Stochastic unpaced line design: Review and further experimental results

Previous design studies of unpaced assembly lines that exhibit stochastic task times indicate that an unbalanced allocation of task times results in optimal output rates. In this article, the authors present a comprehensive review of the previous literature on this topic and discuss the results of simulation experiments that test the bowl distribution for unbalancing unpaced lines. The simulation experiment was designed to test the bowl distribution in more realistic environments than previously tested and illustrates that a balanced line configuration is as good as or better than an unbalanced line configuration when task times are modeled with more typical values of variance. Stochastic unpaced assembly line research employs both simulation and analytical approaches to test the allocation of buffer capacity and task times to work stations. Analytical models are utilized to investigate simple line designs with exponential or Erlang task time distributions. Simulation is used for longer lines and for normal task time distributions. From the review of the previous research using both approaches, the authors note five major findings: (1) unbalancing task time allocation is optimal when task time variation is large; (2) unbalanced allocation of buffer storage capacity improves line output rate when task time variation is large; (3) output rate of an unpaced line decreases as the number of sequential workstations increases; (4) output rate increases as more buffer storage capacity is available; and (5) output rate decreases as the task time variation increases. Most of the previous research on unpaced lines investigated lines with few workstations and large task time variation. Empirical research by Dudley suggests that variation of task times in practice is much less than variations employed in previous unpaced line studies. The authors present the results from simulation experiments that model longer unpaced lines with lower levels of task time variance of the magnitude that is likely to occur in practice. The results of the present simulation experiments verify the benefits of using the bowl distribution for task time allocation when line lengths are short and task times experience large variance. However, when line lengths are extended or task time variation is reduced, the use of the bowl distribution for unbalancing the line degrades the line’s efficiency. In these situations, the optimal task time allocation is a balanced line. Two important implications for managers follow from the results of the present experiments: (1) that unpaced line output rate is relatively insensitive to moderate variations from optimal task time allocations when buffer storage is limited; and (2) that perfectly balanced line designs are optimal for most cases in practice.