A critical assumption in balancing assembly lines is that the line is ‘ serial ’ with no ‘ paralleling’ of tasks allowed. This constrains the cycle time to be at least equal to the maximum task time, which in turn limits the production rate. One alternative to increasing the production rate (hence lowering the cycle time) is by allowing parallel tasks in the assembly line at the cost of additional facilities. In this case, the problem becomes one of selecting the tasks to be paralleled such that the total cost is minimized. This problem is formulated as a mixed integer programme, and a branch and bound algorithm is presented for its solution. The structural properties of this programming problem are discussed, which con be used to improve the computational efficiency of our branch and bound algorithm. An illustrative problem and preliminary computational results are provided.