Industrial robot applications should be designed to allow the robot to provide the best performance for increasing throughput. In this regard, both trajectory and task order optimization are crucial, since they can heavily impact cycle time. Moreover, it is very common for a robotic application to be kinematically or functionally redundant so that multiple arm configurations may fulfill the same task at the working points. In this context, even if the working cycle is composed of a small number of points, the number of possible sequences can be very high, so that the robot programmer usually cannot evaluate them all to obtain the shortest possible cycle time. One of the most well-known problems used to define the optimal task order is the Travelling Salesman Problem (TSP), but in its original formulation, it does not allow to consider different robot configurations at the same working point. This paper aims at overcoming TSP limitations by adding some mathematical and conceptual constraints to the problem. With such improvements, TSP can be used successfully to optimize the cycle time of industrial robotic tasks where multiple configurations are allowed at the working points. Simulation and experimental results are presented to assess how cost (cycle time) and computational time are influenced by the proposed implementation.