This paper addresses the parallel assembly lines balancing problem (PALBP) with multi-line workstations, lines with different cycle times and buffer sizing. When a PALB system works with lines with different cycle times, the lines with multi-line workstations have to produce in batches; thus, the use of buffers may be needed. For the first time in the literature, this study jointly solved the PALBP and the buffer sizing problem (PALBP-B). Due to the multi-objective nature of the problem (minimising the number of workstations and the total buffer size in the multi-line workstations), several multi-objective heuristics and metaheuristics are proposed to solve the PALBP-B. Finally, an extensive computational experiment is carried out to analyse all the procedures presented.