*5.6. Validation*

To validate the simulation, factory floor-data information was used, where a minimum of 1700 and a maximum of 1750 pairs per day were observed. Therefore, before carrying out the experimentation, several tests were run, and details were corrected that lead us to reproduce what happens in the current process. An example of this is that the warehouse between Desma machine and the Flaming process cannot exceed 50 pairs of shoes and that was corrected in the simulation model. The average production per day in each activity is shown in Table 3.


**Table 3.** Average final production per day, current process, Arena ™ Software report.

Because validation is a comparison of the simulation model report against actual data, and the company does not provide us with data after the implementation, this step is not performed in the proposal.

#### *5.7. Experimentation*

The model was run for about 30 replications. Each one starts and ends according to the same rules and uses the same sets of parameters. In the real context, each replication represents a shift. It was decided to use 30 replications because the greater the number of replications, the more reliable the inference is regarding what is happening. There is convincing evidence that a sample size of n = 30 is sufficient to overcome the bias of the population distribution and provides approximately a normal sampling distribution of the random variables [28], which ensures that the sample can infer what is happening in the population. In this case, the simulation can infer what happens in the real process. In the proposal, 30 replications were made as well.

#### *5.8. Analysis of Results*

The indicators to compare the current process with the proposal are the percentage of use of each activity and the units produced at the end of each process, which includes, in this specific case, the pairs of shoes that are processed in the decorating area. As we observe in Table 4, the utilization percentage are registered, line 1 is of a lower percentage compared to line 2, and, when merging both lines into one, we can see that the utilization percentage of each activity increases considerably, which outpaces the current process. See Figures A3 and A4 for more information on the simulation in Arena™.


**Table 4.** Comparison of process indicators, average utilization per day: Current-Proposal.

The average production per day is presented in Table 5, where each activity appears with its respective production. The proposal has the same human resources than the current line 1 and line 2. See Figures A5 and A6 for more information on the simulation in Arena ™.


**Table 5.** Comparison of process indicators, average production per day: Current-Proposal.

Additionally, the inventory in the process is shown in Table 6 and it is useful to validate the simulation model. In the flaming and cleaning activities, whose utilization is higher, there are waiting lines, while, in activities where utilization is less, they do not exist.


**Table 6.** Inventory in the process by operation: Current-Proposal.

When performing an analysis of human resources per day, it was observed that human resources are underutilized. Due to this, it was decided to use OptQuest to maximize production using human resources as a constraint (see Table 7). Once the tool has been used to optimize, there is an increase to 41% of the average final production per day, which is equivalent to 2350 pairs of shoes (Table 8). This preserves the same number of workers. See Figure A7, Figure A8, and Figure A9 for more information on the simulation in Arena™.


**Table 7.** Comparison of human resource use per day Current-Proposal-Optimization.

<sup>1</sup> The total is the sum of human resources per activity of line 1 and 2 in the current process. 2. In the proposal, the same resources were used. 3. The optimization is the OpQuest suggestion to maximize production.



1. The total is the sum of average production per activity of line 1 and 2 in the current process. 2. The average production with the same resources in the proposal. 3. The optimization is the average production with the resource's suggestion of OpQuest.

In order to identify data affected by errors, the Grubbs test was applied for the data of the current process in Table 9 and for the data of the proposal in Table 10. Thirty simulations with one run were performed and the average production was recorded per work shift for both the current system with two lines (see Table 9) and the proposal with a single line (Table 10).

First, a Kolmogorov-Smirnov test was applied to evaluate if the data can be reasonably approximated by a normal distribution before applying the Grubbs test. It was concluded that both the data of the current process and those of the proposal have a normal distribution because the *p* value is greater than the value of α = 0.05. Then, the Grubbs test was made (see Figure 11).


**Table 9.** Average production/day of the current process.

**Table 10.** Average production/day of the proposed process.


**Figure 11.** Grubbs test (**a**) Atypical values, current process. (**b**) Atypical values, proposal.

Grubbs's test is defined for the hypothesis:

$$\begin{array}{l} \mathbf{H}\mathbf{0}: \text{ There are no outliers in the data set} \\ \mathbf{H}\mathbf{1}: \text{ There is at least one outlier in the data set} \end{array} \tag{1}$$

It was concluded that both the data of the current process and the proposal do not have outliers because the *p* value is greater than the value of α = 0.05. Additionally, to formally compare if the proposed method (Table 10) is better in terms of average production per work shift than the current one (Table 9), the following hypothesis test is proposed. The average production/day of the proposed process is higher than the average production/day of the current process, where μ1= proposed process and μ<sup>2</sup> = current process.

$$\begin{array}{ll} \text{H}\_{\mathbf{0}}: & \mu\_{1} = \mu\_{2} \\ \text{H}\_{\mathbf{1}}: & \mu\_{1} > \mu\_{2} \end{array} \tag{2}$$

To perform this test, it is necessary to know if the population variances are the same or different even when they are unknown [29]. Therefore, the following hypothesis test is performed in Minitab™ and presented in Table 11.


**Table 11.** Equality of variances test.

Because the value of *p* = 0.290 is greater than the significance level α = 0.05, there is statistical evidence to accept the null hypothesis, that is, the population variances, although unknown, are equal. This information is used to verify if the means are equal or if the mean of the proposal is greater than that of the current process defined in Equation (2). These calculations are also done with Minitab™ and presented in Table 12.

