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2019亚太杯数学建模B题.pdf
2019 Asia and Pacific Mathematical Contest in Modeling
Problem B
Analysis and Decision-making of Regional Economic Vitality
and Its Influencing Factors
The regional (or urban or provincial) economic vitality is an important part of regional
comprehensive competitiveness. In recent years, in order to improve the economic vitality,
some regions have launched many preferential policies for stimulating the economy vitality,
such as reducing the investment attraction approval steps, providing the capital support to start-
ups and lowering the settlement threshold to attract the talented. However, due to different
resource endowments, these policies have different effects in different regions. How to seize
the key factors and effectively improve the regional economic vitality is a worth study topic.
In order to study how to improve the regional economic vitality, we have obtained some data.
Please build a suitable model and solve the following problems based on these data and your
own data obtained through survey.
1. The regional (or urban or provincial) economic vitality is affected by variety of factors. Take
a region (or city or province) as an example, please build the suitable relational model of
influencing factors of economic vitality, and study the program of action to improve the regional
economic vitality. Analyze the effects on the regional economic vitality change from the
perspective of changing trend of population and enterprise vitality.
2. Select a region (or city or province), and analyze the short-term and long-term effects of
economic policies transformation on the economic vitality of such region (or city ore province)
based on the suitable data surveyed by you.
3. Measuring the regional economic vitality is a complex issue. Please select the suitable index
system, establish the mathematical model which analyzes and measures the regional (or urban
or provincial) economic vitality, and rank the economic vitality of cities in Attachment 3.
4. If you are a decision-maker of regional economic development, according to the conclusions
for Problems 1-3, provide a development proposal for the region (or city or province) discussed
in Problem 2 so that the economic vitality in this region presents the benign sustainable
development and the regional competitiveness is stronger.
Attachment
(5 attachments in total)
Attachment 1
The quantity of enterprises is an important index to measure the regional economic vitality. The
quantity of enterprises has a direct effect on the available job opportunities, and to what extent
the resource circulation is promoted, and decides the economic benefits. According to the data,
from 2009 to 2018, there were 40,176,400 registered and established enterprises (excluding
individual business, the same below) in total in 31 provinces/municipalities directly under the
Central Government/autonomous regions (excluding Hong Kong, Macau and Taiwan Province).
As of September 2019, 9,753,800 enterprises were cancelled (cancellation rate of 24.28%), and
there were still 30,422,600 surviving enterprises. The quantity of enterprises which were
registered and established from 2009 to 2018 and survive up in 2019 is as follows (Unit: 10,000):
Table 1: The quantity of enterprises which were registered and established from 2009 to 2018 and survive
up in 2019
Province
Quantity of Surviving Enterprises in 2019 (Unit: 10,000)
Heilongjiang
Jilin
Liaoning
Beijing
Tianjin
Inner Mongolia
Xinjiang
Qinghai
Tibet
Ningxia
Shanxi
Hebei
Shandong
Henan
Shaanxi
Gansu
Sichuan
Chongqing
Hubei
Anhui
Jiangsu
43.6
44.4
76.1
118.3
43.7
42.1
31.8
10.0
6.7
15.1
55.6
134.8
243.9
146.3
73.0
43.3
122.4
69.8
105.3
113.8
269.4
Shanghai
Zhejiang
Guizhou
Hunan
Jiangxi
Fujian
Yunnan
Guangxi
Guangdong
Hainan
157.4
188.5
64.0
79.9
66.1
105.9
60.6
68.7
420.4
21.5
Attachment 2
Since 2013, the growth of quantity of enterprises in China has accelerated. Although the growth
in different economic regions is obviously different, the annual quantity of newly-added
enterprises in all regions is more than that of last year basically. In terms of region, except the
total quantity, in the difference of average quantity of newly-added enterprises per province in
four economic regions, the eastern region still maintains a great advantage: the provinces in the
eastern region have the largest average registration quantity of enterprises per province and the
highest growth, followed by the central region. In the west and northeast, the enterprise vitality
is relatively weak. The average quantity of newly-added enterprises per province in the
northeast may be surpassed by the western region in recent years. In general, there is still a
relatively great difference in the enterprise vitality between regions. However, regardless of
region, the annual quantity of newly-added enterprises from 2009 to 2018 was relatively stable.
