## 4 Performance Analysis
### Calculation of Cost Savings by Incorporating Forecasting Error Cost  
Finally, in this paper, we derive the adjusted prediction results, which are calculated by recalculating the optimal prediction results reflecting the cost of the prediction error, based on the results of the previously derived point prediction and the interval prediction. First, regression modeling is performed on the transient prediction cost and the underestimation cost. A regression model can be constructed from data from a small company, D, that provided the data used in the study. First, the cost of transient forecasting is directly related to the cost of storage per unit, since unnecessary inventories must be kept. For D firms, the storage cost per unit is fixed at KRW 687, which is linearly increased as the prediction error increases. On the other hand, tribal forecasting costs are the opportunity costs that result from insufficient demand forecasts and high discount rates. Figure 10 illustrates how to derive the underestimation cost. The forecasting cost can be expressed by the following formula. \[Price(V)=(-1331.6296)\times log(V+13175.8341)+37166.7634 \tag{16}\]  
Figure 8: The result of interval prediction for warehousing out data. Figure 9: Warehousing out: What prediction range the actual value belongs to. In this case, \(V\) is the order quantity reflecting the prediction result, and _Price_ is the product price per unit. In order to derive the underestimation cost, we first calculate the commodity price per unit according to the order quantity. The price per unit is not fixed, and the larger the order, the more the discount rate is applied. Therefore, the price per unit is regression modeled by means of curve fitting. The types of kernel functions to be used in the experiments are selected by using three types of functions: linear, log, and inverse. We used the data for 64 orders from D company and the order cost per unit. The experimental results are as follows. The experimental results on Table 4 show that the logarithmic function model is suitable for modeling the order cost per unit. Using this, the price per unit can be modeled as follows. It is possible to calculate the forecasting error cost per unit, depending on the price of the product per calculated unit. We adjust the predicted value over the overestimation cost and underestimation cost per unit according to Equation (16). By means of the above equation, the prediction result is readjusted to reduce the cost according to the weight of each cost. Next, we test the effect of the cost reduction by comparing the prediction result with the existing point prediction and the re-adjusted prediction result according to the above formula. Based on the data for the years 2016-2019, we will output the forecast results for 10 weeks in 2020. As in the above experiments, four validations are done. We compare the predicted results by means of the general LSTM with the predicted results that are readjusted by the interval prediction. (99%, 95%, 90%, 80%, each confidence interval). At this time, the predicted result is not directly related to the order quantity. In order to derive the order quantity, it is necessary to comprehensively consider the quantity of stock currently possessed and the stock quantity to be secured for safety. Therefore, we add the constant value to the predicted result to formulate the order quantity. However, since there is no case where the order quantity becomes negative, the minimum constant value is set to 2000. In the experiment, the change of performance according to the change of the constant value is confirmed. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **RMSE** & **MAPE** \\ \hline Linear & 1257.48 & 7.53 \\ Log & 1091.34 & 6.73 \\ Inverse & 1139.46 & 7.08 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of the linear function model, log function model, and inverse function model. Figure 10: Calculating the underestimation cost.