# Dye Schedule Optimization: A Case Study in a Textile Industry
## 4 Evaluation Model
### Structuring for Test  
To achieve the objectives of the research, which proposes the creation of a model that guides the prediction of reduced setup time, with the adoption of optimization tools, it is necessary to carry out a certain number of tests, in different process configurations, to generate a quantity of data that can provide a function capable of responding to most situations that may be encountered. As mentioned before, it was evaluated those three factors are relevant to the operation, namely: machine group, SKU number and planning horizon. As the machine groups are already known (slasher dye and loop dye) and we know that the planning horizon will vary from one to four weeks, it remains to define the number of SKUs. For this, an analysis was carried out on the company's data to identify the number of processed SKUs by the dyeing machine throughout 2018. According to Table 1, we can identify each machine, the number of dyeing batches and the SKU number processed throughout the month. A single SKU can be processed more than once throughout the month, so the number of batches is greater than the number of SKUs. From these data, it was possible to build a histogram demonstrating the frequency of the number of processed SKU per month for the two groups of machines, as shown in Scheme 1. The importance of this parameter is due to its variability throughout the year, mainly due to market seasonality and fashion trends. Thus, a range of SKU quantities to be tested was defined, which could guarantee a good range of results. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & & & & & & & \\  & Number & Number & Number & Number & Number & Number & Number \\ \hline  & February/18 & 26 & 13 & 21 & 5 & 21 & 8 \\  & March/18 & 21 & 9 & 18 & 6 & 24 & 8 \\  & April/18 & 30 & 7 & 22 & 6 & 19 & 6 \\  & May/18 & 29 & 12 & 24 & 7 & 23 & 9 \\  & June/18 & 14 & 8 & 14 & 4 & 15 & 8 \\  & July/18 & 21 & 9 & 25 & 6 & 21 & 9 \\  & August/18 & 29 & 14 & 24 & 6 & 25 & 9 \\  & September/18 & 28 & 12 & 22 &  
The histograms were thought to select many SKUs for testing to obtain a range of results, which serve as parameters for constructing a linear regression equation. This can be used in other companies with the same similar process. Therefore, for the slasher dye group, the SKU number defined was: 4, 6, 8, 9 and 12. As for the loop dye group, the SKU number was: 5, 7, 9, 11, 12, 13 and 16. This dataset should cover the possible occurrences. Table 2 shows how the configurations of the number of SKUs per dye machine were structured. With the definition of these configurations, it was possible to advance the measurement of setup times according to the empirical sequencing through the company's reports. From the report, it was possible to extract, for each machine, the processing sequence throughout each month, fractionate the horizons. With the setup time matrices, it was possible to measure the setup time to go from SKU \(i\) to SKU \(j\). A total of 52 tests were carried out, 24 tests for the slasher dye machine group and 28 tests for the loop dye machine group. Figure 3 shows an example of setup time measurement performed on machine 7, with 13 SKU, broken down into four horizons. \begin{table}
\begin{tabular}{c c c} \hline Value Group & Machine & SKU Number \\ Slasher Dye & & 6 \\  & 1 & 9 \\  & & 12 \\ \hline  & 3 & 4 \\ \hline  & 4 & 8 \\ \hline Loop Dye & 6 & 5 \\ \hline  & & 11 \\  & 7 & 13 \\  & & 16 \\ \hline  & 8 & 9 \\  & & 12 \\ \hline \end{tabular}
\end{table} 
Table 2: SKU numbers were chosen to test. It is adapting the TSP model to the case study, starting from the need to produce a given amount of \(n\) dyeing batches for each SKU, which must be sequenced to obtain the shortest setup time, represented by \(c_{ij}\) in the Equation (1). There will be situations that, for the same SKU, the demand will be greater than one dyeing batch. Thus, for each batch to be processed, its code will be indexed to construct the setup time matrix. In this way, the same SKU can appear more than once in the matrix.