Four economic regions are divided as follows:
Eastern region: Beijing, Hebei, Tianjin, Shandong, Jiangsu, Shanghai, Zhejiang, Fujian,
Guangdong, Hainan
Central region: Shanxi, Henan, Hubei, Hunan, Jiangxi, Anhui
Western region: Chongqing, Sichuan, Guangxi, Guizhou, Yunnan, Shaanxi, Gansu, Ningxia,
Xinjiang, Qinghai, Tibet
Northeastern region: Heilongjiang, Jilin, Liaoning, Inner Mongolia
Table 2: Trend in Incremental Changes to Enterprises in Four Economic Regions from 2009 to 2018
(Unit: 10,000)
Eastern
Region
Central
Region
Northeastern
Region
Western
Region
7.9
9.4
10.3
9.9
12.7
19.5
23.8
30.3
32.8
35.8
4.4
5.0
5.6
5.7
7.2
11.1
12.9
16.4
19.6
22.6
3.3
3.6
3.8
3.6
4.6
7.0
7.1
8.6
10.1
10.3
2.3
2.6
2.9
3.1
3.7
6.0
7.0
8.6
9.8
10.5
Year
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
Attachment 3
If we look away from economic region and province, and focus on city, in addition to Beijing,
Shanghai, Guangzhou and Shenzhen, the second-tier cities are also worth attention. The data of
stock and cancellation distribution of enterprises in Beijing, Shanghai, Guangzhou and
Shenzhen and some second-tier cities are given as follows. (Unit: 10,000)
Table 2: The data of stock and cancellation distribution of enterprises in Beijing, Shanghai, Guangzhou and
Shenzhen and some second-tier cities (Unit: 10,000)
Quantity of Newly-
City
established Enterprises
Quantity of Surviving
Enterprises in 2019
Quantity of Cancelled
Enterprises from 2009
from 2009 to 2018
to 2018
Shanghai
Shenzhen
Beijing
Guangzhou
Chongqing
Chengdu
Nanjing
Hangzhou
Suzhou
Tianjin
Qingdao
Dongguan
Zhengzhou
Wuhan
204.8
203.1
152.1
110.2
97.5
85.0
64.6
64.1
63.8
62.0
55.6
53.4
53.3
52.6
157.4
174.1
118.3
89.6
69.8
60.6
55.8
48.7
53.6
43.7
41.0
43.4
43.1
39.8
47.4
29.0
33.8
20.6
27.7
24.4
8.8
15.4
10.2
18.3
14.6
10.0
10.2
12.8
Xi’an
Ningbo
Changsha
Shenyang
Kunming
Attachment 4
51.4
44.4
36.8
33.4
33.2
37.5
31.1
28.5
21.8
23.5
13.9
13.4
8.3
11.6
9.7
The registered capital is an index to measure the enterprise size. In the distribution of enterprise
size, there is not so large difference as imagined between the second-tier cities and Beijing,
Shanghai, Guangzhou and Shenzhen. The distribution data of registered capital of enterprise
entity are given as follows:
Table 3: Distribution Data of Registered Capital of Enterprise Entity from 2009 to 2018 (Unit: 10,000)
Nationwide
Beijing
Shanghai Guangzhou
Shenzhen
9%
13%
16%
21%
40%
>10,000,000
5,000,000-
10,000,000
2,000,000-
5,000,000
1,000,000-
2,000,000
0-1,000,000
Attachment 5
13%
16%
16%
21%
35%
9%
14%
16%
22%
39%
9%
11%
13%
25%
42%
8%
12%
12%
25%
44%
Second-tier
Cities
9%
12%
15%
22%
42%
How to narrow the difference in the quantity of enterprises between the second-tier cities and
Beijing, Shanghai, Guangzhou and Shenzhen? “Investment attraction” and “talent attraction
policy” may be common methods. Therefore, the “talent attraction” between cities presently
becomes increasingly fierce. In fact, the resident population in a region is closely related to the
quantity of enterprises in this region. The data of resident population in 2019 are given as
follows.
Table 4: Data of Resident Population and Quantity of Surviving Enterprises in Some Second-tier Cities in
2019
City
Shanghai
Shenzhen
Quantity of Surviving Enterprises in 2019
Resident Population in 2019
Unit: 10,000
157.4
174.1
Unit: 10,000
2419.70
1190.84
Beijing
Guangzhou
Chongqing
Chengdu
Nanjing
Hangzhou
Suzhou
Tianjin
Qingdao
Dongguan
Zhengzhou
Wuhan
Xi’an
Ningbo
Changsha
Shenyang
Kunming
118.3
89.6
69.8
60.6
55.8
48.7
53.6
43.7
41.0
43.4
43.1
39.8
37.5
31.1
28.5
21.8
23.5
2172.9
1404.35
683.07
1194.05
827.0
787.5
1068.4
1562.12
920.4
826.1
972.4
1091.4
992.32
787.5
731.15
752
667
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