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2023年美赛特等奖论文-B-2315379-解密.pdf
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大学生,数学建模,美国大学生数学建模竞赛,MCM/ICM,2023年美赛特等奖O奖论文
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Problem Chosen
B
2023
MCM/ICM
Summary Sheet
Team Control Number
2315379
Build a common paradise for humans and wildlife in the Maasai Mara
Summary
Each year, the world's most spectacular wildlife migration, known by word of mouth as the
"Mara River Crossing," takes place in Kenya's Maasai Mara Reserve. The reserve was originally
established to protect wildlife and natural resources. However, the interests of the people living
in the area cannot be ignored as well.
Before all the models are established, we clean and
visualize
a large amount of data with
high reliability,which is of great help to our subsequent indicator selection work.In addition, we
precisely defined the vague concepts of "lost opportunities" and "negative interactions".
For problem 1, we divided the Maasai Mara roughly equally into
36
grids in order to
facilitate modeling, taking into account its current distribution of natural resources and wildlife.
For each grid, we choose to establish one of
4
functional areas: wildlife sanctuary, agricultural
area, hunting area, or tourism area. In order to balance the interests of wildlife and humans in the
area, we proposed the concept and calculation method of ecological and economic benefits, and
took their maximum value as the objective function.We established
Model I: Maasai Mara
Resource Allocation Strategy Model based on dual-goal planning
. The constraints are:(1)The
size of the ecological benefit constrains the type of functional area;(2) the limitation of the
number of tourists; (3) the guarantee of residents' income, etc. Using Lingo, 3 seanarios are
calculated. Take
scenario 2
as an example: establish
13
wildlife sanctuaries,
13
agricultural
areas,
2
hunting areas, and
9
tourist areas.
For problem 2, in order to determine the management solution that would produce the best
results, we developed
Model II: a minimal interaction model based on Dijkstra and an
economic impact evaluation model
. We specify four types of interactions, analogous to the
influence relationships between the four functional areas, and determine the weights of the paths
in the directed graph.Based on the 3 scenarios obtained from the solution of problem 1, we use
the improved Dijkstra algorithm to measure the interaction impact of each scenario by
calculating its shortest path separately. Meanwhile, the economic benefits of the three scenarios
were calculated as $141,274.438, $154,948.974, and $130,180.760 (unit:million) respectively,
taking into account the economic development level of the Masai Mara region. The results show
that scenario 2 has the best interaction and economic efficiency. Therefore,
scenario 2
is the best.
For problem 3, we developed Model
Ⅲ
: A long-term trend forecasting model for the
Masai Mara region. We first predicted the increase in tourists that might result from a decrease
in negative human-animal interactions. We then fitted a quadratic nonlinear regression equation
to predict the relationship between tourism revenue and the number of tourists in Kenya from
2010-2019, which in turn predicted changes in tourism revenue. Using the COVID-19 pandemic
as an example, in testing the accuracy of the long-term prediction results, we used a t-test and
calculated a p-value of less than 0.05, indicating that tourism revenue in Kenya before and after
the COVID-19 pandemic was significantly different.The COVID-19 pandemic was considered to
have affected tourism. Our model is highly adaptable due to the rich set of influencing factors
and special cases discussed. We examined its application in Yellowstone National Park.
Finally, sensitivity analysis of the index weight shows that our model is not sensitive to
changes in them.After discussing the advantages and improvements of the model, a two-page
non-technical report on resource redistribution plan in the Maasai Mara and its value has been
written for the Kenyan Tourism and Wildlife Committee.
Key Words
:Grid method; Dual-goal planning; Dijkstra's algorithm;Non-linear regression
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Content
1.Introduction ................................................................................................................................ 3
1.1 Background ....................................................................................................................... 3
1.2 Restatement of the problem ...............................................................................................3
1.3 Literature review ............................................................................................................... 3
1.4 Our work ............................................................................................................................3
2.Assumption and Justification .................................................................................................... 4
3.Notations and Definitions .......................................................................................................... 5
3.1 Notations ........................................................................................................................... 5
3.2 Definitions ......................................................................................................................... 5
4.Data ..............................................................................................................................................6
4.1 Data Overview ...................................................................................................................6
4.2 Data Collection ..................................................................................................................6
4.3 Data Screening & Visualization ........................................................................................ 6
5.Problem 1 .................................................................................................................................... 7
5.1 Problem analysis ................................................................................................................7
5.2 Preparation of the model ................................................................................................... 7
5.3 Establishment of the model ............................................................................................... 8
5.3.1 Zoning according to wildlife distribution status .....................................................8
5.3.2 Determination of decision variables and constraints ..............................................9
5.3.3 Determination of objective function .....................................................................11
5.4 Solution of the model ...................................................................................................... 11
6.Problem 2 .................................................................................................................................. 12
6.1 Problem analysis ..............................................................................................................12
6.2 Preparation of the model ................................................................................................. 12
6.2.2 Establishment of the model .................................................................................. 13
6.2.3 Solution of the model ........................................................................................... 15
6.3 Economic impact evaluation model........................................................................ 15
7.Problem 3 .................................................................................................................................. 16
7.1 Problem analysis ..............................................................................................................16
7.2.1 Changes in tourism revenue ................................................................................. 16
7.2.2 Changes in agriculture ..........................................................................................17
7.2.3 Impact of the COVID-19 pandemic on tourism ...................................................17
7.2.4 Long-term impact of policy implementation ........................................................17
7.3 Model Migration: Yellowstone National Park ................................................................ 18
7.3.1 Feasibility analysis of model migration ............................................................... 18
7.3.2 Model improvement and solution .........................................................................19
8.Problem 4 .................................................................................................................................. 20
9. Sensitivity analysis of the model .............................................................................................23
10.Evaluation and extension of the model .................................................................................23
10.1 Advantages .................................................................................................................... 23
10.2 Limitations and Extension of the model........................................................................24
11.Reference .................................................................................................................................24
12.Appendix ................................................................................................................................. 25
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1.Introduction
1.1 Background
Kenya, as an economically underdeveloped African country, spends a large amount of its
fiscal revenue on building protected areas. At the same time, Kenya's tourism industry, which
focuses on wildlife viewing, is a major source of national finance. Masai Mara, as one of the
most famous wildlife reserves in Kenya, is famous for its magnificent grasslands and rich
wildlife species. How to develop policies related to different areas of the reserve, making it
possible to balance the interests of the residents of the area while protecting wildlife and other
natural resources, has become an issue for the government to consider.
