Predictive Analysis of the Ornamental Angelfish Export Market Demand: An Application of the Least Square Method

1.1 Background and motivation

Indonesia, situated within the world's coral reef triangle, is recognized as a biodiversity hotspot, boasting a rich array of ornamental angelfish and diverse coral species [1-3]. The export of ornamental angelfish has emerged as a premium product within Indonesia's special economic zones, enhancing its economic vibrancy [4-6]. A surge in global interest for seawater ornamental angelfish from a variety of export destination countries has stimulated an expansion in the supply of these visually appealing aquatic species [7, 8]. However, enterprises involved in the trade of ornamental angelfish and corals face substantial challenges in accurately predicting demand, which often leads to uncertainties and inventory shortages in the ornamental angelfish stock [9, 10]. The existing reliance on semi-manual inventory computations frequently engenders data inaccuracies.

Several solutions have been proposed to ameliorate the issue of inventory shortages, prominently featuring the implementation of sales predictions or forecasting techniques. Forecasting entails the analysis of historical data with the aim to estimate future trends [11-14]. Accurate forecasts can aid investors in determining the appropriate stock level based on the predicted demand [15, 16], thereby facilitating informed decision-making and more precise predictions. A method or system that can accurately predict the demand for ornamental angelfish is, therefore, an essential prerequisite for maintaining sufficient stock levels.

In this context, the present study utilizes the Least Square prediction method due to its demonstrated efficacy in accurately forecasting the demand for ornamental angelfish. By employing linear equations, the Least Square Method identifies the optimal line that fits a given dataset and consequently enables the prediction of future data points [17-19].

1.2 Literature review

The Least Square Method has been extensively utilized in various predictive models, including forecasting raw material usage in chip production and sales, thereby aiding companies in planning for optimal raw material supplies to maximize chip production [20]. The method, celebrated for its wide application in data modeling, minimizes the sum of the squares of the residuals, furnishing the best fit. Depending on the nature of the residuals, the Least Square Method can be bifurcated into two categories: ordinary or linear Least Squares, and nonlinear Least Squares [21, 22].

Research [23] has successfully utilized the Least Square Method in predicting the intake of new university students, thereby facilitating decision-making during financial estimations. The findings of the study concluded that the Least Square Method, by producing results that are valid or approximate to the ground truth, can be effectively used to predict the number of new student admissions for upcoming periods based on data from previous years. The validity of this method was corroborated by test results over the last three years, demonstrating a validity of 97.8%.

The Least Square Method has also been deployed to predict coffee yields in Pagar Alam City, achieving the lowest prediction error rate with a Mean Percentage Error (MPE) of 13.72 and the highest accuracy using a Mean Absolute Percentage Error (MAPE) of 0.0166, as implemented in the Coffee Harvest Prediction Application. The prediction was based on coffee yield data from prior periods and was analyzed over the previous three years [24].

Furthermore, the Least Square Method has been applied to forecast the sale of palm shells, enabling companies to set more accurate sales targets and estimate sales for the forthcoming month over a year, starting from one month after the actual sales period. The data tested using the Mean Absolute Percentage Error (MAPE) revealed an error rate of 5.935% [25].

From the aforementioned studies, it can be inferred that the Least Square Method can be effectively employed to predict a variety of factors. In the present paper, the method is applied to predict the demand for ornamental angelfish using a website-based Least Square Method. The research is anticipated to assist companies like CV. Rezky Bahari in predicting the necessary types of ornamental angelfish and preparing their stock accordingly.

1.3 Theoretical framework

To construct a prediction system utilizing the Least Square Method, a deep understanding of the relevant theory is imperative, as it forms the foundation and design of the methodology.

1.3.1 Forecasting

Forecasting is a process that anticipates future sales or demand, enabling the determination of the requisite quantity of goods or services and the identification of potential market opportunities in the future [13, 26-28]. In this study, forecasting is employed to estimate the demand for ornamental angelfish.

