This paper propounds a stochastic methodology—SALB—for the solution of a single-model assembly line balancing, which has been developed in response to the problems associated with the allocation of tasks to work stations, especially where uncertainties (and hence risks) abound. The study adopts the methodology of stochastic modelling, whereby various probability distributions are integrated within a modified COMSOAL algorithm, as a means of addressing the uncertainties associated with key assembly line balancing variables, such as cycle time and task times. The proposed methodology incorporates four objective criteria options—minimizing the number of work stations, minimizing the balance delay, minimizing the cycle time, or a combination of two or more thereof. These are designed and equipped with the capability to generate a range of possible solutions to the assembly line balancing problem, from which an ‘optimal’ solution can be ascertained. The SALB methodology is demonstrated with a case study; the results obtained show that the mode is capable of facilitating valuable foresight, as well as enhance effective cost savings, in the planning, designing and scheduling or work tasks, especially in the face of possible perturbations necessitated by uncertainties in tasks and cycle times.