Comparison of Moving Average and Exponential Smoothing Methods in Sales Forecasting of Banana Chips Products in Pd. Dwi

2022

Sales forecasts predict a company's sales. PD Dwi Putra's banana chip sales have fluctuated every month for the past few years, resulting in stock shortages and excesses. Forecasting using historical sales data uses time series methods like moving average and exponential smoothing. This study compares the two forecasting methods to find the lowest error rate and the best method for the company to use for the next four years. The exponential smoothing method outperforms the moving average method for MAPE, MSE, and MAD values, so it is used for future forecasting. According to research, companies should use exponential smoothing with parameter α = 0.6 for the next four years because it has the lowest forecasting error rate. Thus, these parameters are used to forecast the next few years.

LITERATURE REVIEW A. Operation management
Operations management is one of the sciences in the management field, which is concentrated in the operating sector of the company. This field is very important because it is directly involved in the company's production or operational processes. According to (Heizer & Render, 2015), operations management is creating products and services by transforming inputs into outputs. According to (Hendrawaty, 2018), operations management is the process of achieving and utilizing resources to organize or produce useful goods or services to achieve organizational goals and objectives. Meanwhile (Stevenson & Chuong, 2014) argues that operations management is the main figure in the system. It has ultimate responsibility for the creation of goods or the provision of services.

B. Forecasting
Forecasting is one of the interesting topics in research. In addition, forecasting can also provide an overview for a company to decide on the future of the company or business. According to (Wardah & Iskandar, 2016), forecasting is a method for calculating future values using past data. According to (Yuniastari & Wirawan, 2017), forecasting in a company is widely used to provide and describe the company's future conditions that can assist decisionmaking regarding what steps can be taken to meet consumer demand. Forecasting is a way to measure, estimate, and predict what needs are needed to meet consumer demand for goods and services.

C. Moving Average
Moving average or moving average is a forecasting method from a group of observational data. It calculates the average value of the data as a forecast value for the next period. Forecasting using the moving average method performs a calculation process from the most recent data values and deletes old data values (Hajjah & Marlim, 2021). The moving average method can be calculated using the following equation.
= ∑Data requests n previous periods n Ft = forecasting value in period t ∑ = Total data requests for the previous period n = The number of data periods of the moving average

D. Exponential Smoothing
Exponential smoothing or exponential smoothing is a moving average forecasting method with a sophisticated weighting system but is still easy to use. The exponential smoothing method is generally used to predict data with irregular patterns or patterns with large and volatile changes (Hajjah & Marlim, 2021). The exponential smoothing method can be calculated using the following equation.

E. Sale
Sales are the peak of activity in a company. This is because the income earned comes from these sales. A company's profit is also based on how much the product is sold and is useful for customers. According to (Triani et al., 2020), selling introduces, influences, and provides explanations so buyers can find the services or goods provided and reach a transaction or agreement on a price that benefits both parties. According to (Rudiyanto & Hariyanti, 2016), sales are the transfer of ownership rights to goods or the provision of services carried out by sales to purchases at a mutually agreed price with the amount charged to the customer in the sale of goods or services in an accounting period, the success of the sales business can be seen of the sales volume obtained. Factors that affect sales (Swastha, 2012)

F. Production
According to (Anil et al., 2008), production is defined as the step-by-step conversion of one form of material to another through a chemical or mechanical process to create or enhance product usability for the user. According to (Edwood Buffa in Anil Kumar & Suresh, 2008), Edwood Buffa defines production as creating goods and services. Meanwhile, according to (Hendrawaty, 2018), production is the addition or creation of uses or utilities due to form and place, thus requiring factors of production. In economics, the factors of production consist of land, nature, capital, labor, and capabilities, as well as technology.

G. MAD (Mean Absolute Deviation)
MAD is a way to measure the value of forecasting error (error) for a model (Kurniawan et al., 2022). The value is calculated by dividing the absolute total value of each forecasting error by the number of data periods (Amalia et al., 2020). The final mark in this measurement is useful to avoid negative error values. The smaller the MAD value obtained, the better the forecasting results. The following equation can calculate the MAD value.

