As an important way of consumption, online shopping drives the rapid growth of demand for express delivery services and makes an important contribution to my country's economic development. Accurately predicting the quantity of express transportation demand is of great significance for express companies to arrange warehouse sites, save storage costs, and plan transportation routes. Attachments 1, 2, and 3 are the express transportation data between some cities recorded by a domestic express company, including the delivery date, delivery city, and delivery city (the city names have been replaced by letters, and June, November, and June are excluded. month, December data). Please establish a mathematical model based on the attached data and complete the following questions:
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 quantity growth/decrease trend, 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.
Table 1 Results of Question 1
| to sort | 1 | 2 | 3 | 4 | 5 |
| city name |
Question 2: Please use the data in Attachment 1 to establish a mathematical model to predict the number of express delivery between the cities of the "shipping-receiving" sites on April 18, 2019 and April 19, 2019, as well as all the "shipping-receiving" sites on that day. The total number of courier shipments between cities at the "receipt" site, and fill in the number of courier shipments between designated site cities and the total number of courier shipments between all "delivery-receipt" site cities on the day in Table 2 .
Table 2 Results of Question 2
| date | The number of express shipments between "Ship-Receive" cities | The total number of express shipments between all "Ship-Receive" cities | |
| April 18, 2019 | M-U | ||
| Q-V | |||
| K-L | |||
| GV | |||
| April 19, 2019 | VG | ||
| A-Q | |||
| D-A | |||
| L-K |
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.
Table 3 Results of Question 3
| date | "Ship-Receive" site city pair | Whether it can be shipped normally (fill in "yes" or "no") | Express Shipping Quantity |
| April 28, 2023 | I-S | 900-1500 | |
| M-G | |||
| S-Q | |||
| V-A | |||
| YL | |||
| April 29, 2023 | D-R | ||
| J-K | |||
| Q-O | |||
| IN ABOUT | |||
| Y-W |
Question 4: Figure 1 shows the railway transportation network between cities with all stations, and the railway transportation cost is calculated by the following formula:
. In this question, it is assumed that the actual loading volume is allowed to exceed the rated loading volume. The fixed costs and nominal loads of all railways are given in Appendix 3. When transporting express delivery, it is required that the number of routes used between each "delivery-receiving" site city pair does not exceed 5. Please establish a mathematical model to provide the lowest-cost transportation plan for the express company. Using the data in Annex 2 and Annex 3, calculate the company's minimum daily transportation cost from April 23 to 27, 2023, and fill in Table 4.
Remarks: For the convenience of calculation, the weight and size of the courier are not distinguished, assuming that the weight of each courier is unit 1. Only the transportation cost is considered, and other costs such as transit are not considered.
Figure 1 Station intercity railway transportation network
Table 4 Results of Question 4
| date | Lowest Shipping Cost |
| April 23, 2023 | |
| April 24, 2023 | |
| April 25, 2023 | |
| April 26, 2023 | |
| April 27, 2023 |
Question 5: Usually, express delivery demand is composed of two parts, one part is fixed demand, which comes from daily necessary online shopping consumption (generally, it cannot be simply identified as the minimum value of historical data of express delivery demand, usually smaller than the minimum value of demand ); the other part is non-fixed demand, which usually has large fluctuations and is greatly affected by factors such as time. Assume that in the same quarter, the fixed demand of the same "shipping-receiving" site city pair is a definite constant (hereinafter referred to as the fixed demand constant); the non-fixed demand of the same "shipping-receiving" site city pair obeys a certain Probability distribution (the mean and standard deviation of this distribution are respectively called the mean value of non-fixed demand and the standard deviation of non-fixed demand). Please use the data in Attachment 2, regardless of the data that has been eliminated, data that has no delivery demand, and data that cannot be shipped normally, to solve the following problems.
(1) Establish a mathematical model to estimate the constant demand constant on a quarterly basis and verify its accuracy. Fill in Table 5 with the specified quarter, the fixed demand constant of the designated "shipping-receiving" site city pair, and the sum of the fixed demand constants of all "shipping-receiving" city pairs in the current quarter.
(2) Give the estimation method of the probability distribution of non-stationary demand, and the specified quarter, the non-stationary demand mean and standard deviation of the specified "shipping-receiving" site city pair, and all "shipping-receiving" cities in the current quarter The sum of the mean value of the non-fixed demand and the sum of the standard deviation of the non-fixed demand are filled in Table 5.
Table 5 Results of Question 5
| the quarter | The third quarter of 2022 (July-September) | The first quarter of 2023 (January-March) | ||
| "Ship-Receive" site city pair | V-N | V-Q | J-I | O-G |
| fixed demand constant | ||||
| non-stationary demand mean | ||||
| Variable demand standard deviation | ||||
| sum of fixed demand constants | ||||
| Sum of means of non-fixed demands | ||||
| Sum of Standard Deviations of Non-Stationary Demand |