Introduction to competition questions
In fresh food supermarkets, the shelf life of general vegetable products is relatively short, and the quality deteriorates with the increase of sales time. If most varieties are not sold on the same day, they cannot be resold the next day. Therefore, supermarkets usually restock 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, and the purchase and transaction time of vegetables is usually between 3:00 and 4:00 in the morning, merchants must do this without knowing exactly the specific items and purchase prices. Make replenishment decisions for each vegetable category on the day. The pricing of vegetables generally adopts the "cost-plus pricing" method, and 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 variety of vegetables is relatively abundant from April to October, and the restrictions on the sales space of supermarkets make reasonable sales Combination becomes extremely important.
Attachment 1 gives the product information of six vegetable categories distributed by a certain supermarket; Attachments 2 and 3 respectively give the sales details and sales of each commodity in the supermarket from July 1, 2020 to June 30, 2023. Relevant data on wholesale prices; Appendix 4 gives the recent loss rate data of each commodity. Please establish a mathematical model based on the attachment and the actual situation to solve the following problems:
Question 1 There may be certain correlations between different categories or single products of vegetable commodities. Please analyze the distribution patterns and interrelationships of the sales volume of various vegetable categories and single products.
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-plus pricing, and give the forecast for each vegetable category in the next week (July 1-7, 2023) The total daily replenishment volume and pricing strategy maximize the profits of supermarkets.
Question 3: Due to the limited sales space of vegetable products, the supermarket hopes to further develop a replenishment plan for single products. It requires that the total number of single products available for sale be controlled to 27-33, and the order quantity of each single product meets the minimum display quantity requirement of 2.5 kg. . Based on the varieties available for sale from June 24 to 30, 2023, the single product replenishment volume and pricing strategy on July 1 are given, so as to maximize the profits of supermarkets and stores while trying to meet the market demand for various types of vegetable commodities.
Question 4 In order to better make replenishment and pricing decisions for vegetable commodities, what other relevant data do supermarkets need to collect? How can these data help solve the above problems? Please give your opinions and reasons.
Attachment 1 Product information of 6 vegetable categories
Attachment 2 Detailed sales data
Attachment 3 Wholesale price of vegetable products
Attachment 4 Recent loss rate of vegetable products
Note (1) In Appendix 1, the numbers included in some item names indicate different sources of supply.
(2) The loss rate in Appendix 4 reflects the recent loss of goods and is calculated from the data of the recent inventory cycle.
All ideas total 30 to 40 pages
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[Multiple ideas with source code] 2023 Higher Education Society Cup National Competition Mathematical Modeling Question C Question Ideas - Automatic Pricing and Replenishment Decisions for Vegetable Commodities
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Idea analysis
Vegetable commodity replenishment and pricing strategy analysis
In the modern business environment, correctly formulating product replenishment and pricing strategies is critical to merchants' success. In this analysis, we focused on the replenishment and pricing strategies of vegetable products in supermarkets and conducted an in-depth discussion through a data-driven approach.
- Vegetable commodity sales correlation analysis
First, in order to better understand the sales correlation between different vegetables, we adopted the Apriori correlation analysis algorithm. This is an algorithm commonly used in market basket analysis to find combinations of items that often appear together. We found that combinations of multiple vegetables often appear together in sales, which provides merchants with clues about product combination promotions.
In addition to correlation analysis, we also conducted time series analysis of sales volume, heat map analysis and sales volume distribution analysis to gain a more comprehensive understanding of the sales patterns of vegetable commodities.
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Data preprocessing:
- Check for and handle possible missing values.
- Summarize the sales data by date and commodity to get the sales volume of each vegetable per day.
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Sales volume analysis:
- Use visualization methods to display the sales distribution of different vegetable categories and single products.
- Check which vegetable categories or items have the highest and lowest sales volume.
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Association rule mining:
- Use the Apriori algorithm to analyze purchasing behavior and find frequently purchased product combinations.
- Based on the obtained association rules, the association between different vegetable categories or single products is analyzed.
