# An Optimization Tool for Production Planning: A Case Study in a Textile Industry
### Results and Discussion  
After the model validation, the next step was to use the optimization tool to find the best production sequence for the production operation. The GAWizard tool of simulation software by SIEMENS Plant Simulation(r) was used. It follows the steps shown in Figure 5. Some of the parameters involved in the process were: (i) one hundred generations; (ii) population size of ten individuals; (iii) elitist system was used for selection, where the best solutions are used to generate offspring for the next generation; (iv) single objective optimization, and (v) the best solution is stored which maximizes the throughput. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **January** & **February** & **March** & **May** \\ \hline Exp.1 & 8163 & 7428 & 8196 & 7279 \\ Exp.2 & 8509 & 7972 & 8377 & 7296 \\ Exp.3 & 8476 & 7873 & 8410 & 7411 \\ Exp.4 & 8509 & 7971 & 8361 & 7262 \\ Exp.5 & 8575 & 8134 & 8361 & 7345 \\ Exp.6 & 8493 & 8166 & 8361 & 7295 \\ Exp.7 & 8526 & 8117 & 8410 & 7443 \\ Exp.8 & 8690 & 8134 & 8312 & 7377 \\ Exp.9 & 8410 & 8003 & 8427 & 7328 \\ Exp.10 & 8575 & 8166 & 8443 & 7460 \\ Exp.11 & 8295 & 7873 & 8410 & 7394 \\ Exp.12 & 8378 & 7857 & 8295 & 7246 \\ Exp.13 & 8427 & 8021 & 8377 & 7394 \\ Exp.14 & 8674 & 8263 & 8427 & 7476 \\ Exp.15 & 8427 & 8198 & 8410 & 7328 \\ Exp.16 & 8592 & 8086 & 8443 & 7493 \\ Exp.17 & 8542 & 8118 & 8460 & 7476 \\ Exp.18 & 8509 & 7971 & 8460 & 7427 \\ Exp.19 & 8509 & 8118 & 8328 & 7229 \\ Exp.20 & 8394 & 8182 & 8410 & 7329 \\ \hline Average & 8483.65 & 8032.55 & 8383.9 & 7364.4 \\ Standard & 122.39 & 183.97 & 64.42 & 82.29 \\ Deviation & & & & \\ Minimum Value & 8163 & 7428 & 8196 & 7229 \\ Maximum Value & 8690 & 8263 & 8460 & 7493 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Simulated production data for months analyzed. Figure 5: Steps for genetic algorithm—GAWizard (SIEMENS, 2011). In Figure 6, we can observe the evolution of optimized solutions against the number of generations. It is evident that one hundred generations are enough for obtaining the optimization convergence. Moreover, as generations advance, the difference between worst solution and best solution decreases; in other words, the individual's fitness looks similar. Table 6 presents the results of optimization for January. It shows that production mix and lot sizes used initially by the company compared to the optimized production mix found after the optimization procedure. The optimized production mix/sequence takes the least amount of time for monthly production. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{3}{c}{**JANUARY**} \\ \hline
**Start Production** & \multicolumn{1}{c}{**Number**} & \multicolumn{1}{c}{**Optimized**} & \\
**MIX** & & **Production MIX** & **Number** \\ \hline.MUs.PV & 10 &.MUs.PV & 10 \\.MUs.PV & 10 &.MUs.PV & 10 \\.MUs.Piquet & 5 &.MUs.PV & 10 \\.MUs.Cloth & 5 &.MUs.PV & 10 \\.MUs.PV & 10 &.MUs.PV & 10 \\.MUs.PV & 10 &.MUs.PV & 10 \\.MUs.PV & 10 &.MUs.PV & 10 \\.MUs.Rb. PV & 3 &.MUs.PV & 10 \\.MUs.Piquet & 5 &.MUs.Piquet & 10 \\.MUs.Piquet & 5 &.MUs.Piquet & 10 \\.MUs.Piquet & 5 &.MUs.Cloth & 5 \\.MUs.PV & 10 &.MUs.Cloth & 5 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Optimization results for January. Figure 6: Evolution of the results in the months analyzed. With the results of the optimization, Table 7 was obtained presenting the production performance before and after optimization. It is observed that the amount of fabric manufactured is higher and the amount of overtime worked is lower after the optimization. For example, in February, it took the company an extra 91 h to complete the planned production, whereas after the optimization, it took 15 h. Similar improvements were also observed in the other three months simulated. Figure 7 shows the evolution of results with respect to a varying number of generations. For January, the production system produces 8163 units without the application of any optimization (GA) procedure.