Introduction to Mathematical Modeling
Mathematical modeling is a mathematical thinking method, and it is a powerful mathematical means to describe and solve practical problems by using mathematical language and methods through abstraction and simplification. The mathematical model includes many contents, among which the grey prediction method is a typical mathematical prediction model. Grey prediction method is a method based on grey system. The so-called grey system is a grey system between the white system and the black system, that is, the internal information and characteristics of the system are partly known and the other part is unknown. Its specific meaning is: if all information of a system is known as a white system, all information is unknown as a black system, some information is known, and some information is unknown, then the system is a gray system. Gray theory holds that although the behavior of gray system is hazy and the data is complex, it is orderly and has global functions. The generation of grey number is to find out the law from clutter. There are many factors that affect the price changes of goods and services, which have great uncertainty. It is most appropriate to use the grey forecasting method to forecast the price trend.
Two, the specific application of grey forecasting method in the price forecast of some building materials in our city.
1. Price changes in the building materials market in our city in the previous period.
The Information Monitoring Center of the Municipal Price Bureau began to conduct special monitoring on the prices of some building materials such as red bricks and sandstone in May 2009. The monitoring data shows that the prices of some building materials in May-10 are as follows (unit: RMB/ton).
moon
diversification
May
June
July
August
September
10 month
Ordinary brick
0.265
0.265
0.265
0.265
0.265
0.265
sand
Rough
60
60
60
58
58
58
middle
60
60
60
58
58
58
filmy
55
55
55
58
58
58
sandstone
4 cm
36.5
36.5
38
40
40
40
2-4 cm
36.5
36.5
38
40
40
40
2 cm
36.5
36.5
38
40
40
40
2. Forecast the price of building materials in June165438+1October by grey forecasting method.
In order to ensure the feasibility of the model, it is necessary to check the reference series. The calculated values of various building materials data are as follows:
diversification
Polarity ratio
Ordinary brick
( 1, 1, 1, 1, 1)
sand
Rough
( 1, 1,0.96, 1, 1)
middle
( 1, 1,0.96, 1, 1)
filmy
( 1, 1,0.95, 1, 1)
sandstone
4 cm
( 1,0.96,0.95, 1, 1)
2-4 cm
( 1,0.96,0.95, 1, 1)
2 cm
( 1,0.96,0.95, 1, 1)
Through calculation, the tolerance range is (0.75 15, 1.3307), so the polar ratios of all series fall within the tolerance range, and the reference series can be used as GM( 1, 1) model series for grey prediction.
3. According to the grey forecasting theory, the price of some building materials is estimated to be about:
diversification
Ordinary brick
coarse sand
Zhongshazi
fine sand
4 cm gravel
2-4cm sandstone
2 cm gravel
165438+ October price
0.265
58. 1944
58. 1944
57.688
39.7766
39.7766
39.7766
The results of the grey prediction model show that the prices of the above-mentioned building materials in our city will tend to be stable in the next month without major changes in supply and demand.
In order to better see the price trend, combined with the previous data, the prices of various monitored varieties have been counted since May, as shown in the following figure: