Future research

6. Conclusion & recommendations

6.4. Future research

In this research the focus shifted from reducing the setup and failure times to increasing the amount of machines in the system. For the current scale of production this indeed has a bigger impact on the throughput. However if the scale of production increases through the addition of machines, then the reduction of particularly the setup times could have a big impact. Methodologies such as the Single- Minute exchange of Die could prove useful; Cakmakci (2009) reports setup time reductions of up to 90% in the automotive industry using this methodology. Future research into the possibilities might prove worthwhile. Méndez & Rodríguez (2015) present a more in-depth example of how Single- Minute exchange of Die was applied to reduce the setup times at a production line of

Another option that is of interest is a possible change from the current Make To Order system to a Make To Stock system for the more regular products. This would allow for greater control over the setups. This is interesting because there are three different types of setups with different average setup times. Not only would this be helpful with the setups, it would also allow for a planning that takes into account that as the system grows, the bottlenecks will switch from the production

machines to other machines for certain types of products. In a Make To Stock system the location of the bottleneck in the system at a certain point in time would be easier to control. Rajagopalan (2002) offers a heuristic that allows for decisions regarding which products to make to stock and which products to make to order. In this heuristic the products selected for Make To Stock always have a reduction in the number of setups of over 50% compared to if these products were produced according to Make To Stock, showing the possibility for improvements in setups. Federgruen & Katalan (1999) offer different strategies for implementing a hybrid Make To Order and Make To Stop system. As an alternative to the addition of Make To Stock to the system, or as a complementary measure, improvements to the planning system are also interesting. As stated in Section 6.3 the addition of machines will shift the bottleneck for certain product types, thus reducing the throughput at the production machines as a reliable measure for the performance of the system. This has the added consequence that a planning based on the reduction of the setup times at the production machines may not always be optimal. Due to the nature of the system a resource driven planning that takes setup times into account would be worth investigating.

Bibliography

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Appendix A: Distribution fitting

For some of the random variables we conducted goodness-of-fit tests to assess the quality of the fitted theoretical distributions as based on the variable data. The random variables for which this was done were the production times at the production machine, for the bucket of 81 products per tray, the time to repai,r and the time between failures at the production machines. As explained in Chapter 3, there are more random variables but we did not perform goodness-of-fit tests on these for varying reasons.

As the goodness-of-fit test, the chi-squared test (χ2-test) is used. The chi-squared test splits a distribution into multiple bins. Each bin contains the same amount of expected observations. For example, if you have 100 data points, the chi-squared test will make bins where if one draws 100 random data points from the distribution, the same amount of points would be found in each of the bins. Then the amount of data points per bin is counted. If this number differs too much from the expected number of observations then the distribution does not fit with the data. The equation for the chi-squared test can be written as follows:

𝜒2_{= ∑}(𝑂𝑖− 𝐸𝑖)2 𝐸_𝑖 𝑛

𝑖=1

Where n is the number of bins, Oi is the frequency of empirical data in the bin and Ei is the expected frequency of the theoretical distribution. This shows that the χ2 measure is meant to show the difference between the data and the expected distribution.

The probability of obtaining a test result at least as extreme as the one found is shown as the p- value. If the p-value is smaller than 0.05 the theoretical distribution is rejected.

The chi-squared test outcomes for the processing times can be found in Table A.1, the test outcomes for the time to repair can be found in Table A.2 and the test outcomes for the time between failures can be found in Table A.3.

Table A.1: Chi-squared test for processing times

Distribution Beta Normal Erlang Exponential Gamma Lognormal Weibull p-value 1.27*10-10 7.01*10-9 0.0033 0 0.0056 7,39*10-4 8.26*10-10

Table A.2: Chi-squared test for time to repair

Distribution Beta Normal Erlang Exponential Gamma Lognormal Weibull p-value 5.31*10-13 0 0 2.52*10-12 4.42*10-13 8.66*10-13 1.24*10-12

Table A.3: Chi-squared test for time to failure

Distribution Beta Normal Erlang Exponential Gamma Lognormal Weibull p-value 0.17 0.26 x 0.81 0.82 0.40 0.82

For both the processing times and the time to repair all theoretical distribution are rejected. For the time to failure multiple distributions can be fitted, with the exception of the Erlang distribution. The Weibull distribution has the highest p-value.

Appendix B: Combining setup times and failure times reduction

In combining the setup times and failure times reduction we conducted 36 more

experiments. These experiments consist of all the additional configurations that were not

covered in

Table 5.2

. The outcomes for these experiments can be found in

Table B.1

. The

layout of this table is slightly different from

Table 5.2

. We have already established the broad

causes for the variability in the processes so adding a measure for the standard deviation in

this table is not interesting. Therefor the table will only concern the average throughputs.

The percentage of change compared to the current situation will also be shown, to make it

easier to interpret the orders of magnitude of changes. The numbers in the configuration

columns present the multiplier for the random variable. For example, a 0.25 in the Setup

times column means a 75% reduction in setup times, so only 25% remains.

