## 4 Results
### Production Demand Forecast  
To perform aggregate planning, it is needed to identify demand forecast data. As the studied company did not have its demand forecast, it was necessary to perform it. Otherwise, only data would be collected. To prepare the production demand forecast, the historical data of the production of kg of potato were considered in the period of 60 months, from January 2014 to December 2018, given in Appendix A (Table A3). Therefore, the first step was to analyze the data profile surveyed to identify the components present, as shown in Figure 5.  
From Figure 5, it is possible to notice that potato production is a series that shows a slight downward trend with high and low peaks. However, it is also observed that it does not present a well-defined pattern of seasonality and cyclicality. Therefore, the correlogram was plotted to understand if the series was random or if it had any tendency or seasonality, as seen in Figure 6. When the series is random, it has autocorrelations close to zero. However, when there is a trend or a seasonality, the series shows a downward trend or positive peaks in the values. Figure 4: Power demand costs. Figure 5: Potato production history from January 2014 to December 2018. In Figure 6, the vertical axis indicates autocorrelation, and the horizontal axis indicates lag. The blue dashed line indicates where it is significantly different from zero. Note that all values except the first are within the blue dashed line limit. This means zero autocorrelation, indicating that potato production can be random and supposedly stationary. On the other hand, if the values were above the dashed line, the series would not be random and would have to be treated with a moving average, which is not the case. However, to be sure of the statements, it was necessary to carry out a test to prove the assumptions. The Augmented Dickey-Fuller (ADF) test resulted in \(-3.5467\), Lag order = 3, and p-value = 0.0453, confirming the alternative hypothesis that the process is stationary. In this case, potato production can be random and stationary. From the ADF test, the series decomposition into trend and seasonality was performed, as shown in the graph in Figure 7.  
After differentiating the actual demand, the components' performance and behavior show seasonality in the production of potatoes, always in the same period over five years. As for the trend, it is possible to observe a slight growth in 2014; from 2015, it started to  
Figure 6: Correlogram of the potato production time series with normalized data. Figure 7: Components of trend and seasonality. decrease. This can be explained by the crisis in mid-2014, with the drop in the Brazilian Gross Domestic Product (GDP) [36], which directly affected the cooperative's sales. The STL algorithm performs time series smoothing using the LOESS algorithm [37] in two loops; the inner loop iterates between seasonal and trend smoothing, and the outer loop minimizes the effect of outliers. During the inner loop, the seasonal component is calculated first and removed to calculate the trend component. Then, the remainder is calculated by subtracting the seasonal and trend components from the time series. Decomposing seasonal trends using LOESS (STL) is a robust time-series decomposition method often used in economic and environmental analyses. The STL method uses locally adjusted regression models to decompose a time series into trend, seasonal, and remainder components [38; 39; 40]. The series was divided into two sets of data, the first consisting of samples from 1 to 52 and the second from 53 to 60, to check the quality and to plot the profile of the additive and multiplicative Holt-Winters models, as shown in Figure 8.  
It can be noticed from Figure 8 that the profile behavior of the two models is close to the profile of the original data. However, this visual analysis does not define the best model to represent the demand forecast. For this reason, forecast errors were calculated.