**Table 12.** Hypothesis Testing for Comparing Medians of two Populations.


Since the value *p* = 0 is less than the significance level α = 0.05, there is statistical evidence to reject the null hypothesis, that is, the mean of the average production per day is higher than the mean of the current process. Lastly, to know how superior it is, the confidence interval for the difference of the means is presented, 469 < μ\_1 − μ\_2 < 491. This interval determines the number of pairs of shoes that the proposed process can increase when compared to the current process with 95% reliability.

#### *5.9. Implementation*

In order to perform the implementation, the company was recommended to continue with the reengineering team, which is, in this case, the quality manager who served as the reengineering leader. The owner of the process was the production manager. The Reengineering team was formed by the Engineering, Human Resources, Warehouse of Raw Materials and Finished Product chiefs. They were the outside members. Additionally, the inside members were the coordinator of the decoration area and the quality inspector. The steering committee was made up of the chiefs of Human Resources, Purchasing, Accounting, and Engineering. Lastly, the Reengineering Czar had two main functions: to train and support the process owner and the reengineering team, and to coordinate all the reengineering activities that were launched.

To start with the implementation, all the reengineering collaborators met, and the leader spoke to them about the need to redesign the decorating area. The problem was exposed and the proposal that merges both lines was explained, giving rise to a new process flow and a new plant distribution. The amount of resources calculated in Table 8, in the optimization column, were used. The activities, who was accountable for them, approximate time and resources were defined among all, which gave rise to the Gantt Chart of the implementation. The company only granted permission to discuss the implementation in a general way, but implemented it in 35 days. Its historical results show a higher productivity increase than that reported in the proposal analysis with the simulation.

#### **6. Discussion**

As already mentioned, the indicators to study were the percentage of use of each activity and units produced at the end of each process, which, in this case, are the pairs of shoes that are processed in the decorating area. As we observe in Table 4, where the results of the utilization percentage are registered, line 1 is of a lower percentage compared to line 2, and, when merging both lines into one, we can see that the utilization percentage of each activity increases considerably, outpacing the current process. It is necessary to point out that the painting activity is underutilized. This is because, in the previous activity of cleaning, high inventories were generated in the process. Both the original and the proposed models were simulated in Arena™, using the same probability distributions and the original personnel to make the comparison.

In Table 8, it is observed that Line 1 ends the first activity with a production of 975 pairs of shoes during one shift. The following is the cleaning of the shoe with a total of 834, and so on. It is observed that the production is decreasing in each activity, which causes high inventories in the process. At the end of production, 814 pairs of shoes are obtained from Line 1 and 847 pairs of shoes are obtained in Line 2, which is a total of 1661 pairs of shoes obtained per day from the current process. Regarding the proposal, we can see that, at the end of the first activity, the current process is greater with a total of 2856 pairs of shoes, and, at the end of the process, in packaging, the proposal delivers more production, 2138 against 1661 pairs, which increases 29% of the current production. There are few inventories in the process in the proposal since it is observed that the pairs produced at the end of each activity are approximately constant. However, since this model uses the same probability distributions and human resources, even the painting activity is underused. For solving this, another OptQuest tool was used, which is an optimization module designed to facilitate its integration in applications that require the optimization of highly complex systems. In our case, we decided to maximize resources and number of staff that work in the decorating area. These are 24 people distributed in the different activities, as can be seen in Table 7. Once the tool has been used to optimize, there is an increase to 41% of the final average production per day, which is equivalent to 2350 pairs of shoes (see Table 8). Regarding the validation of the data, we have factory floor-data before the implementation but not after. This is a limitation of our work because validation is making a comparison between the results reported in the arena and real data. Therefore, the proposal could not be validated in only the current process.

#### **7. Conclusions**

In this research work, two methodologies were used to solve problems within industries. First, reengineering to conceptualize the problem and generate solution proposals. Second, simulation to compare the proposal conceived with the current process. Both methodologies were used to deal with the current problems presented by the company, and to issue a solution proposal. Despite the fact that, in this work, there is no theoretical contribution, there are practical contributions not only to help

the improvement of the processes, but also to do a complete analysis of the current process with its respective deficiencies, which were analyzed. Once the process where the improvement would be made was selected, a proposal was made that was tested through the simulation. Until the time of this research, there were no articles focused on reengineering in an industrial footwear plant supported by simulation. Moreover, this fusion of methodologies can be used in companies in another sector with their respective adaptations.

After performing the simulation experiments, the results indicate that the production rate increases by approximately 29% with the new configuration, and up to 41% when the human resources are optimized through OptQuest. The company implemented the configuration of the proposal, or more precisely the optimization, which brings significant improvements such as making better use of the factory space, eliminating unnecessary work, allowing better mobility, better use of resources, and more. Some of the limitations of this work was dealing with people by convincing them to get them out of preconceived ideas. The other was that we have factory floor-data after the implementation. In future work, we would like to implement the methodology but only when using other process analysis techniques.

**Author Contributions:** Conceptualization, E.S.H.-G., M.A.M.B., and R.C.-A. Methodology, E.S.H.-G. Software, R.C.-A. and M.A.M.B. Validation, E.S.H.-G. and R.C.-A. Formal analysis, E.S.H.-G. and M.A.M.B. Investigation, R.C.-A. and E.S.H.-G. Resources, E.S.H.-G. Data curation, R.C.-A. Writing—original draft preparation, E.S.H.-G. and R.C.-A. Writing—review and editing, E.S.H.-G. All authors have read and agreed to the published version of the manuscript for the term explanation.

**Funding:** This research did not receive external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.