Table B.1: Outcomes additional experiments

Production Gluing robots Handgluing System

Setup times Failure times Average Percentage Average Percentage Average Percentage Average Percentage

Current situation 1 1 4624 1.00 4624 1.00 6219 1.00 4625 1.00 Experiment 1 0 0 5500 1.19 5500 1.19 7311 1.18 5500 1.19 Experiment 2 0.25 0 5320 1.15 5320 1.15 7069 1.14 5319 1.15 Experiment 3 0.5 0 5146 1.11 5146 1.11 6857 1.10 5142 1.11 Experiment 4 0.75 0 4996 1.08 4995 1.08 6652 1.07 4988 1.08 Experiment 5 1.25 0 4724 1.02 4724 1.02 6323 1.02 4726 1.02 Experiment 6 1.5 0 4605 1.00 4604 1.00 6199 1.00 4604 1.00 Experiment 7 0 0.25 5423 1.17 5423 1.17 7186 1.16 5417 1.17 Experiment 8 0.25 0.25 5242 1.13 5241 1.13 6983 1.12 5241 1.13 Experiment 9 0.5 0.25 5077 1.10 5077 1.10 6776 1.09 5075 1.10 Experiment 10 0.75 0.25 4921 1.06 4921 1.06 6534 1.05 4916 1.06 Experiment 11 1.25 0.25 4661 1.01 4661 1.01 6262 1.01 4666 1.01 Experiment 12 1.5 0.25 4547 0.98 4546 0.98 6143 0.99 4549 0.98 Experiment 13 0 0.5 5354 1.16 5354 1.16 7101 1.14 5353 1.16 Experiment 14 0.25 0.5 5168 1.12 5173 1.12 6882 1.11 5170 1.12 Experiment 15 0.5 0.5 5010 1.08 5009 1.08 6658 1.07 5000 1.08 Experiment 16 0.75 0.5 4861 1.05 4861 1.05 6458 1.04 4859 1.05 Experiment 17 1.25 0.5 4608 1.00 4608 1.00 6206 1.00 4611 1.00 Experiment 18 1.5 0.5 4503 0.97 4503 0.97 6098 0.98 4504 0.97 Experiment 19 0 0.75 5290 1.14 5289 1.14 7028 1.13 5286 1.14 Experiment 20 0.25 0.75 5110 1.11 5110 1.11 6810 1.10 5110 1.10 Experiment 21 0.5 0.75 4948 1.07 4948 1.07 6560 1.05 4943 1.07 Experiment 22 0.75 0.75 4804 1.04 4803 1.04 6403 1.03 4805 1.04 Experiment 23 1.25 0.75 4560 0.99 4560 0.99 6153 0.99 4559 0.99 Experiment 24 1.5 0.75 4456 0.96 4456 0.96 6047 0.97 4457 0.96

52 Experiment 25 0 1.25 5160 1.12 5159 1.12 6852 1.10 5155 1.11 Experiment 26 0.25 1.25 4984 1.08 4984 1.08 6614 1.06 4978 1.08 Experiment 27 0.5 1.25 4836 1.05 4835 1.05 6433 1.03 4835 1.05 Experiment 28 0.75 1.25 4695 1.02 4695 1.02 6292 1.01 4697 1.02 Experiment 29 1.25 1.25 4472 0.97 4472 0.97 6061 0.97 4471 0.97 Experiment 30 1.5 1.25 4365 0.94 4365 0.94 5899 0.95 4361 0.94 Experiment 31 0 1.5 5090 1.10 5089 1.10 6744 1.08 5083 1.10 Experiment 32 0.25 1.5 4930 1.07 4930 1.07 6542 1.05 4930 1.07 Experiment 33 0.5 1.5 4779 1.03 4779 1.03 6375 1.03 4778 1.03 Experiment 34 0.75 1.5 4648 1.01 4648 1.01 6246 1.00 4651 1.01 Experiment 35 1.25 1.5 4424 0.96 4423 0.96 5987 0.96 4421 0.96 Experiment 36 1.5 1.5 4325 0.94 4325 0.94 5841 0.94 4324 0.93

Appendix C: Changing the product mix

In Section 5.2 we mentioned that there is a process by which we can use the outcomes of the experiments with the extreme product mixes to construct any potential product mix that may occur in the future. Here we illustrate how this is possible. For our example we use the current situation, after this we discuss how this approach can be applied to all product mixes. The data used will be from Table 5.4. This means that in our example we will use the data from the individual machines to construct their individual maximum average throughput

From the experiments we have the following data: - Total amount of products produced

- Total amount of products produced per bucket - Average throughput of products

- Average throughput of products per bucket

From these the averages of these indicators we construct the throughput for the product mixes.

