1. Introduction
In today’s competitive market environment, fresh food superstores, as an important part of the retail industry, not only face a rich variety of commodity categories and differences in origin, but are also affected by the challenges of the short freshness period of vegetable commodities, easy to change in appearance, and price fluctuations. Especially in the face of vegetables which are fresh commodities, with the dynamic changes of quality and prices, the replenishment needs of supermarkets, the pricing decisions become challenging. To cope with this challenge more effectively, this paper aims to combine Auto Regressive Integrated Moving Average (ARIMA) and Back Propagation (in neural networks) (BP) models to predict the future sales and pricing of various categories of vegetables, so as to provide a certain reference for the replenishment and pricing decisions of supermarkets.
1.1. Literature review
A lot of research has been carried out by scholars at home and abroad in the field of fresh food sales forecasting and pricing decision-making (1, 2). Zhang Yanliang and Dai Peipei explored the customer-perceived product information contained in online review data to assess the accuracy of fresh produce demand prediction, constructed a multivariate Support Vector Regression (SVR) demand prediction model, and found that the extraction of customer-perceived factors in online reviews can effectively improve the accuracy of fresh produce demand prediction (3). Lin and Hu (1) mentioned that review characteristics, transaction characteristics, shop characteristics, service characteristics, and product characteristics have different degrees of influence on the sales of fresh food e-commerce products, among which the influence of review characteristics is the most significant (4, 5). Lu Chao and Xing Miao constructed a pricing decision model for fresh produce supply chain through online reviews and found that when the cost sharing coefficient is high, the optimal level of preservation effort is higher than that in the centralized decision-making model under the decentralized decision-making model with cost sharing and revenue sharing (6, 7). Bi and Zhou (2) combined the characteristics of fresh products to model the problem and define it as a Markov decision process, and then designed a joint inventory control and dynamic pricing algorithm for fresh products based on deep reinforcement learning (2, 8). Tian Zhongwei and Dong Ming developed and solved a two-stage model for the optimal pricing and ordering decisions of retailers for fresh products with different quality levels due to deterioration in the sales process (9, 10). This paper is based on the historical sales data of six vegetable categories distributed by a supermarket to carry out an in-depth study. Firstly, an ARIMA model was used to predict the replenishment volume of each category in the next 7 days to better understand the potential trend of sales. Secondly, through the BP neural network, we try to fit the complex relationship between sales volume, cost-plus rate, and wholesale price, combined with the “cost-plus pricing” strategy, to provide a novel approach to set reasonable pricing for products to adapt to the fast-paced and dynamic changes in the market environment and to provide support and reference.
2. Data description
2.1. Basic description
The data in this paper come from the historical sales data of vegetable commodities in a fresh food supermarket, including 6 categories of vegetables, commodity information of 251 single vegetable products, sales flow detail data, wholesale prices of vegetable commodities, and other data. After data collation, the daily sales data, wholesale price data and cost-plus rate data of various types of vegetables are obtained. After collation, the data table has a total of 1095 rows from July 1, 2020 to June 30, 2023, and a total of 18 columns for the sales volume, wholesale price, and cost-plus rate of each category of vegetables.
2.2. Distribution pattern
Overall, vegetable commodities are divided into six categories, 251 kinds of individual products, in which the sales of cauliflower and leafy category are the highest, followed by chili and edible mushrooms; nightshades have the lowest sales, the sales of cauliflower and leafy category are concentrated in the range of 0–500 kg; the sales fluctuation range is large; cauliflower, aquaticrhizomes, nightshades, chili, and edible mushrooms sales have a relatively small range of fluctuation. The specific results are shown in Figure 1; each category of vegetables is subjected to the null value checking, and these null values are filled to a very small value of 0.01 to ensure the integrity of the data.
Figure 1. Box line diagram for each category.
2.3. Correlation
Spearman’s rank correlation coefficient is a non-parametric statistical method that does not require the data to satisfy the assumption of normal distribution and is used to measure the correlation between two continuous variables and is calculated by the formula:
where n is the number of samples, and d represents the rank difference between data x and y. The correlation coefficient matrix was calculated by recoding these six categories and further plotted as a heat map for each vegetable category.
By recoding these six categories, the matrix of correlation coefficients was calculated, and the correlation heat map of each vegetable category was further plotted, which is shown in Figure 2. In this heat map, the color of each grid indicates the correlation between the corresponding categories, and the redder the color the higher the gene expression, and the bluer the color the lower the gene expression. By observing the correlation heat map, the following results can be obtained: the correlation between the leafy category, cauliflower, aquatic rhizomes, chili, and edible mushrooms is strong, with correlation coefficients greater than 0.5, while the correlation between night shades and other categories is weak, with correlation coefficients less than 0.5.
Figure 2. Heat map for each correlation category.
