In this paper, a methodology is developed to solve the single-model, stochastic assembly line balancing problem for the objective of minimizing the total labor cost and the expected incompletion cost arising from tasks not completed within the prescribed cycle time. The methodology is based on determining an initial DP based solution and its improvement using a branch-and-bound procedure which uses an approximate solution instead of a lower bound for fathoming nodes. Detailed experimentation shows the superiority of this method over the most promising one from the literature.