Recent advances in computer vision and arc-welding technology have motivated a rethinking of several postulates and conventions incorporated in the existing robot off-line programming methods. This paper addresses relaxing of the downhand-position assumption, which became a de facto standard in robotic welding and requires the weldline to be horizontal and the weld normal vector to be opposite to gravity. In contrast to the standard techniques, the developed method explicitly assumes that a weld may be processed in the out-of-position location, which differs from the downhand location within given tolerances. However, to ensure the prescribed quality, the downhand deviation is charged by a reduction in the welding speed. For such settings, a novel method is proposed for the cluster-level welding operations planning for a robotic cell with a positioning table. The objective is to minimize the overall manufacturing time by finding a reasonable trade-off between the positioner motion times and the cluster processing times. It is shown that the associated optimization problem may be presented as a specific case of the generalized travelling salesman problem, for which an efficient heuristic algorithm has been developed that produces both the optimal welding cluster sequence and corresponding optimal motions of the positioner. The algorithm effectiveness was verified for a number of randomly generated test problems, for which the results are reported and analysed in detail. An industrial case study is also presented, confirming the validity of the developed technique.