The effect of the “COV” (coefficient of variation of the operation cycle time) factor setting on throughput rate performance of all four production methods is shown in Table 9. The high setting of COV was 50% (the standard deviation is 50% of the average operation cycle time). The low setting was 10%.
One-Piece DBR DynDBR TTG Average COV = 1 (50%) 8022 9079 9345 9556 Average COV = 0 (10%) 8119 9092 9365 9587 Difference 0 vs. 1 Setting 97 13 20 31 % Difference 1.19% 0.14% .21% 0.33% p-value <0.0001 0.596 0.512 0.032
Table 9: Average Throughput Rate Results for Operation Cycle Time Variation Factor Settings – Light Machining Process
Of the four methods, high operation cycle time variation had the largest
(throughput rate degradation) effect when using the one-piece flow method. The delta from the high COV setting (standard deviation = 50% of each operations’ cycle time) to the low setting (standard deviation = 10% of each operations’ cycle time) was 97 units, or 1.19%. This was statistically significant (p-value < 0.0001); and was also expected. The one-piece flow method had the least WIP in the production cell (average of 11 units) and the smallest transfer-batch size (one unit). Both WIP and large transfer-batches dampen the effect of variation. The reasoning is as follows. Operation cycle time variation can create gaps of “no-WIP” at certain operations. If a cycle of an operation was on the faster end of the probability distribution, followed by a cycle on the slower end of the
process. When there was ample WIP between operations this negates the effect of variation, as there are usually items to process. Minimal WIP, therefore, can create gaps of “no WIP” in the process. Additional support for this hypothesis, and for one-piece flow’s underperformance under high operation cycle time variation, can be seen more clearly in Figure 5 (below), which shows the average WIP level in the one-piece flow cell reported out once each hour. Whenever WIP was below six units, at least one of the flow cell operations was idle. Note, not shown on this graph is that for some replications, at several time-periods, the one-piece flow cell had zero WIP, which implies that all operations are idle, resulting in zero throughput. Essentially, the one-piece flow cell, by design, did not provide enough WIP to overcome the gaps of “no WIP” that result from variation in operation cycle time. These gaps created “lost utilization” on constraint operations, resulting in lost throughput. As opposed to DBR and TTG, which allow larger amounts of WIP in the flow cell (discussed later), one-piece flow “starved” itself at various points in time.
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Figure 5: One-Piece Flow WIP by Hour – Light Machining Process
The one unit transfer-batch size used in one-piece flow also hurt throughput rate performance under conditions of high operation cycle time variation. One piece flow’s transfer-batch size of one unit resulted in each operation realizing the full operation cycle time variation. According to the Law of large numbers, processing time variation of a large batch will be reduced relative to the mean of the batch (realized variation = 1 / transfer-batch1/2). With one unit in the transfer-batch, the Law of large numbers has no
effect. This confirms the findings of Yavuz and Satir (1995). It should be noted that Yavuz and Satir (1995) evaluated many more levels of COV; from 10% up to 90%. Their study showed greater degradation in throughput rate as COV increased beyond 50%. (Note a COV setting of 50% was used in this study, as this was the highest
observed operation cycle time variation provided by the case study company. We wanted to use a high, but realistic, level of variation in this experiment.)
However, despite the reasons that high operation cycle time variation affected throughput rate performance of a one-piece flow cell more than DBR or TTG, it is interesting that high operation cycle time variation only degraded throughput rate by 1.19%. This may, or may not be important to practitioners. This was the least
“impactful” of the three factors for one-piece flow. Therefore, for this light machining process, with a high operation cycle time variation, even one piece flow may be a reasonable choice of production method. This would depend, of course, on the value of 1% improvement in throughput rate to the firm.
The effect of high operation cycle time variation, for the DBR and DynDBR methods, was not significant. When operation cycle time variation was high versus low, the impact was negligible. The delta from high to low for DBR was only 13 units, and for DynDBR it was only 20 units. This was not statistically significant (p-value = 0.596 and 0.512). The DBR and DynDBR methods had similarly large quantities of WIP in the production cell. In addition, they had the largest amount of WIP at every operation (see Figure 6 below). As mentioned above, WIP dampens the effect of variation. Therefore, it was no surprise that the methods with the most WIP would be least affected by high operation cycle time variation. In addition, transfer-batches used in the DBR and DynDBR methods reduce variation of the batch, as supported by the Law of large numbers. With a transfer-batch size of 15 units, the variation, relative to an individual unit, realized in any transfer-batch was reduced by 74% (1 – 1/151/2). DBR and
DynDBR’s combination of high WIP levels and the use of transfer-batches negate the impact of operation cycle time variation on this light machining process; even with
Revision: July 2, 2014 Copyright, Mitchell A. Millstein, 2014 66 unbalanced cycle times and moving constraints. Therefore, processes with high
operation cycle time variation may lend themselves to the use of DBR or DynDBR as the choice of scheduling / WIP control method.
For the TTG process, the difference of operation cycle time variation at the high versus low setting was statistically significant. However, the degradation can be
considered practically unimportant. While the p-value was 0.032, the delta from high to low was only 31 units, or a 0.33% reduction in throughput rate. TTG was robust with regards to operation cycle time variation for the same reasons as DBR (discussed above). With an average transfer-batch size of 30 units, the variation realized by the batch was reduced by 82% (1 – 1/301/2). The fact that it was impacted more (a reduction in
throughput rate of 13 for DBR and 20 for DynDBR versus 31for TTG) is due to the lower level of WIP in the TTG process (see Figure 6). However, this difference in the
reduction for the TTG versus the DBR method (18 units over an entire week) and DynDBR method (11 units over an entire week) may not be something that would be important to practitioners.
Figure 6: WIP in Each Operation – Light Machining Process
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Section 7.4: Effect of Set-Up Time on Throughput Rate – Light Machining