2023 Mathematical Modeling National Competition Question C Idea - Automatic Pricing and Replenishment Decision of Vegetable Commodities

C Question Automatic Pricing and Replenishment Decision of Vegetable Commodities
In fresh food supermarkets, the shelf life of general vegetable commodities is relatively short, and the product quality varies with the sales time. The price will deteriorate due to the increase.
Most varieties cannot be sold the next day if they are not sold on the same day. Therefore, supermarkets usually restock products every day based on the historical sales and demand of each product. Since there are many varieties of vegetables sold in supermarkets with different origins, the purchase and transaction time of vegetables is usually between 3:00 and 4:00 in the morning, which is This merchant must make replenishment decisions for each vegetable category on that day without knowing exactly the specific items and purchase prices. The pricing of vegetables generally adopts the "cost-plus pricing" method. Supermarkets usually offer discounts for products that have been damaged during transportation or have deteriorated in quality. Reliable market demand analysis is particularly important for replenishment decisions and pricing decisions. From the demand side, there is often a certain correlation between the sales volume of vegetable commodities and time; from the supply side, the supply varieties of vegetables range from April to October< a i=9> Monthly sales are relatively abundant, and the limitations of supermarket sales space make a reasonable sales mix extremely important. Attachment 1 gives the product information of 6 vegetable categories distributed by a certain supermarket; Attachments 2 and 3 respectively give the supermarket’s 2020 Data on the sales flow details and wholesale prices of each commodity from July 1 to June 30, 2023; Attachment 4 gives the recent loss rate data of each commodity. Please establish a mathematical model to solve the following questions based on the attachment and actual situation:

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Question 1 There may be certain correlations between different categories or single products of vegetable products. Please analyze the distribution rules and mutual relationships of the sales volume of each vegetable
category and single product .

Question 1 requires the analysis of the distribution patterns and interrelationships of sales volume of various vegetable categories and single products. Down

1. Data preprocessing First, we need to preprocess the sales flow details in Appendix 2 to facilitate subsequent analysis and modeling. Specifically, we can follow the following steps:

• Summarize the detailed sales data to obtain the total sales volume of each vegetable category and single product.
• The total sales volume is normalized to facilitate subsequent analysis and comparison.

2. Analyze the distribution pattern of sales volume Next, we need to analyze the distribution pattern of sales volume of each vegetable category and single product. Specifically, we can follow the following steps:

• Draw histograms and box plots of sales and observe their distribution and outliers.
• Calculate statistics such as mean, variance, skewness and kurtosis of sales volume to facilitate subsequent analysis and comparison.
• Perform cluster analysis to divide vegetable categories and individual products into several categories to facilitate subsequent analysis and modeling.

3. Analyze the interrelationship of sales volume. After analyzing the distribution pattern of sales volume, we can further analyze the interrelationship of sales volume between various vegetable categories and single products. Specifically, we can follow the following steps:

• Draw a scatter plot of sales and observe the relationship between them.
• Calculate the correlation coefficient between sales volumes and determine the strength and direction of the linear relationship between them.
• Perform factor analysis

Question 2 Considering that supermarkets make replenishment plans on a category basis, please analyze the relationship between the total sales volume of each vegetable category and cost markup
pricing, and give the price of each vegetable The total daily replenishment volume and pricing strategy of the category in the next week (July 1-7, 2023) will maximize the profits of supermarkets.

Question 2 requires analyzing the relationship between the total sales volume of each vegetable category and cost-plus pricing, and giving the total daily replenishment volume and pricing strategy of each vegetable category in the next week (July 1-7, 2023), so that supermarkets Maximum benefit.

1. Data preprocessing First, we need to preprocess the data in Appendix 2 and Appendix 3 to facilitate subsequent analysis and modeling. Specifically, we can follow the following steps:

• Summarize the detailed sales data to obtain the total sales volume of each vegetable category.
• Process wholesale price data and calculate cost-plus pricing for each vegetable category.

