Certain types of manufacturing processes can be modelled by assembly line balancing problems. In this work we deal with a specific assembly line balancing problem that is know as the assembly line worker assignment and balancing problem (ALWABP). This problem appears in settings where tasks must be assigned to workers, and workers to work stations. Task processing times are worker specific, and workers might even be incompatible with certain tasks. The ALWABP was introduced to model assembly lines typical for sheltered work centers for the Disabled. In this paper we introduce an algorithm based on beam search for solving the ALWABP with the objective of minimizing the cycle time when given a fixed number of work stations, respectively workers. The experimental results show that our algorithm is currently a state-of-the-art method for this version of the ALWABP. In comparison to results from the literature, our algorithm obtains better or equal results in all cases. Moreover, the algorithm is very robust for what concerns the application to problem instances of different characteristics.