# A System Dynamics Approach to Optimize Milk Production in an Industrial Ranch
## 3 Research Model
### Identification of Important Variables and Their Optimization through DOE Technique  
Although the modeling approach of system dynamics is applicable to identify the system's behavior over time, the determination of the rate of the effect of different factors in problem-solving is also important. Therefore, the DOE technique is used to determine the interaction of all factors together and the adjustment of different factors. The DOE technique, as a statistical tool, is widely used to systematically analyze the identification of the effect of different factors as well as the interactions they have with each other [24]. In this article, the DOE technique was used to identify important variables and to optimize the response variable. The used software was Minitab software version 17.1. To obtain the optimal results, the important variables must first be recognized in order to maximize milk production. The DEO technique route in Minitab software to identify important variables is as follows:  
Stat\(\rightarrow\) DOE\(\rightarrow\) Factorial\(\rightarrow\) Create Factorial Design... \(\rightarrow\) Plackett-Burman design  
The number of auxiliary variables of the designed stock-flow diagram is equal to 18. These variables indicate the effective factors in milk production. To identify the important variables in the DOE technique, it is necessary to consider the high level and low level of each factor. These levels have been considered by collecting the ideas of five experts from different sections of the Fereidan Ahrar ranch and investigating the previous statistics. The given low and high levels are shown in Table 2. Figures 6 and 7 show the results obtained from 40 experiments on the response variable of production in year 12. As can be seen in these diagrams, among the 18 auxiliary variables, the variables that were the most important in milk production were production cycle rate, voluntary omission rate 2, input rate 1, input rate 2, and finally the effect of medical costs 3, respectively. From these experiments, it can also be concluded that the obligatory omission was controlled in two classes of heifer and calf, and there was no need to spend more costs to control it. Therefore, it is important to control obligatory and voluntary omissions from the dairy herd. \begin{table}
\begin{tabular}{l c c} \hline
**Variable Name** & **Low Level** & **High Level** \\ \hline BR: Birth Rate & 0.014 & 0.016 \\ \hline OOR 1: Obligatory Omission Rate 1 & \(-\)0.005 & \(-\)0.0044 \\ \hline MC 1: Medical Cost 1 & 860,000 & 900,000 \\ \hline MCE 1: Medical Cost Effect 1 & 418,000 & 420,000 \\ \hline VOR 1: Voluntary Omission Rate 1 & 0.012 & 0.014 \\ \hline IR 1: Input Rate 1 & 0.026 & 0.03 \\ \hline OOR 2: Obligatory Omission Rate 2 & \(-\)0.029 & \(-\)0.0278 \\ \hline MC 2: Medical Cost 2 & 609,000 & 631,000 \\ \hline MCE 2: Medical Cost Effect 2 & 1,031,000 & 1,049,000 \\ \hline IR 2: Input Rate 2 & 0.078 & 0.08 \\ \hline OOR 3: Obligatory Omission Rate 3 & 0.0016 & 0.0017 \\ \hline MC 3: Medical Cost 3 & 1,368,000 & 1,392,000 \\ \hline MCE 3: Medical Cost Effect 3 & 365,000 & 377,000 \\ \hline VOR 2: Voluntary Omission Rate 2 & 0.049 & 0.051 \\ \hline PCR: Production Cycle Rate & 0.72 & 0.76 \\ \hline PA: Production Amount & 12,240 & 12,250 \\ \hline SR: Sale Rate & 0.97 & 0.98 \\ \hline IUA: Internal Use Amount & 55,700 & 55,712 \\ \hline \end{tabular}
\end{table} 
Table 2: High and low levels of auxiliary variables. Figure 6: Pareto chart for the identification of important variables in production. After the identification of important variables, three levels were considered including two high and low levels and the real rate of the important variable, and then the full tests were carried out to gain the optimal value of each variable. The route for conducting tests in software Minitab is as follows:  
Stat\(\rightarrow\) DOE\(\rightarrow\) Factorial\(\rightarrow\) Create Factorial Design \(\ldots\rightarrow\) General Full Factorial Design  
Figures 8 and 9 show the results obtained from 243 experiments.