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Results visualization and analysis:
Other data analysis to increase innovation points
Heat map: Shows the sales correlation between different vegetable categories.
Pie chart: Shows the sales proportion of each vegetable category.
Bar chart: Compare the total sales volume of each vegetable category.
Line chart: Shows the sales trend of a specific vegetable category or single product over time.
- Provide corresponding charts and text descriptions for the results of each step.
This is an entry point for data analysis. You can explore new values and patterns of data from multiple dimensions, and combine the following questions to set a limit on the data analysis of the revised questions, which is conducive to step-by-step progress.
For specific implementation code, please refer to the documentation.
- Replenishment and pricing strategies based on historical sales data
Considering that supermarkets formulate replenishment plans on a category basis, we used a linear regression model to explore the relationship between price and sales volume. Through multiple linear regression analysis, we found that there is a clear negative correlation between sales volume and price, that is, as price increases, sales volume decreases.
Additionally, we considered a cost-plus pricing model, where price is determined by unit cost and cost margin. Using optimization algorithms, we determine the cost profit rate that maximizes the supermarket's profits.
You can also use time series algorithms to predict sales seasonally. The prediction algorithms here also have certain requirements. For details, you can refer to the description in my ideas, which gives a detailed description of each method.
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Step 1: Data preparation
- Calculate the total sales volume of each vegetable category.
- Calculate the average wholesale price for each vegetable category.
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Step 2: Multivariate linear fitting
- As a first approach, a multiple linear regression model is used to fit the relationship between total sales volume and wholesale price and shrinkage rate.
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Step 3: Other methods
- As a second approach, we can use a decision tree or random forest model to predict sales for the coming week.
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Step 4: Pricing Strategy
- Provide a pricing strategy for the week ahead based on forecasted sales volumes and wholesale prices.
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Time series analysis:
- In addition to linear fitting, we can also use time series analysis to predict future sales.
- This approach takes into account the chronological order of sales data and may more accurately predict future sales.
Model selection and trade-offs
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Model complexity:
- Multiple linear regression: relatively simple, easy to understand and interpret. It assumes a linear relationship between the dependent and independent variables.
- ARIMA time series analysis: relatively complex and specialized for time series data. It can capture seasonality, trends, and cyclicality in data.
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Data requirements:
- Multiple linear regression: A sufficient number of observations are needed to ensure the stability of the model. Sensitive to outliers and multicollinearity.
- ARIMA time series analysis: Continuous time series data is required and the data volume needs to be large enough to capture underlying trends and seasonality.
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Prediction accuracy:
- Multiple Linear Regression: If the true relationship is nonlinear, or the model fails to include all important independent variables, the predictions may deviate from the true value.
- ARIMA time series analysis: If the model parameters are properly selected and the data has obvious trends and seasonality, ARIMA can usually provide more accurate forecasts.
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Application scope:
- Multiple linear regression: Applicable to various types of data as long as there is a linear relationship between the dependent variable and the independent variable.
- ARIMA time series analysis: specifically used for time series data.
For this specific question:
If we are mainly interested in the relationship between the dependent variable (sales volume) and the independent variable (such as wholesale price) and want a simple, intuitive model, then multiple linear regression may be a good choice.
If we are primarily concerned with future sales forecasts, and the data has clear seasonality and trends, ARIMA may be more appropriate.
For specific implementation code, please refer to the documentation.
- Single product replenishment and pricing strategy
After considering the replenishment and pricing strategies on a category basis, we further developed a replenishment and pricing strategy for individual products. Considering the limitation of sales space, we set a constraint that the total number of single products needs to be controlled between 27-33. Through optimization algorithms, we determine the optimal replenishment quantity and pricing strategy for each item.
We need to predict the sales volume on July 1 based on the sales data from June 24-30, 2023.
When selecting which items to replenish, we need to ensure that the total number of selected items is between 27-33. We need to ensure that the replenishment quantity of each item is at least 2.5kg.
