Transfer line balancing problems (TLBP) deal with the optimization of serial machining lines. At every machine, the operations are performed by blocks. The operations within each block are executed simultaneously by the same multi-spindle head. In the lines considered here, the spindle heads of each machine are activated sequentially. The objective of TLBP is to group the operations into blocks and to assign the blocks to machines in order to minimize the total amount of the required equipment (spindle heads and machines). This problem is described and all the most promising exact and heuristic algorithms, recently suggested for it, are compared via detailed computational experiments.