Topología de las redes HFC.

On request of PMA, the influence of different delivery numbers and intervals will be experimented. In the base model, it is assumed that the delivery day is fixed (Monday). Moreover, it is also assumed that the delivery numbers are always the same (6 AC-types and 12 B-types). Though, in reality, this is not the case. Customer X delivers different numbers quite arbitrarily to PMA, resulting in a lot of variability which influences the operations heavily. In this section, this variability will be investigated. Scenario 1 was modeled by allowing every day to be a potential delivery day. Furthermore, the intervals between these delivery days are either 3 or 11 days. The simulation model selects a random

74 number of days and sets this as a new interval such that the average interval length remains a week, but the variance that is present is also modeled. In this way, the situations can be compared with all other values equal.

Scenario 2 was modeled by setting a fixed delivery day (Monday), just like in the base model. Though, the numbers that will be delivered are not fixed (18) but different. For the AC-type, this number fluctuates randomly between 4 and 8, whereas for type B, this number fluctuates between 8 and 16. Again, it was made sure that the average remains equal such that the situations can be compared with all other values equal.

Scenario 3 was modeled by combining scenario 1 and 2 into one model. These experiments resulted in the following confidence intervals (95%) for the average total throughput time (sec):

Figure 5: Confidence intervals for the average total throughput time, for the variability experiments (base model only).

The confidence intervals are partially overlapping. Though, the average of the combined model lays higher than the other scenarios, whereas the average of the different intervals is higher than the average of the different numbers. The average of the base model is much lower. This confidence interval does also not overlap with any other confidence intervals. So, the base models looks like the best-performing model.

The following confidence intervals (95%) for the average WIP level (pc.) have been constructed:

Figure 6: Confidence intervals for the average total WIP, for the variability experiments (base model only).

In this graph, the WIP of the combination model and the model with only different delivery numbers seem to be similar. The confidence interval of the combination model is slightly larger. The average of the confidence interval of the different delivery intervals seem to lay lower. Though, the base

5600000 5700000 5800000 5900000 6000000 6100000 6200000 6300000 6400000 Different delivery intervals Different delivery numbers

Combination Base model

Av ar age to ta l T T (s ec) Scenario Interval Left bound Interval right bound Average 166 171 176 181 Different delivery intervals Different delivery numbers

Combination Base model

WIP (p c.) Scenario Interval Left bound Interval right bound Average

75 model is, again, lower and smaller than all other scenarios. So, it seems that it is again the

best-performing model. To better compare the scenarios, a paired-T approach (confidence level 95%) was used in order to say something about the difference between the scenarios. This was done in

appendix F.4. In addition, on request of the project supervisor, also the difference in WIP and WIP value is added. This is, however, not based on a statistical test, but simply on the difference between the two means.

Table 22: Comparing variability based on time gains, WIP, and WIP value (base model).

Approximate extra time regarding base model

Difference in mean WIP regarding the base model

Difference in mean WIP value regarding the base model

Different delivery intervals

4 days and 8 hours to 5 days and 23 hours.

4,14 €20716

Different delivery numbers

2 days and 5 hours to 4 days and 14 hours.

9,03 €45174

Combination 5 days and 16 hours to 8

days and 16 hours.

9,4 €47046

The table shows considerable time gains in total throughput time. Other interesting results are:

Table 23: Waiting times in the base model and the models with variability (base model).

Avg. Waiting for Palmary (DD:HH:MM:SS)

Avg. Waiting for Grob (DD:HH:MM:SS)

Avg. Weekly output (pc.)

Different delivery intervals 04:13:08:10 09:12:46:21 17,08

Different delivery numbers 05:16:57:36 07:04:58:09 18,03

Combination 05:21:01:57 10:02:34:07 17,12

Base model 02:20:05:40 06:21:12:57 18

The goal of this table is to show the increase in waiting times while lower or similar outputs are attained. For the MRP model, only the combination (both delivering different numbers and in different intervals) was compared. This resulted in the same conclusion with similar numbers. On request of the project supervisor, one extra experiment is run. In this experiment, the interval varies between 6, 7 or 8 days, and the number of delivered bearing supports vary between 5, 6, or 7 AC types, and 11, 12, or 13 B types bearing supports. This would, based on the assumptions, perhaps be more realistic in the future. In this way, not only the two extremes are compared (no variability vs. a lot of variability), but also something in between. The average total throughput time gain regarding the base model would then be (based on paired-t approach, sign. level 95%) and the difference between mean WIP and WIP value:

Table 24: The influence of little variability on the base model.

Extra throughput time regarding base model

WIP gain regarding base model

WIP value gain regarding base model Model with little

variability

2 days and 4 hours to 2 days and 18 hours.

3,35 €167746

76 throughput time saving regarding the model with more variability would then be (based on paired-t approach, sign. level 95%) and the difference between mean WIP and WIP value:

Table 25: Savings by reducing variability.

Throughput time saving

WIP saving WIP value saving

Model with little variability

3 days and 3 hours to 6 days and 7 hours

6,06 €30300

Analyzing the results

The assumption in the base model, in which the delivery numbers and delivery intervals are fixed, heavily influences the results total average throughput time and WIP levels. As expected and

underlined in literature several times, variance heavily influences waiting times and thus the average total throughput times. In all scenarios, the average total throughput time was longer and the WIP-levels were larger while attaining a lower or similar output. This output is lower since more parts are in the WIP. Moreover, the variance of this WIP is much larger together with the variance in the total throughput time (Little’s Law). Interestingly, the increase in WIP in the combination model is not much larger than the WIP in the model where only the delivery numbers are varying while the throughput time is much larger. The variability in WIP in the combination model is much larger though, as displayed by the confidence interval. Perhaps, this has some influence on this result. Lastly, the MRP-model shows a similar increase in its average total throughput time. This is because the variability affects the same things as in the base model, which do not depend on the used planning approach.

Based on these results, PMA would heavily improve its efficiency if a fixed delivery day together with fixed numbers will be negotiated with customer X. This was also underlined by the director. This thesis provided extra prove in these negotiations. Perhaps, this variability cannot be completely removed. Though, it shows that reducing variability already decreases the total throughput time significantly. As shown by the differences in WIP value, this can also be beneficial for the customer since less of their bearing supports will be in the WIP. In this way, the customer would have less capital tied up in stock. Furthermore, it can also be statistically proven that negotiating fixed numbers is more effective than negotiating fixed intervals.

To conclude this section, I want to mention that I believe that in reality, the effects would perhaps be even more severe. In reality, much more randomness is present than is assumed in the model. Think about machine break downs, illness of employees, production errors. These are only a few examples, but I can think of many more examples. All this randomness does create even more variability (even though the added randomness is less than the sum of the two). Since all machines are running on high utilization, waiting times would increase significantly, as shown by Slack, Brandon-Jones, and Johnston (2013, p. 119).