Table C.1: Total amount of products produced under the normal production schedule

Production machines Bucket 81 2x Bucket 81 1x Bucket 36&49 Bucket 25 Total Total amount of products produced 244686 37276 181673 58812 522446

Percentage of product mix 0.47 0.07 0.35 0.11 1.00

Gluing robots Bucket 81 2x Bucket 81 1x Bucket 36&49 Bucket 25 Total

Total amount of products produced 362969 61390 312927 108225 845511

Percentage of product mix 0.43 0.07 0.37 0.13 1.00

Hand gluing machine Bucket 81 2x Bucket 81 1x Bucket 36&49 Bucket 25 Total

Total amount of products produced 439206 45879 279388 96519 860992

Percentage of product mix 0.51 0.05 0.32 0.11 1.00

System Bucket 81 2x Bucket 81 1x Bucket 36&49 Bucket 25 Total

Total amount of products produced 270210 45405 268851 57025 680777

Percentage of product mix 0.40 0.07 0.39 0.08 1.00 In Table C.1 we can see the total amounts of products produced per station and how much of the product mix consists of products from the different buckets. Due to different total amounts the product mixes differ slightly. This is expected in this situation. If a normal production run was used, these numbers would be more the same, except for the hand gluing machine due to rework.

Table C.2: Total amount of products produced under extreme production schedule

Production machines Bucket 81 2x Bucket 81 1x Bucket 36&49 Bucket 25 Average amount of products produced 633516 633516 460978 377757

Gluing robots

Average amount of products produced 734362 966022 1048629 758875

Hand gluing machine

Average amount of products produced 1262821 1262821 763929 389740

System

Average amount of products produced 776918 1262821 763929 389740

In Table C.2 we can see the total amounts of products produced per station for the extreme product mixes. For example a production machine is able to product 633516 products if it is only making products of the size 1 inch by 1 inch.

With these two tables we can now formulate how much of the production time is spent on making different products. For example: 47% of the product mix consists of products form the bucket 81 2x at the production machine. This amounts to the total number of 244686 products. The amount of production time spent on making these products is 244686/633516 = 39%. As we can see, while the product accounts for 47% of the product mix it is only being produced 39% of the time. Table C.3 shows these calculations being applied to all the other stations and buckets as well.

Table C.3: Average time spent on production

Production machines Bucket 81 2x Bucket 81 1x Bucket 36&49 Bucket 25 Average time spent on production 0.39 0.06 0.39 0.16

Gluing robots

Average time spent on production 0.49 0.06 0.30 0.14

Hand gluing machine

Average time spent on production 0.35 0.04 0.37 0.25

System

Average time spent on production 0.34 0.04 0.35 0.15

With these percentages we now know how much time is spent on each bucket for each individual station. The next step is to multiply these percentages with the throughputs found under the extreme product mixes. The idea behind this is that 39% of the time the production machine is running at the throughput found for bucket 81 2x, 6% of the time it is running at the throughput found for bucket 81 1x, 39% of the time it is running at the throughput found for bucket 36&49 and 16% of the time it is running at the throughput found for bucket 25. The results of multiplying these numbers with the throughputs from Table 5.4 can be found in Table C.4

Table C.4: Average constructed throughputs

Production machines Bucket 81 2x Bucket 81 1x Bucket 36&49 Bucket 25 Total Average throughput 2447 373 1817 588 5225 Gluing robots Average throughput 3631 614 3130 1082 8457 Hand gluing machine

Average throughput 4401 459 2794 965 8619 System

Average throughput 2702 454 2689 963 6808

If we compare the throughputs from Table 5.4 with the throughputs from Table C.4 we find that the outcomes are indeed close to each other. 5225 compared to 5223 for the production machines, 8457 compared to 8458 for the gluing robots, 8619 compared to 8614 for the hand gluing station, and 6808 compared to 6808 for the system as a whole.

Using the same approach, the average throughput for any other product mix can be constructed, both for the characteristics of individual machines, as shown here, and for the system as a whole, such as the results found in Table 5.3.

Appendix D: Incremental machine addition

Table D.1: Incremental addition approach full results

Machine added: Product mix 1 2 3 4 5 6 7 8 9 10

Production machine Current situation 6808 6808 8457 8457 11560 12686 12686 13616 16183 16914

Bucket 81 x2 6328 6328 7346 7346 11019 11019 11019 12656 14691 14691

Bucket 81 x1 8410 9662 9662 9662 14017 14493 14493 19325 19325 19325

Bucket 49&36 6120 7639 8160 10200 10200 12239 14279 14279 14279 16319

Bucket 25 3897 3897 6686 7589 7795 7795 7795 7795 11692 11692

Gluing robot Current situation 4624 6808 6936 9248 9248 11560 13616 13616 13871 16183

Bucket 81 x2 5607 6328 8410 11019 11213 12656 12656 12656 16820 18364

Bucket 81 x1 5607 8410 8410 11213 11213 14017 16820 16820 16820 19623

Bucket 49&36 4080 6120 6120 8160 8160 10200 12239 12239 12239 14279

Bucket 25 3343 3897 5015 6686 6686 7795 7795 7795 10030 11692

Hand gluing machine Current situation 4624 6936 6936 8457 9248 11560 12686 13871 13871 16183

Bucket 81 x2 5607 7346 7346 7346 11019 11019 11019 14691 14691 14691

Bucket 81 x1 5607 8410 8410 9662 11213 14017 14493 16820 16820 19325