We need to think about how to price to maximize profits.This is a fairly complex optimization problem. To simplify the problem, we can first consider the following strategy:
Forecast demand for each item using sales data from the past week. Select the 27-33 products with the highest expected demand for replenishment. Use the previously calculated optimal profit margin to set the price.
The cost-plus pricing model and the price-sales linear relationship we established in the second question are used to optimize the cost profit margin, and based on this optimized cost profit margin, the replenishment volume and pricing strategy are determined.
Specific steps are as follows:
Using the linear model established before, the relationship between sales volume Q and price PP is: Q=a×P+b According to the cost-plus pricing model, the price can be expressed as: P=C(1+r) where C is the unit cost
, r is the cost margin. Substituting into the linear model of price-sales volume, we get: Q=a×C(1+r)+b Use the optimization algorithm to optimize
r, which is the cost profit margin, to maximize profits.Profit Π can be expressed as: Π=Q×(P−C) Substituting into the above formula, we get: Π=(a×C(1+r)+b)×(C(1+r)−C)
Our goal is to maximize ΠΠ. Using the constraint 0≤r≤0.20 (that is, the cost profit margin is between 0 and 20%), we can use the optimization algorithm to solve for the optimal r.
For specific implementation code, please refer to the documentation.
- Recommended additional data collection
In order to better formulate replenishment and pricing strategies for vegetable products, we recommend that supermarkets collect more relevant data, such as customer feedback, inventory data, promotion data, competitor pricing strategies, seasonal and weather data, and supply chain data. These recommendations are based on the fact that these data can provide supermarkets with more comprehensive information on market trends, customer needs and supply chain conditions, thereby helping them formulate more effective replenishment and pricing strategies.
in conclusion
Through the above analysis, we have provided supermarkets with a comprehensive vegetable commodity replenishment and pricing strategy framework. We use a variety of data analysis and optimization methods, such as Apriori correlation analysis, linear regression, optimization algorithms, etc., to ensure the scientificity and practicality of the strategy. In addition, we provided recommendations to supermarkets on how to further improve replenishment and pricing strategies.
Overall, this analysis not only provides supermarkets with specific replenishment and pricing strategies, but also provides them with a systematic, data-driven decision-making method.
In order to better make replenishment and pricing decisions for vegetable products, in addition to sales history data and wholesale price data, supermarkets can also consider collecting the following related data:
Customer feedback and satisfaction data:
Opinion: Understanding customer feedback and satisfaction with current products can help supermarkets adjust the quality, variety and price of products.
Reason: If the feedback of some products is not good, you may need to consider changing suppliers or reducing the replenishment quantity; if the feedback of some products is good, you can increase the replenishment quantity and optimize the pricing strategy.
Inventory data:
Opinion: Knowing current inventory levels can help supermarkets and supermarkets make more precise decisions about replenishment quantities.
Why: Avoid over-replenishment or stock-outs and ensure inventory matches demand.
Promotion and marketing activity data:
Opinion: Understanding the effectiveness of promotion and marketing activities can help supermarkets optimize future promotion strategies.
Why: Determine which promotions are most effective and how to price them to attract more customers.
Competitor pricing and promotion strategy data:
Opinion: Understanding how competitors in the market price and promote can help merchants and supermarkets develop more competitive strategies.
Reason: Ensure that supermarket prices and promotions match market trends and competitor strategies.
Seasonal and weather data:
Opinion: Demand for certain vegetables can be affected by season and weather.
Reason: For example, in hot summer, customers may be more inclined to buy cool vegetables, such as cucumbers and tomatoes; while in winter, they may be more inclined to buy vegetables suitable for stew, such as cabbage and carrots.
Supply chain data:
Opinion: Understanding the efficiency, reliability and cost of the supply chain can help supermarkets select better suppliers and optimize replenishment strategies.
Reason: If a supplier frequently delays delivery or provides poor quality goods, the supermarket may need to consider changing suppliers.
In short, in addition to traditional sales and price data, supermarkets can also consider collecting a variety of related data to more comprehensively understand market trends, customer needs and supply chain conditions, so as to formulate more effective replenishment and pricing strategies.
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