2023美国大学生数学建模竞赛MCM/ICM赛题发布

ilikenba

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2023 MCM
Problem A: Drought-Stricken Plant Communities
Photo Credit: Pixabay.com
Background
Different species of plants react to stresses in different ways. For example, grasslands are quite
sensitive to drought. Droughts occur at varying frequencies and varying levels of severity.
Numerous observations suggest that the number of different species present plays a role in how a
plant community adapts when exposed to cycles of drought over successive generations. In some
communities with only one species of plant, the generations that follow are not as well adapted
to drought conditions as the individual plants in communities with four or more species. These
observations raise many questions. For example, what is the minimal number of species
necessary for a plant community to benefit from this type of localized biodiversity? How does
this phenomenon scale as the number of species increases? What does this imply for the long
term survivability of a plant community?
Requirement
Considering the relationship of drought adaptability with respect to the number of species in a
plant community, your task is to explore and better understand this phenomenon. Specifically,
you should:
 Develop a mathematical model to predict how a plant community changes over time as it
is exposed to various irregular weather cycles. Include times of drought when
precipitation should be abundant. The model should account for interactions between
different species during cycles of drought.
 Explore what conclusions you can draw from your model with respect to the long-term
interactions of a community of plants and the larger environment. Consider the following
questions:
 How many different plant species are required for the community to benefit and what
happens as the number of species grows?
 How do the types of species in the community impact your results?
 What are the impact of a greater frequency and wider variation of the occurrence of
droughts in future weather cycles? If droughts are less frequent, does the number of
species have the same impact on the overall population?  How do other factors such as pollution and habitat reduction impact your
conclusions?
 What does your model indicate should be done to ensure the long-term viability of a
plant community and what are the impacts on the larger environment?
Your PDF solution of no more than 25 total pages should include:
 One-page Summary Sheet.
 Table of Contents.
 Your complete solution.
 Reference List.
Note: The MCM Contest has a 25-page limit. All aspects of your submission count toward the
25-page limit (Summary Sheet, Table of Contents, Report, Reference List, and any Appendices).
You must cite the sources for your ideas, images, and any other materials used in your report.
Glossary
Biodiversity: The variety of life in the world or in a particular habitat or ecosystem.


2023 MCM
Problem B: Reimagining Maasai Mara
Photo Credit: Pixabay.com
Background
Kenya’s wildlife preserves were originally created primarily to protect wildlife and other natural
resources. Kenya’s parliament passed the Wildlife Conservation and Management Act, 2013 to
provide more equitable sharing of resources, as well as to allow alternative, community-based
management efforts[1]. Kenya has since added amendments to address gaps in the legislation to
provide more clear governance, finance, and penalties for violators[2].
Requirement
Focusing on one large game preserve, the Maasai Mara, your task is to determine alternate ways
to manage the resources within and outside the current boundaries of the park. Specifically, you
should:
• Consider and recommend specific policies and management strategies for different areas
within the current preserve that will protect wildlife and other natural resources while
also balancing the interests of the people who live in the area. These policies and
strategies should help mitigate the impacts of lost opportunities experienced by the
people who live near the preserve, as well as minimize negative interactions between
animals and the people attracted to the preserve.
• Develop and describe a methodology to determine which policies and management
strategies will result in the best outcomes. Your report should discuss how to rank and
compare outcomes from your methodology. Be sure to include descriptions and analyses
of the models used to predict the interactions between animals and people, as well as the
resulting economic impacts in the area within and around the preserve.
• Given your proposed plan, provide predictions about the long-term trends that will result
from your recommendations. Analyze and provide estimates of the certainties and
impacts of the possible long-term outcomes. You should also describe how your
approach could be applied to other wildlife management areas.
Finally, provide a two-page non-technical report for the Kenyan Tourism and Wildlife
Committee discussing your proposed plan and its value for the preserve.
| ©2023 by COMAP, Inc. | www.comap.com | www.mathmodels.org | info@comap.com |Your PDF solution of no more than 25 total pages should include:
• One-page Summary Sheet.
• Table of Contents.
• Your complete solution.
• Two-page non-technical report.
• Reference List.
Note: The MCM Contest has a 25-page limit. All aspects of your submission count toward the
25-page limit (Summary Sheet, Table of Contents, Report, Non-Technical Report, Reference
List, and any Appendices). You must cite the sources for your ideas, images, and any other
materials used in your report.
References
[1] The Wildlife Conservation and Management Act, 2013. Republic of Kenya, Kenya Gazette
Supplement No. 181 (Acts No. 47), 2013.
[2] The Wildlife Conservation and Management Act (No. 47 of 2013). Legal Notice No. 155.
Republic of Kenya, Kenya Gazette Supplement No 141 (Acts No. 47), 2020.

