On the robustness of the bowl phenomenon

The bowl phenomenon provides a way of increasing the throughput of some production line systems with variable processing times by purposely unbalancing the line in a certain manner. However, achieving this increase in throughput depends on correctly identifying the values of the system parameters to estimate the optimal amount of unbalance and then actually being able to assign work to stations according to the optimal bowl allocation. In this paper we study the robustness of the bowl phenomenon by examining the effect of inaccurately estimating the optimal amount of unbalance and the effect of deviating from the optimal bowl allocation. Our results show that the bowl phenomenon is relatively robust in the sense that fairly large errors (even 50%) in the amount of unbalance still provide most of the potential improvement in throughput over a perfectly balanced line. Moreover, the throughput still exceeds that of a perfectly balanced line in most cases even when the work allocation to each station deviates from the optimal bowl allocation by as much as 10%. We also address the question of whether the optimal bowl allocation or the balanced line provides a more robust ‘target’ when assigning work to stations. When the deviations from these two targets are of the same magnitude, we found that the optimal bowl allocation target yields the larger throughput in most cases, where the average difference between their throughputs is roughly the same as the difference between the optimal throughput and the throughput of a balanced line. Furthermore, for the same magnitude of deviation, the throughput depends more heavily on the direction of the deviation from the balanced line than that from the optimal bowl allocation, so that the risk of a substantially reduced throughput is much larger when using the balanced line as the target. Therefore, the optimal bowl allocation provides a much more robust target than the balanced line.