How to design a production line that has a bottleneck

Three production lines have been optimized in the figure. That is, we have found the minimal total inventory space required to produce .88 parts per minute for three different lines. The figure displays how that space is distributed.

Case 2 and 3 are similar to Case 1, except that Machine 5 (and only Machine 5) is replaced by a less reliable model. In both cases, the reliability of Machine 5 is reduced to .905. In Case 2, MTTF = 100 and MTTR = 10.5 minutes; In Case 3, MTTF = 200 and MTTR = 21 minutes. There is thus a well-defined bottleneck.

With no buffering between the machines, the production rate of both Cases 2 and 3 would be .475. Again, each machine (including the bottleneck) could meet the required production rate in isolation, but the complete system cannot without inventory buffering between the machines. The minimal required total inventory space is room for 485 parts for Case 2 and 523 for Case 3.

Line | Production rate with no buffers | Minimal buffer space for production rate target (.88 parts/min) |
---|---|---|

Case 1 | .487 | 430 |

Case 2 | .475 | 485 |

Case 3 | .475 | 523 |

- The additional inventory space is allocated approximately
symmetrically around the bottleneck, but it is not all placed
precisely at the bottleneck.
- Case 3 needs more space than Case 2. This suggests that increased
repair time is worse than increased failure frequency.
- Case 1 exhibits the
*inverted bowl phenomenon*, observed by Hillier, So, and Boling (1993). A line with identical machines requires less buffer space at the ends because of the usual assumption that the first machine is never starved and the last machine is never blocked. - Especially sharp-eyed readers may notice that the graphs look a
little uneven. This is due mainly to the fact that we have restricted
the solution to integers: we are assuming that the line is producing
discrete items. In addition, the results shown may be slightly
non-optimal.

The zero-buffer production rates were calculated from the work of Buzacott (1968). The optimal distributions of buffer space were calculated from Gershwin and Goldis (1995) and Schor (1995).

*References:*

J. A. Buzacott (1968), ``Prediction of the Efficiency of Production
Systems without Internal Storage,'' *Int. J. Prod. Res.*, Vol. 6,
No. 3, pp. 173-188.

S. B. Gershwin and Y. Goldis (1995), ``Efficient Algorithms for Transfer Line Design,'' MIT Laboratory for Manufacturing and Productivity Report LMP-95-005, November, 1995, 50 pages.

F. S. Hillier, K. C. So, and R. W. Boling (1993), ``Toward
Characterizing the Optimal Allocation of Storage Space in Production
Line Systems with Variable Processing Times,'' *Management
Science*, Volume 39, Number 1, January, 1993, pp. 126-133.

Copyright © Massachusetts Institute of Technology 1996. All rights reserved.