Notes: Toward Characterizing the Optimal Allocation of Storage Space in Production Line Systems with Variable Processing Times

This investigation considers certain issues regarding the optimal design of unpaced production lines with variable processing times. Under certain assumptions, including an equal allocation of buffer storage space between the respective pairs of stations, it is known that the optimal allocation of work is characterized by the "bowl phenomenon" whereby the interior stations (especially the center ones) are given preferential treatment (less work) over the end stations. The key question now being posed is: given an equal allocation of work to the respective stations, does the optimal allocation of buffer storage space between the respective pairs of stations follow an analogous pattern (the "storage bowl phenomenon") whereby the interior buffers (especially the center ones) are given preferential treatment (more space) over the end buffers? Because the decision variables now are discrete instead of continuous, the answer found in this study is: sometimes, but not in general. Characterizing the optimal allocation of storage space is a surprisingly subtle and complex problem. Despite the ambiguities, one dominant theme that runs throughout all of the results obtained is that, to the extent that preferential treatment in storage space allocations should be given, priority should be given to the interior buffers (especially the center ones) over the end buffers. The other key conclusion is that, when the total amount of storage space also is a decision variable, the overall optimal solution commonly follows a storage bowl phenomenon whereby the allocation of buffer storage space fits an inverted bowl pattern.