A Decision Model for Pricing and Replenishment of Vegetable Products Based on Lagrangian Function Optimization

Abstract

In the era of big data, superstores usually replenish and price their products based on the historical sales and demand of each item. Based on data mining, this paper analyzes the correlation between different categories using a gray correlation analysis model, then fits the relationship between total sales and cost-plus pricing for each vegetable category, and uses a time series forecasting model to predict the wholesale price and sales volume of six types of vegetables in the week of July 1st to 7th. By establishing a Lagrangian function-based optimization model with the objective function of maximizing the profit of the superstore, the total daily replenishment of each category and the cost-plus pricing as the decision variables, and traversing the solution with a step size of 0.5 sales, the total daily replenishment and the pricing strategy for the next seven days can be formulated, and the total return of the superstore in the coming week is found to be 2264.41 yuan. The optimization model based on profit maximization of superstores used in this paper provides reliable theoretical support and practical guidance for merchants to predict market conditions and plan future replenishment and pricing strategies.