1.2 Restatement of the problem
For problem1, we need to consider whether to improve specific policies and management
strategies for different areas of the current protected area. In considering new policies and
management strategies, we need to balance the ecological benefits with the economic benefits,
while avoiding negative impacts on the people attracted to the reserve by tourism.
For problem2, we need to determine which policies and management strategies work best.
We need to build a model to rank and compare the results from task1. The principles of ranking
and comparing include whether animal-human interactions under this policy are mostly positive,
and whether they have a positive impact on the economy in and around the reserve.
For problem3, we need to predict the impact of the plan proposed in task1 on future
development. We need to analyze the results of the corresponding policies and management
strategies, and how these management strategies should be applied to other nature reserves.
For problem4, we need to provide a non-technical report for the Kenya Tourism and
Wildlife Commission. In the report, we need to describe our proposed plan and analyze the
impact and value of the plan for the Masai Mara Reserve.
1.3 Literature review
Scholars have conducted numerous studies on the zoning of nature reserves and the
development of industries in the vicinity of the Masai Mara Nature Reserve.Bob E.L. Wishitemi
et al. studied the linkages between poverty, environment, and ecotourism development in areas
near the Masai Mara Reserve in Kenya
[1]
.Kathleen Krafte Hollanda et al. analyzed the impact of
tourism on conservation support, local livelihoods, and community resilience around the Masai
Mara National Reserve in Kenya
[2]
. J. O. Ogutu1 et al. analyzed changes in wildlife populations
in the Mara region of Kenya between 1977 and 2009
[3]
.Xue Fan analyzed network selection
algorithms for nature reserve planning and design using the Daiyunshan National Nature Reserve
as an example
[4]
.
1.4 Our work
To avoid complicated description , intuitively reflect our work process, the flow chart is
show as the following Figure 1:
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Figure 1. Our work
2.Assumption and Justification
To simplify the problem, we make the following basic assumptions, each of which is
properly justified.
Assumption 1: All data sources in this paper are true and reliable.
Justification: We need to rely on historical data from the Masai Mara and the surrounding
area to analyze its trends in terms of economy, climate, and biodiversity. Therefore, the
reliability of data is very important.
Assumption 2: No major natural disasters will occur in the Masai Mara and the
surrounding area in the next 50 years.
Justification: Earthquakes, mudslides, tsunamis, and other natural hazards are force majeure
factors, and we cannot accurately predict or quantify their impact on model stability.
Assumption 3: The human-nature balance in the Masai Mara region is not governed
by factors other than the influences we have discussed.
Justification: We have envisioned as far as possible the relevant factors that may influence
the problem and given reasons why the influence of other factors is almost absent. Therefore, in
order to simplify the model, we can make the assumptions as above.
Team#2315379 Page
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Assumption 4: For the 36 regions divided by the Maasai Mara, it can be assumed that
environmental, economic and other conditions are the same within each small region.
Justification: A reasonable idealization of the zoning of the Masai Mara region. Assuming
the same conditions within the region helps us to calculate the associated benefits and costs.
Assumption 5: For the partially difficult-to-obtain data for the Masai Mara region,
data from Kenya can be substituted.
Justification: Due to the difficulty of obtaining data for parts of the Masai Mara, we had to
substitute relevant data from Kenya, however, based on the similarity of the known data, we can
conclude that the effect of this practice on the accuracy of our model is within a reasonable error.
·Note:Relevant assumptions of game theory model will be shown below.
3.Notations and Definitions
3.1 Notations
Table 1. Notations
Notations Descriptions
Whether to build a nature reserve in the j-th geographical area
Ecological benefit value
Power generation of the i-th hydropower station
Number of people in the j-th geographic area
The intensity of human-animal interaction
Construction of protected areas when implementing the i-th program
·
Note
:
Some variables are not listed. Their specific meanings will be introduced below.
3.2 Definitions
Some vague concepts appear in the description of the topic. We define precisely those
words or sentences that may be ambiguous.
✧ Resources: Original text mentions that the resources within and outside the current
boundaries of the park, we consider resources here as the ecological value of wildlife
(biodiversity), vegetation resources, water resources, land resources, etc.
✧
Lost Opportunities: Original text mentions that the impacts of lost opportunities experienced
by the people who live near the preserve. We consider lost opportunity here to mean that people
have to lose some of their arable land due to the presence of the reserve. Livestock raised and
their own lives might be safe from some dangerous large wild animals.
✧ The people attracted to the preserve :Original text mentions that minimize negative
interactions between animals and the people attracted to the preserve, We consider the people
attracted to the preserve here as domestic and foreign tourists from Kenya to the Masai
Mara(excluding local residents).
✧
Negative interactions: We group the negative interactions here into two categories.
Category 1(People → Wildlife):Some visitors may feed unclean food to wildlife. In addition,
there may also be some illegal poachers.
Category 2(Wildlife → People):Some visitors may be injured by dangerous large wild animals,
such as elephants and lions, during their visit.
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