Characterizing the optimal allocation of storage space in production line systems with variable processing times

We consider the optimal allocation of buffer storage spaces in unpaced production lines with variable processing times. It is known that for a fixed total number of buffer spaces, the production rate can often be improved by deliberately unbalancing the buffer allocations in an inverted bowl pattern (the "storage bowl phenomenon"), with more storage space allocated to the internal stations than to the end stations. It has been hypothesized that if the total number of buffer spaces is also a decision variable, then for a reasonable cost model the optimal allocation would have one additional storage space at each of the internal stations. This paper uses a cost model to show that the optimal allocation is more complicated than this. For balanced lines, the inverted bowl pattern is typically optimal, but the bowl shape becomes more and more pronounced (in an absolute sense) with larger numbers of buffer spaces. However, the relative shape of the bowl stays fairly constant. However, if the workload is unbalanced, the buffer space pattern deviates from the bowl pattern by reducing the number of buffer spaces in buffers that are not adjacent to the bottleneck machine.