Hello everyone, the National College Student Mathematical Modeling Contest starts this afternoon. Here are some preliminary suggestions and ideas for topic selection.
At present, the team is writing complete papers on questions B and C, and will continue to update them in the future. The following is only a brief explanation of the graphic version. The team is currently writing a complete paper on questions B and C, which will be updated later. Detailed video version explanations Please move to:
First is the main tone:
In this national competition, it is recommended that novice teams choose question C, which is a typical data analysis and optimization question. If you have a slightly better mathematical foundation, you can choose question B. The most difficult part is actually the derivation of mathematical formulas. We will complete this. Just refer to ours when the time comes. Question A is a relatively hard-core physics question and is not recommended for people without relevant professional background. This time the team will work on the BC questions at the same time, and try to update the complete paper and explanation video on the evening of September 8.
Let’s start with a detailed explanation:
Question B: Multi-beam line survey problem
Question 1
The intersection of a plane perpendicular to the direction of the survey line and the seafloor slope forms an oblique line with an angle of 0 to the horizontal plane (Figure 7), which is called the slope. Please establish a mathematical model of the coverage width of multi-beam bathymetry and the overlap rate between adjacent strips.
If the opening angle of the multi-beam transducer is 120∘, the slope is 1.5∘, and the seawater depth at the center of the sea area is 70 m, the above model is used to calculate the index values of the positions listed in Table 1, and the results are in the format of Table 1 Place it in the text and save it to the result1.xlsx file.
For the first question, we first need these pictures and basic formulas based on the background information of the question:
Carry out the specific derivation of the theoretical formula:
After the derivation, we use matlab for actual solution:
After solving, the results can be obtained as follows:
It can be seen that the depth, width and overlap rate data for different distances have been solved:
The first question is over. Of course, the above is only the preliminary solution code I have determined in the past few days, and it may be further optimized when I complete the complete thesis.
Question 2:
Question 2 Consider a rectangular sea area to be measured (Figure 8). The angle between the direction of the survey line and the normal of the seabed slope projected on the horizontal plane is . Please establish a mathematical model for the coverage width of multi-beam bathymetry.
If the opening angle of the multi-beam transducer is 120∘, the slope is 1.5∘, and the seawater depth at the center of the sea area is 120 m, the above model is used to calculate the coverage width of the multi-beam sounding at the positions listed in Table 2, and the results are expressed as The format of Table 2 is placed in the text and saved to the result2.xlsx file.
The second question is essentially based on the first question, changing the derivation and calculation of the two-dimensional plane into three dimensions:
What we ultimately need to complete is to calculate the coverage width based on the angle between different survey line directions and the distance/nautical mile between the measured ship and the center point of the sea area.
Then it is still the same process as the first question. First derive the theoretical formula for calculating the width, and then solve the actual code. I will update this later.
When it comes to the third and fourth questions, you need to design the survey line based on the first and second questions. I will answer this in detail later.
Question C: Automatic pricing and replenishment decisions for vegetable commodities
Question 1:
Question 1 There may be a certain correlation between different categories of vegetable commodities or different single products. Please analyze the distribution and mutual relationship of the sales volume of each category and single product of vegetables.
What is the law of distribution? The distribution rules I have initially determined here are:
The first is the statistical rules of categories and individual products, such as the sales volume arrangement of individual products, the sales volume arrangement of categories, etc. You can see which one is the highest.
Secondly, there is also the distribution of time and seasons. Here we need to draw time series diagrams and perform actual seasonal time series analysis. This is because we have been told in the topic background:
But how do we obtain the specific sales data of the category? Let’s take a look at attachment 2:
Attachment 2 does not give category information, so we need to match the category data in Attachment 1. This is still relatively difficult, because there are more than 80w data in Attachment 2, but I have also completed the merger so far:
I will also distribute the above combined data tables for free. For an explanation of the complete data tables, you can watch the video at the bottom of this article.
After the merger is completed, we can start to directly classify and summarize the distribution and perform time series analysis. Let's see my specific results at that time, and wait for my update.
For the relationship, we need to do a correlation analysis, divide the six categories into 6 tables, and then aggregate them together. After processing the missing values, we can directly conduct the correlation analysis to get the specific correlation size.
End of first question
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 provide the daily replenishment for each vegetable category in the next week (July 1-7, 2023) The total volume of goods and pricing strategy maximize the profits of supermarkets.
Still based on category, there are 6 categories in total:
Let’s first study the relationship between sales volume and pricing. Here we can first use machine learning and directly insert it into a regression model without any brain.
Next, in order to predict the total amount of replenishment, we first predict the sales volume, and we will replenish as much as the sales volume of the day. This is because the title and the attachment do not give the concept of inventory. For the prediction here, we can directly use time series prediction.
Next is the pricing strategy, which is more difficult because we need to calculate the profit first, and then we can give the best pricing strategy based on the maximum profit.
For the calculation of profit, we need to take into account the cost of attachment 3 and the loss of attachment 4. The final optimization goal I give here is:
For explanations of each symbol, please watch my video explanation. I don’t have time to type.
Then perform the actual solution of the code:
Question 3:
Due to the limited sales space of vegetable products, the supermarket hopes to further develop a replenishment plan for single products, requiring the total number of single products available for sale to be controlled to 27-33, and the order quantity of each single product must meet 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.
Essentially, categories are not analyzed here, but there is no need to analyze so many detailed categories. We only need to analyze 27-33 single products under restricted conditions. It is still necessary to give the optimization objective and function and then actually solve it. Please wait for my actual update later.
To receive the above free data forms, codes and subsequent complete finished products, please see my personal card below↓: