On the Optimal Allocation of Work in Symmetrically Unbalanced Production Line Systems with Variable Operation Times

This paper provides results related to the optimal design of unpaced production lines. It has been shown previously that unbalancing an unpaced production line in an appropriate way will increase its production rate. Results are presented here which show how the optimal allocation of work between stations changes with respect to -- the number of work stations in the line, -- the limit on the amount of work-in-progress, and -- the variance of station operation times. -- An analysis of results given here demonstrate the following system characteristics. When the number of stations in the production line increases, the average amount of unbalance in the optimal allocation remains about the same, but the increase in mean production rate obtained by using the optimal allocation rather than the balanced line becomes substantially larger. If the operation times are highly variable (exponential distribution), the effect of increasing in-process storage space is to substantially decrease the average amount of unbalance in the optimal allocation but to only slightly decrease the resulting improvement over the balanced line. If the amount of in-process storage space is very small, the effect of decreasing the variability of operation times is to decrease these same quantities but at a surprisingly slow rate. On the other hand, the effect of simultaneously increasing in-process storage space and decreasing the variability of operation times is to very rapidly decrease both the optimal unbalance and the resulting improvement. The model used to characterize an unpaced production line system is the classical queueing system with finite queues in series.