mathematical expression, i.e., the problem's objective function.