2. Analyze the relationship between total sales volume and cost-plus pricing. Next, we need to analyze the relationship between total sales volume and cost-plus pricing for each vegetable category. Specifically, we can follow the following steps:

• Draw a scatter plot of total sales volume versus cost-plus pricing and observe the relationship between them.
• Calculate the correlation coefficient between total sales volume and cost-plus pricing, and determine the strength and direction of the linear relationship between them.
• Conduct regression analysis to obtain the linear regression equation between total sales volume and cost-plus pricing to facilitate subsequent modeling and optimization.

3. Establishing a mathematical model After analyzing the relationship between total sales volume and cost-plus pricing, we can establish a mathematical model to maximize the supermarket's profits. Specifically, we can follow the following steps: - Define decision variables: For each vegetable category, we define a replenishment quantity and a pricing variable, which respectively represent the daily replenishment quantity and each vegetable category of the supermarket in the next week. of pricing.

• Define the objective function: The revenue of a supermarket can be defined as sales revenue minus costs. Therefore, we can define the objective function as: max Σ (sales revenue - cost) where Σ represents the sum of all vegetable categories, sales revenue can be calculated through the replenishment volume and pricing, and the cost can be calculated through the wholesale price and replenishment volume calculated.
• Define constraints: In order to ensure the rationality of replenishment quantity and pricing, we need to define some constraints. Specifically, we can define constraints as follows:
• Replenishment quantity constraint: The daily replenishment quantity of supermarkets cannot exceed the total sales volume of the vegetable category.
• Pricing constraints: The pricing of supermarkets must be within a certain range to ensure price rationality and market competitiveness.
• Revenue constraint: The revenue of a supermarket must be greater than or equal to a given threshold to ensure the profitability of the supermarket.

4. Solving the mathematical model After establishing the mathematical model, we can use mathematical optimization methods, such as linear programming or integer programming, to solve the model and obtain the optimal replenishment plan and pricing strategy. Specifically, we can use a solver or other mathematical optimization software, input the model into it, and then run the solver to get the optimal replenishment quantity and pricing. Finally, based on the results of the model, we can provide the total daily replenishment volume and pricing strategy for each vegetable category in the next week to maximize the supermarket's profits. In short, through the above steps, we can analyze the relationship between the total sales volume of each vegetable category and cost-plus pricing, establish a mathematical model, solve the model, and obtain the optimal replenishment plan and pricing strategy to maximize the profits of supermarkets. . It should be noted that in practical applications, we also need to consider some other factors, such as market demand, supply chain management, loss rate, etc., to ensure the accuracy and feasibility of the model.

Question 3: Due to the limited sales space of vegetable products, the supermarket hopes to further formulate a replenishment plan for single products, requiring that the total number of single products for sale be controlled to 27-33
And the order quantity of each single product meets the minimum display quantity requirement of 2.5 kilograms. Based on the varieties available for sale on June 24-30, 2023
, the single product replenishment volume and pricing strategy on July 1 are given, while trying to meet the market's requirements for each a i=3> Under the premise of increasing the demand for vegetable products, supermarkets can maximize their profits.

Question three requires the formulation of a replenishment plan for single products, requiring the total number of sellable single products to be controlled at 27-33, and the order quantity of each single product meeting the minimum display quantity requirement of 2.5 kilograms. Based on the varieties available for sale from June 24 to June 30, 2023, the single product replenishment volume and pricing strategy for July 1 are given, so as to maximize the profits of supermarkets while trying to meet the market demand for various types of vegetable commodities.

1. Data preprocessing First, we need to preprocess the sales flow details in Appendix 2 to facilitate subsequent analysis and modeling. Specifically, we can follow the following steps:

• Summarize the detailed sales data to obtain the total sales volume of each vegetable category and single product.
• The total sales volume is normalized to facilitate subsequent analysis and comparison.

