Deterministic Equivalents for Stochastic Assembly Line Balancing

Two methods for considering variations in task completion times in the assembly line balancing problem are (1) assign tasks to stations such that the sum of the completion times is less than a fixed proportion of the cycle time and (2) assign tasks to stations such that the probability for completing all tasks within the cycle time is greater than a fixed value. In this paper, we show that for certain classes of distributions of task completion times, the first method, which is basically a deterministic approach to the problem, is equivalent to the second, which requires a stochastic formulation. The nature of the relationship is also demonstrated.