The design of a production system is a strategic level decision. One of the key problems to solve is the line balancing problem that determines the efficiency of a production or assembly line. This class of problem has been widely studied in the literature. It determines important features, such as the number of stations, the takt time or the working conditions. Most of the variants of this problem consider only one objective function, but nowadays companies have to take into account different criteria. In this study, we consider a bi-objective variant of the simple assembly line balancing problem. We present a generic branch-and-bound method to solve exactly this problem. The objective functions are to minimise the takt time and the number of stations. To do so, bounds and bound sets are developed. The resulting method is numerically tested and compared to an ϵ-constraint method. These experiments show that the bi-objective branch-and-bound algorithm outperforms an ϵ-constraint method using a state-of-the-art single objective algorithm for more than 80% of the instances. Finally, we propose an analysis of the cases where the branch-and-bound method is outperformed.