3. ARIMA model
The ARIMA model is a commonly used time series analysis method that uses difference methods to convert non-stationary time series data into stationary time series data. Based on this data for future data forecasting and modeling, the model combines the characteristics of the autoregressive (AR) model, the difference (I) operation, and the sliding average (MA) model, and its three main parameters are expressed as the autoregressive order (p), the difference number (d), and the sliding average order (q). The general form of the ARIMA (p, d, and q) model is as follows:
t represents the moment, Wt represents the smooth sequence obtained after d-order differencing, μt represents the random disturbance sequence, δ is the constant term, p is the autoregressive partial order, q is the moving average partial order, ϕp is the coefficient of the autoregressive term of order p, and θq is the coefficient of the moving average term of order q (11).
3.1. Observation of time series chart
To study the trend of the sales volume of superstores over time, we choose days as the unit of measurement and draw the time-series plot of each category of vegetables over time, and it can be seen that the sales volume of each category shows an oscillating trend of change, and basically smooth. The specific results are shown in Figure 3; Combined with the box-and-line diagram in Section 2.1 and the time-series plot below, it can be easily found that there are some values in each category far more than the normal range of fluctuation values of this type of dish in each category, and these values can be considered as outliers, and these values will be replaced by the average value in the subsequent modeling.
Figure 3. Timing diagram for each category.
3.2. Smoothness and white noise test
The p-value of smoothness test of the daily sales volume of the leafy category = 6.60e-04 < 0.05, which rejects the original hypothesis that there is no unit root, indicating that the time series is smooth; the p-value of stochasticity test of the daily sales volume of the leafy category = 4.30e-08 < 0.05, which indicates that the time series is non-white noise. The p-value of the remaining types of smoothness and white noise test is as follows (Table 1).
Table 1. Smoothness and white noise test p-values for the remaining five categories.
From Table 1, it can be seen that all classes pass the white noise test and smoothness test.
3.3. Determination of p, d, and q parameters
First of all, we draw the Autocorrelation Function (ACF) and Partial Autocorrelation Function (PACF) diagrams for each category; the specific results are shown in Figures 4–6. Take the leafy category as an example. It can be seen from the diagram that the ACF and PACF are trailing, and the original data of the leafy category are smooth and do not need to be differentiated. The order of p and q in the general ARIMA model will not be more than 3 (12); the value of p and q will lead to the overfitting of the model, and there will be a large error in the prediction of the future data. Therefore, the preliminary ARIMA model parameters for the leafy category are (3,0,3). However, the model obtained at this time is not necessarily optimal; the next use of the aic, bic criterion to more accurately select the final order of the model, through the selection of the aic, bic value, is found to be the smallest when the parameter is (2,0,1), and so the parameter is selected as the leafy category ARIMA model parameters. The rest of the ARIMA model parameters are shown in Table 2.
Figure 4. ACF and PACF charts for leafy categories and cauliflowers.
Figure 5. ACF and PACF plots of chili_peppers and edible_mushrooms.
Figure 6. ACF and PACF plots of aquatic_rhizomes and nightshades.
Table 2. ARIMA parameters for the remaining five categories.
3.4. Replenishment prediction
Firstly, it is assumed that the market supply and demand are equal, that is, the replenishment volume is equal to the sales volume, and then the original sales volume data of various types of dishes are divided, with 90% as the training set and 10% as the test set, and the model test is carried out. Taking the leafy category as an example, the established ARIMA (2,0,1) model was used to predict the replenishment quantity in the coming week, and the specific results were obtained as follows (Table 3).
Table 3. Forecast for restocking of the leafy category in the coming week.
Moreover, the Mean Squared Error (MSE) of the model on the test set is 4.14e-02, which is relatively small, and it can be considered that the model is more reliable, and the average error range on the data scale is 18.62%, which is also small, and the comparison between the actual values and the predicted values on the test set is shown in Figure 7.
Figure 7. Plot of actual versus predicted values on the test set for the leafy category.
From Figure 7, we can see that the fitting effect is relatively good. The MSE on the rest of the various test sets, the average error ranges are shown in Table 4, the predicted values of the replenishment volume for the next 7 days are shown in Table 5, and the comparison of the actual and predicted values on the test sets is shown in Figure 8.
Table 4. MSE and mean error ranges on the remaining five category test sets.
Table 5. Restocking of the remaining five categories for the next 7 days.
Figure 8. Comparison of actual and predicted values on the remaining five types of test sets.
As can be seen from Figure 8, the remaining five categories also fit better on the test set, and the model is relatively reliable.
4. BP neural network modeling for predictive pricing
4.1. Model construction and fitting
For fresh commodities, the core of the pricing strategy is to use low gross profit to stimulate sales and maintain the freshness and turnover of commodities. Cost-plus pricing is a method of setting product prices based on the unit cost of the product plus a certain percentage of profit, which is calculated by the formula:
Where, P denotes the price, C denotes the average cost, and w denotes the cost-plus rate, w = (selling price - purchase price)/selling price × × 100%, which reflects the profit margin of the enterprise in selling the product or service (13).