H. MSE (Mean Squared Error)
MSE is a way to measure forecast error through an absolute average value or an overall average that is squared (Kurniawan et al., 2022). MSE is a calculation technique by calculating the difference between the forecast data and the actual data, which is then squared. The smaller the MSE value generated, the better the forecasting results. The following equation can calculate the MSE value. Research from (Hajjah & Marlim, 2021) states that the forecasting results are good if the MAPE value obtained is smaller. The criteria for the MAPE score are as follows:

J. POM-QM Software
Production and Operation Management Quantitative Methods or more commonly known as POM-QM, is a software or software that can be used on a computer to solve a problem in production and operations in a quantitative way. This software is also very useful in carrying out a sales forecast using historical data from company sales that have occurred in previous years to be implemented or implied in the future. According to (Weiss et al., 2018), POM-QM software or software is software designed for production and operations management, quantitative methods, management science, and operations research. The POM-QM software can be used either to solve a problem or to check an answer that has been created manually.

METHOD 1. Research Design
This study uses comparative quantitative research to find the method with the lowest forecasting error. Quantitative research methods like comparative function compare two or more variables or treatments (Bungin, 2014). Quantitative research compares two or more events, activities, or programs. The research component's relationships show the comparison. Similarities and differences in planning, implementation, and supporting factors are calculated. The snack food trading company PD Dwi Putra, which makes kapok banana chips, conducted this research. Jalan Raya Murni Jaya, Daya Asri, Tumijajar District, West Tulang Bawang Regency, Lampung Province, houses the company. We use sales from April 2019 to March 2023 were forecasted for April 2023 to March 2027 in this study. PD Dwi Putra's main product, banana chips, is the focus of this research.

Data Type, Source, and Collection
This study uses quantitative data. This study uses PD Dwi Putra's 2019-2023 banana chip sales data. This study's qualitative data comes from interviewees. This study's primary data source will be used to write this scientific paper and support quantitative data forecasts for April 2023 to March 2027. Secondary data is data. Researchers gathered them from company documents. This data provides PD Dwi Putra's history and employee count. Forecasting research also used product sales archives. Data collection is crucial to research. The researcher interviewed and documented PD Dwi Putra in this study to obtain information and company data.

Observation Time
The relevant company, PD Dwi Putra, permitted researchers to observe and collect data. Researchers observed and communicated with the company in October 2022 and collected data in January 2023. April 2023 collected more data. Researchers did this because data adequacy tests needed more data. So data is collected again for 48 months (four years) from April 2019 to March 2023 to forecast from April 2023 to March 2027.

Statistical Analysis
After collecting research data, test its adequacy before analyzing it. Research data sample size affects forecast confidence and accuracy. Next, plot the data results in graphical form to determine if the data is trend, seasonal, constant, or cyclical. This study forecast errors using POM-QM for Windows v5. MAD, MSE, and MAPE calculate forecasting errors. Figure 3.1 shows POM-QM's Windows v5 debut. The data was also tested for adequacy, plots, and normality. Amalia et al. (2020) calculate MAD by dividing the total absolute value of each forecasting error by the number of data periods. This MAD calculation removes plus and minus signs to simplify data processing. MSE is the average forecasting error squared (Amalia et al., 2020). Forecasting will be more accurate if the MSE value is close to zero. MAPE (Mean Absolute Percentage Error) is the average absolute difference between predicted and actual values expressed as a percentage of the actual value (Amalia et al., 2020). Because it shows a percentage of the forecasted data, the MAPE value makes forecast data analysis easier.

RESARCH RESULT A. Data collection
Sales data or demand data for PD Dwi Putra's banana chips were collected directly from the company located on Jalan Raya Murni Jaya, Daya Asri, Tumijajar District, West Tulang Bawang Regency, Lampung Province. The data was taken as an Excel file through the Accosys software used at the company. In this study, the data used for analysis is PD Dwi Putra's historical sales data from 2019 to 2023 or, in more detail, from April 2019 to March 2023. PD Dwi Putra's historical sales data can be seen in the following table.

B. Data Adequacy Test
The data adequacy test is carried out after obtaining the historical sales data needed to be processed and forecast sales for the next few years. This data adequacy test is carried out to see whether the data that has been collected is sufficient or not sufficient to carry out a sales forecast. If the value of N', which is the required data in this case, is smaller than that of N, which is the current amount of data, then the research data obtained is sufficient and acceptable. Meanwhile, if the value of N' is greater than that of N, then data must be taken again to be sufficient. The level of accuracy used by the researcher is 10%, namely the maximum deviation from the measurement results to the actual value, and the level of confidence used by the researcher is 95%, namely the amount of confidence or probability that the data that has been obtained lies at a predetermined level of accuracy. Then with a level of accuracy of 10% and a confidence level of 95%, the value of K/S = 20. The data adequacy test above obtained a value of N' of 30.67019279 < the value of N, namely 48. Thus, because the value of N' is smaller than that of N, the historical sales data of PD Dwi Putra can be accepted for processing sales forecasting data for the next few years.

C. Data Plots
The data plot is done in graphical form to see the properties of the data. Each periodic data series obtained is shown as a point. The data period is located in the coordinates (x-axis), and the number of sales is in the coordinates (y-axis). PD Dwi Putra's sales historical data plot can be seen in the following figure.

Figure.1 Sales Data Plot of PD Dwi Putra April 2019 -March 2023 (Source: Data Processed by Researchers, 2023)
Based on the data plots in Figure below, it can be concluded that the total sales of PD Dwi Putra from April 2019 to March 2023 have the form of a seasonal pattern seen in the graph, which often experiences repetition in the same period. Sales increases often occur in October and December. The decline in sales often occurs in September and November. The data plot also detects an upward trend in sales from 2019 to 2023.

D. Normality test
The Kolmogorov-Smirnov normality test used in this study is the principle of finding the largest deviation from the cumulative distribution function of the observation data to the theoretical cumulative distribution function. In the normality test, the data is normally distributed if the statistical Z value is > 0.05. Meanwhile, the data is not normally distributed if the statistical Z value is <0.05. The results of the normality test in the table above, which were carried out using the Kolmogorov Smirnov test type, obtained a significance value for the normality test of 0.166 which in this case is greater than 0.05, which means that the data processed in this study is normally distributed.

E. Measuring Forecasting Error
Measurement of forecasting errors or errors in this study was carried out using the help of POM-QM software with three forecasting error measurement tools in it, namely MAD (Mean Absolute Deviation), MSE (Mean Squared Error), and MAPE (Mean Absolute Percentage Error). This study focuses on the MAPE (Mean Absolute Percentage Error) value results, which are used to determine the lowest error rate in forecasting sales data, which is processed as a percentage error. If the error rate is smaller and closer to 0, the forecast will be better and more accurate.
Data plots that have been done previously show a seasonal data pattern and have also confirmed the method used in this study. This study used two research methods, namely moving average and exponential smoothing, which then compared the results of forecasting errors between the two methods. The moving average method uses the parameters MA1, MA2, MA3, MA4, and MA6. Meanwhile, the exponential smoothing method uses the parameter α (alpha) 0.1; 0.2; 0.3; 0.4; 0.5; 0.6; 0.7; 0.8; and 0.9. The recapitulation of error measurement results was carried out using the help of Microsoft Excel.
The results of forecasting error measurements can be seen in the following Journal of Finance and Business Digital (JFBD) Vol. 2, No. 6, 2023: 193-208 203 The results of forecasting errors are obtained after the data is processed using the POM-QM software using the moving average and exponential smoothing methods. Processing to calculate forecasting errors is carried out individually with the period parameter set in the moving average method and the alpha parameter set in the exponential smoothing method. The moving average method selects the MA1, MA2, MA3, MA4, and MA6 periods based on these periods that can be used in division within one year. In the exponential smoothing method, the data is processed with the alpha parameter as a whole with a value of 0.1 to 0.9.
Recapitulation of the results of forecasting errors is then carried out to make it easier to read the result of the data processing that has been done. By focusing on the objective results of this study, namely, to find out which method has the lowest error rate, the MAPE (Mean Absolute Percentage Error) value is used as a reference or basis for decision-making. The MAPE score criteria in this study refer to Table MAPE Score Criteria.

Figure 1. Results of MAPE Values on Measurement of Forecasting Errors (Source: Data Processed by Researchers, 2023)
The results of forecasting error data processing in this study show that the MAPE (Mean Absolute Percentage Error) value with the smallest number is in the exponential smoothing method with the parameter alpha (α) set at 0.6 with a percentage value of 16.65%. With the value that has been obtained, if the percentage of forecasting error has a value of 10% ≤ x <20%, then this percentage value is included in the MAPE value criteria with good forecasting ability.

