Balancing stochastic two-sided assembly lines

In a two-sided assembly line, tasks can be executed simultaneously on both sides of the line. One task cannot be started until both of its direct predecessors on the left and right sides are completed. Therefore, the start time of the task is the maximum of the two predecessors’ finish times. In many realistic situations, it is assumed that the task times are independent and normally distributed with known means and variances. However, the maximum of two normal variables is not normally distributed, but can be well approximated by results from extreme value theory. In this paper, we utilise these results to develop a solution methodology to balance two-sided assembly lines with stochastic task times, minimising the line length and the number of stations while guaranteeing all tasks are completed within the cycle time with a given confidence level.