All the codes for question C are completed, you can see the business card at the end of the article
Let’s first look at the background of Question C
In fresh food supermarkets, vegetable products have a short shelf life, and their quality will deteriorate as sales time increases. Supermarkets need to replenish goods every day based on historical sales and demand. Since there are many varieties of vegetables and different origins, the replenishment time is in the early morning. Merchants must make replenishment decisions without knowing the specific items and prices.
Attachment 1 gives the commodity information of 6 vegetable categories; Appendix 2 and 3 respectively give the sales flow and wholesale price of each commodity from July 2020 to June 2023; Appendix 4 gives the recent loss rate of each commodity , give a preliminary idea first, update later
Question 1. There may be a certain correlation between different categories of vegetable commodities or different single products. Please analyze the distribution rules and mutual relationships of the sales volume of various vegetable categories and single products.
We first need to do data preprocessing and visualization
We first calculate the average sales volume, median, mode, variance, etc. of each category and single product to understand its distribution characteristics. You can also use time series analysis to identify sales trends or seasonality.
Then, based on the results of descriptive statistics, consider whether to use Pearson or Spearman correlation coefficients to quantify the correlation between different categories or single products. Use a clustering algorithm (K-means or hierarchical clustering) to identify categories or items with similar sales patterns.
Question 2. Considering that supermarkets make replenishment plans based on categories, please analyze the relationship between the total sales of each vegetable category and cost-plus pricing, and give the next week of each vegetable category (July 1-7, 2023) The total daily replenishment volume and pricing strategy maximize the profits of supermarkets.
Analyze the relationship between sales volume and cost (wholesale price). We can consider using correlation analysis, regression analysis, etc. Then use time series analysis, random forest, and XGBoost to predict the daily sales volume of each category in the next week.
Use a linear or nonlinear programming model, with sales revenue minus costs and losses as the objective function, to solve the optimal daily replenishment volume and pricing for each category in the coming week.
Constraints include things like inventory limits, sales space limits, costs, etc.
Based on the results of the optimization model, we formulate pricing strategies for each category. A "cost-plus pricing" approach may be used, taking into account market demand and competitive conditions. Also based on the optimization model, the total daily replenishment volume of each category is formulated.
Finally, do a sensitivity analysis on key parameters (such as cost, demand forecast, etc.) to evaluate the robustness of the model.
Question 3 Due to the limited sales space of vegetable products, Shangchao hopes to further develop a single-item replenishment plan, requiring the total number of sellable single-items to be controlled at 27-33, and the order quantity of each single-item meets the minimum display quantity requirement of 2.5 kg . 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.
Question 3: Since the total number of single products has upper and lower limits, this is an integer programming problem.
Our objective function is to maximize revenue (sales-cost-loss).
Our st constraints are the total number of single products (27-33), the minimum display quantity (2.5 kg), inventory and space restrictions.
PuLP, CVXPY, Gurobi and other tools can be used to solve the problem and obtain the optimal decision variable xi of whether to order each item.
Based on the optimal solution xi, determine the order quantity qi and pricing pi of each item. The order quantity qi is determined based on the minimum display quantity requirements; the pricing pi can be determined based on historical pricing levels, combined with factors such as cost and demand.
We select the items that should be replenished based on the model results. Then formulate pricing strategies for each selected item. Then determine the replenishment quantity of each selected item. Finally, sensitivity analysis is performed on key parameters in the model (such as forecast demand, cost, etc.).