The May 1st Mathematical Modeling ABC question idea has been updated, get it at the end of the article!
Question B ideas:
Question 1: Attachment 1 is the courier transportation data recorded by the courier company between April 19, 2018 and April 17, 2019 (shipping city-receiving city). Consider multiple perspectives such as cargo volume, express delivery volume growth/decrease trend, and correlation, etc., establish a mathematical model, comprehensively rank the importance of each site city, and give the names of the top 5 site cities in terms of importance, and fill in the results in the table 1.
We first process the data, including extracting the shipping date, shipping city, receiving city, and calculating the shipping and receiving volume for each city. At the same time, the growth/decrease trend of the number of express delivery in each city is counted. Then for each city, we extract the following features:
- Shipment volume: the total shipment volume of the city;
- Receipt quantity: the total quantity of goods received by the city;
- Growth/decrease trend of courier volume: Linear regression analysis can be used to calculate the growth/decrease trend of courier volume for each city;
d. Correlation: The correlation between shipments and receipts between cities can be calculated, and the Pearson correlation coefficient can be used.
Finally, establish an evaluation model: for the extracted features, we can establish a weighted evaluation model. For example, Analytic Hierarchy Process (AHP) can be used to determine the weight of each feature, and then calculate the composite score of each city. According to the comprehensive score of each city, the ranking of the city's importance is obtained. Extract the top 5 cities and fill in Table 1.
Question 2 : Please use the data in Attachment 1 to establish a mathematical model to predict the number of express transportation between the cities of the "delivery-receipt" sites on April 18 , 2019 and April 19 , 2019 , as well as all "shipments " on that day - The total number of courier shipments between cities at the "receipt" site, and fill in the number of courier shipments between the designated site cities in Table 2, as well as the total number of courier shipments between all "delivery-receipt" site cities on the day quantity.
According to the data processed in question 1, for the express transportation quantity between cities of each "delivery-receipt" site, a time series analysis method (such as ARIMA) can be used to build a model and make predictions. The stationarity test is performed on the historical data of each city pair, and then an appropriate model is selected according to the stationarity. After the model training is completed, it is possible to predict the number of express transportation between the cities of each "delivery-receipt" site on April 18, 2019 and April 19, 2019. Add all the predicted express delivery volumes between the "shipping-receiving" site cities to get the total express delivery volume between all "shipping-receiving" site cities on that day. Fill in Table 2 with the predicted number of express delivery between cities at designated sites and the total number of express delivery between cities at all "delivery-receipt" sites on that day.
Question 3: Attachment 2 is the number of express shipments recorded by the express company from April 28, 2020 to April 27, 2023. Due to the impact of emergencies, the express lines between some cities cannot be transported normally, resulting in the inability to deliver or receive goods normally between the site cities (no data indicates that delivery cannot be received normally, and 0 indicates that there is no delivery demand). Please use the data in Attachment 2 to establish a mathematical model to predict the city pairs (shipping city-receiving city) that can be normally "delivered-received" on April 28, 2023 and April 29, 2023, and judge the table Whether the site city pair specified in 3 can deliver normally, if it can deliver normally, give the corresponding express delivery quantity, and fill in the result in Table 3.
We first process the data in Attachment 2 to extract the delivery date, delivery city, receiving city, and the number of express delivery between each city. At the same time, find out the cities that cannot be delivered or received normally due to the impact of emergencies. For the quantity of express transportation between the cities of each "delivery-receipt" site, we use the time series analysis method (such as ARIMA) in question 2 to build a model and make predictions. The stationarity test is performed on the historical data of each city pair, and then an appropriate model is selected according to the stationarity. After the model training is completed, it is possible to predict the number of express transportation between the cities of each "delivery-receipt" site on April 28, 2023 and April 29, 2023. For the station-city pairs specified in Table 3, we need to check whether they are affected by emergencies. If it is found in the data in Attachment 2 that the goods cannot be shipped or received normally, fill in "No" in Form 3. If no failure to deliver or receive goods is found in the data in Attachment 2, then fill in "Yes" in Form 3. For the site city pairs that can deliver normally, fill in Table 3 with the predicted express delivery quantity. For site city pairs that cannot be shipped normally, leave the express delivery quantity column blank.