A brief analysis of the competition questions of the 2023 Higher Education Society Cup Mathematical Modeling National Competition

The 2023 National Competition is coming as scheduled. In order to facilitate everyone to determine the topic as soon as possible, here will be a brief analysis of the competition topic to analyze the main difficulties of the competition topic, ideas for setting the topic, and explanations of the difficulties that may be encountered after selection, so as to facilitate everyone to determine the topic as soon as possible. Determine the topic.

Sort by difficulty B>A>C

Number of people choosing topics C>A>B (estimated results, detailed results will not be announced until statistics on the 8th)

Problem A: Optimal design of heliostat field 

Question A conforms to the conventional question formula for question A in the national competition. It uses the heliostat field as the background of the question and sets physics-related questions. Question 1 requires calculating the annual average optical efficiency, annual average thermal output power, and annual average thermal output power per unit mirror area based on the relevant calculation formulas and relevant data given in the question. It is a physical calculation problem, not too difficult, moderate. It takes a lot of time to figure out the formula and then perform the calculation. This kind of question usually has high accuracy requirements for the results. The result score is set at about 5 points for each result, and the three results total 15 points. The total score for question one is 25-30 points, and half of the score is determined by the result.

Questions 2 and 3 are classic optimization problems. Taking the maximum annual average thermal power output as the objective function , an optimization model is constructed. The position coordinates of the absorption tower, heliostat size, installation height, position coordinates and other data are set as decision variables . The constraints of question 2 can be translated sentence by sentence, (limits on rated power, heliostat size and installation height, etc.)

Question 3: The size of the introduced heliostat can be different, and the installation height can also be different. Therefore, just introduce new constraints to build the model. The main difficulty lies in finding and constructing constraints and solving the optimization model.

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Question B : Multi-beam line survey problem  

Question B changed from the conventional question formula of question B in previous national competitions, and set physics-related questions based on multi-beam measurement. This kind of title design has not appeared in the past ten years. Therefore, it is also the most difficult question. Question 1: Construct a mathematical model of coverage width and overlap rate between adjacent strips. Question 2: Construct a mathematical model of multi-beam bathymetry coverage width. The construction of this kind of model requires a deep understanding of the topic and then combined with the corresponding physical knowledge to construct it. It is highly professional, so it is not recommended for novices or weak teams. It is easy to Hit a wall.

Questions three and four are equivalent to practical applications, using the model constructed in question one and two to calculate a practical situation.

Overall, question B is the most difficult question in this competition, which is a great test for the professionalism and knowledge reserve of the participating team members. Therefore, I hope everyone will make a careful decision.

Question C : Automatic pricing and replenishment decisions for vegetable commodities  

The proposition of question C is similar to the proposition of question C in previous regular national competitions. It is a data processing analysis + optimization problem. Set relevant propositions with vegetable sales as the background. The first step for data-based questions must be data processing.  In such a huge data set, there must be outliers, missing values, etc., which require us to search and determine. Usually for this part, the final score is about 5-10 points, which must be processed!!!!!

Question 1: Analyze distribution patterns and interrelationships. Remember there are two issues, distribution law and correlation. Distribution rules, just draw the corresponding scatter plot and add text description. Correlation is a type of evaluation model and belongs to correlation analysis. You can refer to the figure below to choose the appropriate method.

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Problems 2 and 3 optimization model, three-element objective function, decision variables, and constraints. For the corresponding translation question, just find the constraints and construct it

Question 2: Solving the Maximum Value Problem Optimization Problems (Six Categories)

Objective function Profit

Decision variable  daily replenishment amount

Constraints and equations

Inequality relation

Problem 3  : Optimization problem solution (251 sketches)

Objective function Profit

Decision variable  single product replenishment quantity

Constraints and equations

Inequality relationship (control of total number of items available for sale, order quantity)

Question 4 Non-technical article. For other data searches, you can formulate a general direction and then use the smaller direction. It can be divided into macro and micro; or dynamic indicators and static indicators. In short, it makes sense.

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Origin blog.csdn.net/qq_33690821/article/details/132745234