F. Sales Forecasting for 2023-2027
Sales forecasting is carried out for the next four years, to be exact, from April 2023 to March 2027, with a focus on collecting company sales data. This is because this research focuses on forecasting products already in the form of finished goods. The method chosen and used to predict sales or demand in the next few years in this study is the exponential smoothing method with parameter alpha (α) = 0.6 with a forecasting error rate of 16.65%. This research is a type of comparative quantitative research that compares two or more methods to see the best results obtained and can be implemented in related companies in the future. The methods used in this study are the moving average method and the exponential smoothing method. The moving average method is processed using the parameters MA1, MA2, MA3, MA4, and MA6, while the exponential smoothing method is processed using the parameter alpha (α) 0.1; 0.2; 0.3; 0.4; 0.5; 0.6; 0.7; 0.8; and 0.9. This research uses historical data on sales of PD Dwi Putra from April 2019 to March 2023. Before entering the forecasting stage, the first step must be to collect historical sales data and ensure that the data is sufficient for forecasting in the coming several years. The data collected and obtained must be tested with a data adequacy test beforehand when a forecast is to be made.
Data adequacy testing is carried out so that the processed data meets or meets the requirements specified in forecasting. This study uses an accuracy level of 10% and a confidence level of 95% with a K/S value of 20. The data is considered sufficient if N', which in this case is the amount currently required, has a value smaller than the value of N, which is the amount of data-used for processing. Based on the results of the data adequacy test in this study, which in this case obtained an N' value of 30.67019279 which in this case was smaller than the N value of 48, therefore the data was declared sufficient or accepted and could be used for the next stage for plotted data. Data plots in graphical form in this study were carried out to see the nature of the historical data on the sales of PD Dwi Putra that were formed. When plotting the data, the result is that the data is in seasonal form with graphical indications showing an increase in sales which always occurs in October and December. Sales decline also always occurs in September and November. Apart from that, there is an increasing trend in the data from 2019 to 2023. When the data plots have been done, the next step is to test the normality of the data.
The data normality test in this study was conducted to see whether the data taken as research samples were normally distributed or not normally distributed. In the normality test conducted using the Kolmogorov Smirnov with parameters, the data is normally distributed if the Z statistic value is > 0.05. The data is not normally distributed if the Z statistic value is <0.05. The normality test conducted using Kolmogorov Smirnov found that the significant value in the sample or research data was 0.166, which in this case had a value greater than 0.05. Thus, the data or sample in this study is normally distributed. In addition, the data plot in a histogram graph also shows normally distributed data marked by an inverted bellshaped curve, in which case most of the data is inside the curve. So that the data in this study are normally distributed. After the normality test, the next step is to measure the forecasting data error.
Forecasting error measurement is carried out using POM-QM software using MAD (Mean Absolute Deviation), MSE (Mean Squared Error), and MAPE (Mean Absolute Percentage Error) tools. However, this study focuses on the results of the MAPE score concerning the criteria for the MAPE value. Based on the results of calculating forecasting error measurements in this study, it was found that the exponential smoothing method using the parameter alpha (α) 0.6 has the lowest error rate compared to other parameters, namely with a MAPE value of (16.65%), MSE of (3634189), and MAD of (1405.29), so for forecasting the next four years using the values of these methods and parameters.
This study's results align with previous research (Hajjah & Marlim, 2021) with the title "Error Analysis Toward Sales Data Forecasting" to predict LED lamp sales by comparing two methods, namely moving average and exponential smoothing. The results of this study show that the exponential smoothing method has the lowest error rate compared to the moving average method. The results of this study also contradict previous research from (Achmadani & Rochmoeljati, 2021) with the title "Sales Forecasting Analysis of Sea Snack at PD Adi Nugraha Food Industry" and previous research from (Kurniawan et al., 2022) with the title "Model Comparison Single Moving Average & Exponential Smoothing for Forecasting Sales of NUCless AMDK, both of which get the result that the forecasting method using the moving average method has better results compared to the exponential smoothing method in making a forecast.

CONCLUSION AND RECOMMENDATION
Data collection, adequacy tests, plots, and processing show seasonal patterns. The exponential smoothing method outperforms the moving average method, with the parameter alpha (α) 0.6 yielding the lowest forecasting error with MAPE values of (16.65%), MSE of (3634189), and MAD of (1405.29). The selected methods and parameters are used to forecast the next few years. Researchers recommend that companies review their methods for predicting future requests after four years or by April 2027. The latest historical data can change the value of K/S = 20, used in this study, affecting the forecasting method. The company should implement the exponential smoothing method with an alpha (α) parameter of 0.6 for the next four years to predict future requests and reduce seasonal requests. Forecasting research should start with data plots and data adequacy tests to determine whether data patterns are seasonal, constant, trend, or a combination of patterns. The data adequacy test also verifies data needed for forecasting.

ADVANCED RESEARCH
Other researchers who discuss the topic of forecasting should pay attention to several initial things, such as data plots and data adequacy tests, in order to determine whether the pattern contained in the data is in the form of a seasonal pattern, a constant trend, or a combination of a few different patterns. In addition, the data's authenticity, required as a prerequisite before making a forecast, is evaluated as part of the data adequacy test.