Question A: Thoughts on vaccine production.

Confirm the answer to the first question, and think about other questions. COVID-19 has ravaged the whole world and brought profound disasters to the world. All countries have developed COVID-19 vaccine to control the epidemic. Suppose that vaccine production needs to go through four technological processes: CJ 1 station, CJ2 station, CJ3 station and CJ4 station.

Each process can process 100 dose of vaccine at a time, and this 100 dose of vaccine is put into a processing box and sent to the equipment in the station for processing. In addition, the production is not completed until all four stations are processed in the order of CJ 1-CJ2-CJ3-CJ4.

In order to prevent the confusion of vaccine packaging, the production department of a vaccine production company stipulates that each station cannot produce different types of vaccines at the same time, and vaccine production is not allowed to jump the queue.

That is to say, once the production order of each type of vaccine arranged by the first station is determined, it must remain unchanged, and the former type of vaccine can only enter the station after leaving the station.

Game thinking on fire rescue problem b.

Description of competition questions

With the rapid development of China's economy, the complexity of urban space environment has risen sharply, and various accidents and disasters have occurred frequently, and security risks have been increasing. The tasks undertaken by the fire rescue team are also diversified and complicated. For each police incident, the fire rescue team will make a detailed record.

Question 1:

Divide the day into three time periods (0:00-8:00 as time period I, 8:00- 16:00 as time period II, 16:00-24:00 as time period III), and arrange at least 5 people on duty in each time period.

Assuming that the fire brigade has 30 people on duty every day, please establish a mathematical model according to the attached data, and determine how many people the fire brigade will arrange to be on duty in February 1 day, May 1 day, August 1 day,165438+1October each year.

Question 2:

Based on the data of 20 16, 1 10 to 20 19, 12, 3 1 2, a monthly prediction model of fire rescue calls was established.

Taking the data from June 65438+1 October1to February 3 1 in 2020 as the verification data set of the model, the accuracy and stability of the model are evaluated, and the number of fire rescue calls in 20021month is predicted.

Question 3:

According to the occurrence time of seven kinds of events, a variety of mathematical models of the relationship between the occurrence time and month of various events are established, and the optimal model of the occurrence time of various events is determined with the optimal fitting degree as the evaluation standard.

Question 4:

Please establish a mathematical model to analyze the spatial correlation of various event densities in the area of 20 16-2020, and give the event categories with the strongest correlation in different areas (event density refers to the number of events per square kilometer per week).

Question 5:

Please establish a mathematical model to analyze the relationship between the density of various events and population density (population density refers to the number of people per square kilometer).

Question 6:

At present, there are two fire stations in this area, which are located in Zone J and Zone N respectively. Considering all kinds of factors, a mathematical model is established to determine which area the new 1 fire station should be built in.

If 1 fire station is built every three years from 202 1 to 2029, which areas should it be built in turn?

Ideas:

Basically, it is similar to the fire rescue problem in the national competition. Simply speaking, it belongs to the path optimization problem.

The idea of data-driven anomaly detection and early warning in question C.

Title description

To promote the high-quality development of production enterprises, the most fundamental bottom line is to ensure safety and prevent risks, and the data generated in the production process can reflect potential risks in real time.

From 00: 00: 00 to 22: 59: 59 on a certain day, the time series data (desensitization) recorded by the instruments and equipment in the production area of the production enterprise, the specific name of the data is not given in this topic, and these data may be closely related to the safety of temperature, concentration and pressure.

Establish a mathematical model to complete the following questions:

Question 1:

The given data may fluctuate, and all fluctuations are within the safe range. Some fluctuations may be normal fluctuations, such as fluctuations with changes in external temperature or output, or may be false alarms of sensors.

These fluctuations have the characteristics of regularity, independence and contingency, and will not cause security risks. We regard them as risk-free anomalies and do not need human intervention. Some fluctuations have the characteristics of persistence and linkage.

These abnormal fluctuations are caused by unstable factors in the production process, which indicates that there may be potential safety hazards. We regard them as abnormal risks and need manual intervention, analysis and evaluation of risk level.

Please establish a mathematical model and give a method to judge the risk-free abnormal data and the risk abnormal data.

Question 2:

Combined with the results of 1 problem, a mathematical model is established, and a quantitative evaluation method of abnormal degree of risk abnormal data is given. The percentage system (0- 100) is required to evaluate the abnormal degree of data at each moment (the higher the score, the higher the abnormal degree).

By applying the established model and the data in appendix 1, the five moments with the highest anomaly scores in the data and the corresponding anomaly sensor numbers are found. Only fill in the number of the five sensors with the highest degree of abnormality at each moment. If there are less than five abnormal sensors, it is not necessary to fill in.

If the score is 0, there is no need to fill in the number of abnormal sensors, and a mathematical model is given to evaluate the results.

Ideas:

Classical anomaly analysis problem, abnormal data can generally be done by machine learning method, commonly used clustering.

Kmeans, dbscan, decision tree, isolated deep forest and LSTM can all be applied.