Automatic Pricing and Replenishment Decision for Vegetables Based on Nonlinear Programming

Due to the vegetable commodities with perishable, short shelf life characteristics, their appearance will gradually deteriorate with the growth of the sales time, so the fresh food superstore is often based on the previous sales of each commodity and demand for the day of replenishment of goods. In this paper, for the relationship between total sales and pricing, the paper first determines that the data show normal distribution through the frequency histogram. Next, the distribution of data points on the scatterplot is used to derive the trend of the total sales volume of each category with the average unit price of each category. Finally, by fitting the data points on the scatterplot once, twice, and three times, the relationship between total sales and pricing for each category is nonlinear. For giving the total daily replenishment and pricing strategy of the superstore from July 1–7, this paper uses a model of nonlinear programming problem to answer. Firstly, the ARIMA time series forecasting model is used to predict the total daily sales volume of each category of vegetables in the superstore for the next seven days based on the relevant data of June 2023, and accordingly, the range of daily replenishment and pricing of each category of vegetables in the superstore is determined. In addition, this paper also constrains the two based on the functional relationship equation between sales volume and pricing of each category. Finally, a series of results are calculated using the fmincon function in MATLAB.