To analyze the relationship between the replenishment quantity and cost-plus pricing of each category of vegetables, firstly, we consider the replenishment quantity and merchant’s wholesale price and cost-plus rate and carry out linear regression and multivariate binomial regression and find that the fitting coefficients obtained under linear regression R2 = 0.0536 and R2 = 0.0467 under multivariate binomial regression, the fitting effect is poor; therefore, we use the BP neural network to build a model for prediction BP neural network model structure, including input layer, intermediate layer (hidden layer), and output layer. The training algorithm of the neural network is to continuously adjust the connection weights through the back-propagation algorithm, trainlm, to improve the training speed and fitting accuracy to achieve the goal of minimizing the training error so that the prediction effect of the whole network is better (14). According to the data set obtained from the collation, the neural network input neuron cell number is 1, indicating the replenishment of each category; the hidden layer has 10 cells; the output layer neuron cell number is 2, indicating the wholesale price and the cost of markup coefficients; and its model structure is shown in the following Figure 9.
Figure 9. Structure of the constructed BP neural network.
At the same time, the BP neural network model uses the activation function to add nonlinear factors to the network to solve the problems that cannot be solved by the linear model, and by limiting the range of the output result of the activation function, it helps to make the gradient decrease smoothly (15). The activation function added in this paper is as follows:
The loss function is also added to the BP neural network to evaluate and validate the model and evaluate the model fit. In this paper, the performance function MSE is set to 1e-1, below which the iteration stops, and its specific formula is as follows:
where t denotes the actual value and y denotes the predicted value. Then 90% of the historical sales volume data of various types of food in supermarkets are used as the training set and 10% as the test set, so that the replenishment volume data in the input layer are obtained, and then the historical wholesale price data and historical cost markup rate data are brought into the output layer to fit the BP neural network. Taking the leafy category as an example, its mean squared loss function image is shown in Figure 10, and the model fitting is shown in Figure 11.
Figure 10. Image of the mean-variance loss function for the leafy category.
Figure 11. Fitting of the leafy category.
From Figure 11, it can be seen that the leafy category reaches the set value of the mean square loss function after 20 iterations in the test set, and the fit coefficient of the model in the test set reaches 0.85, which is a good fit of the model. The number of iterations and the fitting coefficients on the test set for the remaining classes are shown in Table 6.
Table 6. Number of iterations and fit coefficients for the remaining categories.
From Table 6, it can be seen that except for chili peppers, the fitting coefficients of the other categories are high, and it can be considered that the model is effective.
4.2 Predictive pricing
The content in Section 4.1 indicates that the BP neural network model successfully fits the relationship between replenishment quantity, wholesale price, and cost markup rate. Building on this, combined with the replenishment quantities forecasted for the next seven days by the ARIMA model in Section 3, it is possible to calculate the wholesale prices and cost markup rates for each category over the next seven days, thereby determining the pricing strategy. Taking leafy vegetables as an example, the pricing results are shown in Table 7, while the pricing strategies for other categories are detailed in Table 8.
Table 7. Pricing strategy for the leafy category.
Table 8. Pricing strategies for the remaining categories.
The remaining types of pricing strategies are shown in Table 8.
5. Summary and prospect
Through the research in this paper, the sales data of the vegetable category is deeply analyzed, and a restocking and pricing decision-making framework based on the ARIMA model and BP neural network is proposed. By predicting the replenishment and pricing in the next 7 days, the framework allows supermarkets to make more targeted purchases and pricing, thus better meeting market demand and improving operational efficiency. However, it should be noted that any model has its limitations due to the changing market environment. Therefore, it should be flexibly adjusted in the actual situation and combined with other decision-making tools to improve the overall decision-making level, and future research can be more specific to the replenishment volume and pricing decisions for each single product and continuously expand the model to provide more useful references and insights for the efficient and effective development of the fresh food retailing industry.
With the continuous progress of science and technology and the evolution of the business environment, the replenishment and pricing decision-making framework based on the ARIMA model and BP neural network proposed in this paper can provide some references for the operational decision-making of supermarkets to a certain extent. In the future, more complex models and algorithms can be further explored to improve the accuracy of market demand and sensitivity to sales trends. At the same time, by combining big data, artificial intelligence, and other technologies, the decision-making system can be further improved to make it more real-time and adaptive, so as to better adapt to the dynamic changes of the market. In addition, with the development of digitalization and intelligence in the fresh food supply chain, supermarkets can consider introducing more advanced technological means, such as the Internet of Things (IoT), blockchain, etc., to improve the traceability of vegetable commodities and the level of quality assurance. This will not only help consumers better understand the source and quality of goods, but also help supermarkets to realize more efficient management and coordination in the supply chain.
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