A robust forecast is characterized by several key criteria: (1) accuracy, measured by the consistency and reliability of the forecasts, (2) cost-effectiveness, and (3) simplicity [29-32].

1.3.2 Ornamental angelfish

Ornamental angelfish, otherwise known as Marine Angelfish, are perciform fish of the family Pomacanthidae, widely coveted for their mesmerizing appearance. Inhabiting the shallow reefs of the tropical Atlantic, Indian, and an extensive part of the western Pacific Oceans [33, 34], these fish, celebrated for their vibrant colors and elegant appearance, have captured the hearts of aquarium enthusiasts and collectors globally. Bearing resemblance to butterfly fish, they have become a favored choice for marine aquariums.

CV. Rezky Bahari offers a diverse range of ornamental angelfish, encompassing Three-spot Angelfish Adult, Golden Angelfish, Bicolor Angelfish, Coralbeauty Angelfish, Keyhole Angelfish, Pearl-Scaled Angelfish, Multy-barred Angelfish, Whitetail Vermiculated Angelfish, Bellus Angelfish Male, Bellus Angelfish Female, Blackspot Angelfish Male, Blackspot Angelfish Female, Emperor Angelfish Adult, Emperor Angelfish Juvenile, Blue-Girdled Angelfish Adult, and Blue-Faced Angelfish Adult (W).

1.3.3 Least Square Method

The Least Square Method, a widely adopted technique in statistical modeling and time series analysis, estimates trends and generates predictions based on historical data [30, 35, 36]. In the context of forecasting the demand for ornamental angelfish in the export market, the Least Square Method is utilized to discern the inherent patterns and dynamics of the market. The analysis of past sales data and the identification of the linear relationship between time and demand is facilitated by the Least Square Method, thereby providing valuable insights into future demand trends for ornamental angelfish. The formula for the Least Square Method is represented in Eq. (1).

$Y=a+b X$              (1)

where:

Y: Number of Sales.

a and b: Coefficients.

X: The value is predetermined by time.

The description of X can be done using an alternative technique by assigning a score or code. The Least Square Method can be categorized into two cases: even data cases and odd data cases.

(1) For even data, the X value can be scored as: ..., -7, -5, -3, -1, 1, 3, 5, 7, …

(2) For odd data, the X value can be scored as: ..., -4, -3, -2, -1, 0, 1, 2, 3, 4, ...

Then, the coefficients a and b can be found by using Eqns. (2) and (3).

$a=\frac{\sum Y}{n}$               (2)

$b=\frac{\sum X Y}{\sum X^2}$           (3)

where,

a: the trend value in the base period.

b: the average growth rate of the trend value per period.

n: the number of periods.

ΣY: the cumulative volume of sales.

ΣXY: the sum of the products of the period number and its corresponding sales value.

ΣX²: the sum of the squared period numbers.

1.3.4 Error analysis

The accuracy of the Least Square Method in predicting the demand for ornamental angelfish is assessed through error analysis, wherein the predicted values are juxtaposed with the actual values [37]. This study employs three distinct types of comparative analyses for this purpose: Mean Absolute Deviation (MAD), Mean Squared Error (MSE), and Mean Absolute Percentage Error (MAPE). The application of these metrics ensures a robust evaluation of the prediction accuracy and aids in identifying areas for further refinement.

$M A D=\frac{\sum_{t=1}^n\left|A_t-F_t\right|}{n}$          (3)

$M S E=\frac{\sum_{t=1}^n\left(A_t-F_t\right)^2}{n}$           (4)

$M A P E=\frac{\sum_{t=1}^n\left|\frac{A_t-F_t}{A_t}\right|}{n} * 100$             (5)

1.4 Use Case Diagram

The Use Case Diagram, a component of Unified Modeling Language (UML), offers a comprehensive perspective on user interactions within the system [38, 39]. In a UML diagram, use cases are visualized as horizontal ellipses, with users connected to these ellipses via straight lines [40, 41]. Within the context of this study, the Use Case Diagram is employed to delineate the relationships among actors and activities within the prediction system designed for ornamental angelfish demand.

