Automatic Pricing and Replenishment Strategy for Vegetable Products based on ARIMA Time Series Forecasting and Nonlinear Programming

Supermarket vegetable sales are often subject to discount promotions due to factors such as short shelf life and perishability, so accurate market demand analysis is essential for optimal management. In this study, multiple data analysis methods were used to optimize the pricing and replenishment strategies of vegetable products. First, Pearson's correlation analysis was used to quantitatively analyze the sales relationship between each individual vegetable product and category. Second, the elbow rule was used to determine the optimal number of clusters to scientifically categorize the vegetable categories. Then, a nonlinear programming model was constructed to explore the relationship between sales volume and average sales price of vegetable categories. Finally, based on time series analysis, an ARIMA model was built to predict the sales price of each vegetable category in the coming week. Through systematic data analysis, the research conclusions of this paper are as follows: Pearson correlation analysis shows that the sales correlation between different vegetable individual products is weak, indicating that the sales of each product are relatively independent. Cluster analysis identified six optimal vegetable category groupings, a result that is consistent with actual sales. The prediction results of the ARIMA model showed that the accuracy of the prediction of vegetable prices for the coming week reached 92%, which is significantly better than the traditional prediction methods. The application of the nonlinear programming model improved the total profit of the supermarket by 18%, while reducing the inventory waste by 15%. In summary, this study provides a scientific solution for pricing and replenishment decisions of supermarket vegetable products by integrating multiple data analysis methods.