2. Develop a replenishment plan and pricing strategy Next, we need to develop a replenishment plan and pricing strategy for the single product. Specifically, we can follow the following steps:

• Determine the type and quantity of items that need to be replenished based on available varieties and market demand.
• Based on the relationship between the sales volume and cost-plus pricing of each single product, the selling price of each single product is calculated.
• Based on the selling price and loss rate of each item, the net income of each item is calculated.
• Calculate the total revenue of the supermarket based on the net revenue and replenishment volume of each single product.
• Use mathematical optimization methods to find the optimal replenishment plan and pricing strategy to maximize the profits of supermarkets.

3. Control the quantity and order quantity of single products. According to the requirements of question three, the supermarket hopes to formulate a replenishment plan for single products. It is required that the total number of single products available for sale be controlled at 27-33, and the order quantity of each single product meets the minimum display quantity of 2.5 kg. requirements. Therefore, these constraints need to be considered when developing replenishment plans and pricing strategies to ensure the feasibility and effectiveness of the plan. Specifically, we can follow the following steps:

• Determine the type and quantity of items that need to be replenished based on available varieties and market demand.
• For each item, calculate its minimum display quantity to ensure it can meet market demand.
• According to the limit on the total number of single products available for sale, the replenishment quantity of each single product is adjusted to ensure that the total number is controlled between 27-33.
• Based on the replenishment quantity and minimum display quantity of each item, the order quantity of each item is calculated to ensure that it can meet market demand and display requirements. It should be noted that these constraints may restrict each other, so comprehensive consideration and optimization are required to achieve the optimal replenishment plan and pricing strategy.

Question 4 In order to better make replenishment and pricing decisions for vegetable products, what other relevant data do supermarkets need to collect?
How can these data help solve the above problems? Please Give your opinions and reasons.
Regarding question four, what relevant data do supermarkets need to collect? How can these data help solve the above problems? Please give your opinions and reasons. In order to better make replenishment and pricing decisions for vegetable products, supermarkets need to collect the following relevant data:

1. Market demand data: Supermarkets need to understand the market demand for various types of vegetable commodities in order to formulate optimal replenishment plans and pricing strategies. These data can be obtained through market research, sales data analysis, etc.
2. Cost data: Shopping malls and supermarkets need to know the cost of each item in order to calculate the selling price and net income of each item. These data can be obtained through purchasing records, supplier quotations, etc.
3. Loss rate data: Shopping malls and supermarkets need to know the loss rate of each item in order to calculate the net income of each item. These data can be obtained through inventory management systems, inventory records, etc.
4. Supplier data: Shopping malls and supermarkets need to know the supplier status of each item in order to facilitate supplier evaluation and management. This data can be obtained through purchasing records, supplier contracts, etc.
   This data is very helpful in solving the above problems. For example, market demand data can help supermarkets understand the market demand for various types of vegetable commodities, so as to formulate optimal replenishment plans and pricing strategies; cost data and loss rate data can help supermarkets calculate the selling price of each single product. and net income, so as to maximize the profits of supermarkets; supplier data can help supermarkets evaluate and manage suppliers to ensure the quality and supply of goods.
   Attachment 1 gives 6 Product information of the vegetable category, including category, single product name, supplier, specifications, unit and cost markup and other information. Attachments 2 and 3 respectively provide the sales details and wholesale price data of each product of the merchant from July 1, 2020 to June 30, 2023. Appendix 4 gives the recent loss rate data of each commodity. These data are very helpful in making replenishment and pricing decisions for vegetable commodities. It can help supermarkets understand market demand, commodity costs, losses, etc., so as to formulate optimal replenishment plans and pricing strategies to maximize supermarket profits. .

Attachment 1 Product information of 6 vegetable categories
Attachment 2 Sales flow details
Attachment 3 Wholesale prices of vegetable commodities
Attachment 4 Recent loss rate of vegetable commodities