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Figure 1. Use Case Diagram of the ornamental angelfish prediction system

The Use Case Diagram serves as a visual guide to the anticipated functionalities of the system, mapping out the interactions between the actors and the system. Within the context of the application for predicting ornamental angelfish demand, there exists one primary actor: the administrator. The administrator's responsibilities encompass management of various activities, such as data management for fish types, handling request data, and reviewing prediction results. Figure 1 presents a visual representation of these interactions and activities, as detailed in the Use Case Diagram.

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Figure 2. User interaction with the system through the web interface

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Figure 3. Ornamental fish demand data page

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Figure 4. Prediction results for the demand of Apolemichthys Trimaculatus ornamental angelfish and data visualization

Figure 4 delineates the prediction results for the demand of Apolemichthys Trimaculatus ornamental angelfish in 2021 (A) and showcases a data visualization in the form of a graph. This graph plots the actual data line (red) and the predicted data line (blue).

Upon observing the data points on the graph, it's noticeable that the predicted demand closely mirrors the actual demand in most months. For instance, in January, the actual demand was recorded at 24, while the predicted demand was slightly higher at 27. Similarly, in February, the actual demand was 26, marginally lower than the predicted demand of 28.

However, there are instances where the predicted demand diverges from the actual demand. For example, in June, the actual demand was 26, whereas the predicted demand was higher at 30, indicating a difference of 4 units between the actual and predicted values. In December, the actual demand was 34, but the predicted demand was slightly lower at 32, showing a difference of 2 units.

These variations between the actual and predicted demand values propose that the prediction model may have limitations in precisely forecasting the demand for Apolemichthys Trimaculatus ornamental angelfish in certain months. Various factors can impact the demand for ornamental angelfish, such as the exchange rate of the rupiah against the US dollar, weather conditions, and an excessive supply of ornamental angelfish resulting from overexploitation.

In conclusion, the findings of the research indicate that the ornamental angelfish demand prediction system, employing the Least Square Method, has exhibited notable proficiency in accurately forecasting future demand. The evaluation of the prediction results was conducted using Mean Absolute Deviation (MAD), Mean Square Error (MSE), and Mean Absolute Percentage Error (MAPE). An average MAD value of 5 was achieved by the system, highlighting a high level of precision in predicting ornamental angelfish demand. The MAPE calculation produced an average value of 5%, corroborating the accuracy of the predictions. The average value derived from the MSE calculation was 39, implying some divergence from the actual demand but nonetheless denoting a relatively accurate prediction overall.

This degree of accuracy carries substantial implications for the ornamental fish industry, offering invaluable insights for inventory management, production planning, and catering to customer demands. However, to further augment accuracy, future research may benefit from incorporating additional factors, such as seasonality and market trends, into the predictive model. Furthermore, the exploration of advanced modeling techniques, such as machine learning algorithms, may bolster the robustness and precision of the predictions.

The implementation of demand prediction systems predicated on accurate forecasting can facilitate businesses in optimizing their operations, curtailing waste, and efficiently meeting customer demands, thereby leading to enhanced profitability and customer satisfaction. Moreover, to maximize the advantages and impact of the demand prediction system, future research should concentrate on addressing the identified limitations, broadening the system to encompass other fish species, and evaluating its performance in various market contexts. The integration of real-time data sources and the inclusion of external factors such as economic indicators and environmental conditions may enhance the system's accuracy and reliability.

This research advances demand prediction methodologies and provides valuable insights for industry practitioners and researchers seeking to enhance their forecasting capabilities. The accurate demand prediction system possesses the potential to transform decision-making processes and operational efficiency across industries.