## 3 Results
### Prediction of the Number of Orders--Exponential Smoothing  
As part of the research, a universal model was selected to suit diverse time series of various types of research and provide precise data on the number of orders aggregated monthly. The chosen forecasting model is based on exponential smoothing, which uses a weighted moving average to reduce variance and predict future values of the series. The exponential methods employed include Brown's Model, Holt's Linear Model, and Winters' Model, all time series forecasting techniques. Figure 3: Graphs of accuracy and losses in training the recurrent neural network model. The Winters' Exponential Smoothing Model is an extension of the classic exponential smoothing model and takes into account seasonality and trends in the data [15]. * Level Component: Represents the baseline level of data over a given period of time. In [PERSON]'s Exponential Smoothing Model, it is updated according to the last observation and takes into account current level changes. * Seasonal Component: Represents cyclical changes in data, such as months of the year, days of the week, etc. It is accounted for in [PERSON]'s model by including a seasonal factor modifying the forecasts. * Trend Component: Represents a long-term upward or downward trend in the data. It is included to predict future trend changes. Exponential smoothing is a forecasting technique that assigns exponentially decreasing weights to historical observations. This means that the future value is not only dependent on the last observed value but on the entire series of values. The influence of older values is smaller than that of newer values. It is important to note that this technique assumes that the future value depends on the entire series of values. Exponential smoothing models are characterized by four parameters (\(\alpha\), \(\beta\), \(\gamma\), \(\phi\)), and various initialization methods are considered. The \(\beta\) parameter controls the trend, while the \(\phi\) parameter controls the strength of extinguishing the trend. The \(\gamma\) value is responsible for seasonality in the model. The main challenge in the algorithm is selecting the appropriate parameters to achieve the most accurate forecasts. Furthermore, the model allows for an independent determination of the nature of each component--trend, seasonality, and residuals--detecting whether each component is either additive or multiplicative. It is also possible to assume that a component does not appear in the series, particularly for trend and seasonality. To shorten the notation, we use the standard ETS designation for exponential smoothing models. The model components are represented by the letters E for error, T for trend, and S for seasonality. The appropriate symbols for each component type are then inserted: A for additive, M for multiplicative, and N for none (only for trend and seasonality). In the case of a damped trend, the letter 'd' is added. For instance, a model refers to a set of models with additive errors, a multiplicative damped trend, and no seasonality. Subsequent modifications and extensions of this algorithm gave it the form currently popularly used: AAA ETS, i.e., AAA = Additive Error, Additive Trend, and Additive Seasonality; ETS = Exponential Triple Smoothing algorithm [16]. The research scenario stated that the ten parameters with the highest reagent consumption (i.e., the largest number of tests) would be selected for testing. A list of the ten most frequently performed tests was compiled, taking into account that some tests do not require reagents (such as blood count tests or urinalysis). Although bHCG was only ranked 43 rd, it was included in the list due to the repeated tests on this hormone and its prediction being used as a reference value. Three separate forecast sub-models were developed for each of the tests mentioned in Table 1, one for each patient profile. Furthermore, it was noted that order values on weekends seldom exceed 5%. As a result, separate models were created for weekend forecasts.