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2023 MCM
Problem C: Predicting Wordle Results
Image: nytco.com[1]
Background
Wordle is a popular puzzle currently offered daily by the New York Times. Players try to solve
the puzzle by guessing a five-letter word in six tries or less, receiving feedback with every guess.
For this version, each guess must be an actual word in English. Guesses that are not recognized
as words by the contest are not allowed. Wordle continues to grow in popularity and versions of
the game are now available in over 60 languages.
The New York Times website directions for Wordle state that the color of the tiles will change
after you submit your word. A yellow tile indicates the letter in that tile is in the word, but it is in
the wrong location. A green tile indicates that the letter in that tile is in the word and is in the
correct location. A gray tile indicates that the letter in that tile is not included in the word at all
(see Attachment 2)[2]. Figure 1 is an example solution where the correct result was found in
three tries.
Figure 1: Example Solution of Wordle Puzzle from July 21, 2022[3]Players can play in regular mode or “Hard Mode.” Wordle’s Hard Mode makes the game more
difficult by requiring that once a player has found a correct letter in a word (the tile is yellow or
green), those letters must be used in subsequent guesses. The example in Figure 1 was played in
Hard Mode.
Many (but not all) users report their scores on Twitter. For this problem, MCM has generated a
file of daily results for January 7, 2022 through December 31, 2022 (see Attachment 1). This
file includes the date, contest number, word of the day, the number of people reporting scores
that day, the number of players on hard mode, and the percentage that guessed the word in one
try, two tries, three tries, four tries, five tries, six tries, or could not solve the puzzle (indicated by
X). For example, in Figure 2 the word on July 20, 2022 was “TRITE” and the results were
obtained by mining Twitter. Although the percentages in Figure 2 sum to 100%, in some cases
this may not be true due to rounding.
Figure 2: Distribution of the Reported Results for July 20, 2022 to Twitter[4]
Requirement
You have been asked by the New York Times to do an analysis of the results in this file to
answer several questions.
• The number of reported results vary daily. Develop a model to explain this variation and
use your model to create a prediction interval for the number of reported results on March
1, 2023. Do any attributes of the word affect the percentage of scores reported that were
played in Hard Mode? If so, how? If not, why not?
• For a given future solution word on a future date, develop a model that allows you to
predict the distribution of the reported results. In other words, to predict the associated
percentages of (1, 2, 3, 4, 5, 6, X) for a future date. What uncertainties are associated with
your model and predictions? Give a specific example of your prediction for the word
EERIE on March 1, 2023. How confident are you in your model’s prediction?
| ©2023 by COMAP, Inc. | www.comap.com | www.mathmodels.org | info@comap.com |• Develop and summarize a model to classify solution words by difficulty. Identify the
attributes of a given word that are associated with each classification. Using your model,
how difficult is the word EERIE? Discuss the accuracy of your classification model.
• List and describe some other interesting features of this data set.
Finally, summarize your results in a one- to two-page letter to the Puzzle Editor of the New York
Times.
Your PDF solution of no more than 25 total pages should include:
• One-page Summary Sheet.
• Table of Contents.
• Your complete solution.
• One- to two-page letter.
• Reference List.
Note: The MCM Contest has a 25-page limit. All aspects of your submission count toward the
25-page limit (Summary Sheet, Table of Contents, Report, Reference List, and any Appendices).
You must cite the sources for your ideas, images, and any other materials used in your report.
Attachments
1. Data File. Problem C Data Wordle.xlsx
THE ATTACHED DATA FILE CONTAINS THE ONLY DATA YOU SHOULD USE FOR THIS
PROBLEM. All information needed for this problem is given in the problem statement and the data file.
You do not need to visit the New York Times website nor Twitter website. There is no additional
information to be found on these sites.
Data File Entry Descriptions
Date: The date in mm-dd-yyyy (month-day-year) format of a given Wordle puzzle.
Contest number: An index of the Wordle puzzles, beginning with 202 on January 7, 2022.
Word: The solution word players are trying to guess on the associated date and contest
number.
Number of reported results: The total number scores that were recorded on Twitter that
day.
Number in hard mode: The number of scores on Hard mode recorded on Twitter that day.
1 try: The percentage of players solving the puzzle in one guess.
2 tries: The percentage of players solving the puzzle in two guesses.
3 tries: The percentage of players solving the puzzle in three guesses.
4 tries: The percentage of players solving the puzzle in four guesses.
5 tries: The percentage of players solving the puzzle in five guesses.
6 tries: The percentage of players solving the puzzle in six guesses.
7 or more tries (X): The percentage of players that could not solve the puzzle in six or fewer
tries. Note: the percentages may not always sum to 100% due to rounding.
| ©2023 by COMAP, Inc. | www.comap.com | www.mathmodels.org | info@comap.com |2. Directions of Wordle posted to the New York Times website.[2]
Glossary
New York Times: A daily newspaper based in New York City, New York, USA published in
print and online.
Twitter: A social networking site that allows users to broadcast short posts of no more than 280
characters (increased from initial 140 characters).
Solve (the Wordle puzzle): Enter the correct letters in the correct order to form the Wordle word
of the day.
References
Note: We provide the following citations to support the Problem Statement. We have pulled the
important ideas from these resources. There is no additional information on these websites
needed to solve this MCM problem. Access to the New York Times or Twitter website is not
required to solve this problem.
[1] Wordle logo from The New York Times website. Accessed on December 13, 2022 at
.
[2] “Wordle-The New York Times.” The New York Times, 2022. Accessed December 13, 2022
at https://www.nytimes.com/games/wordle/index.html.
[3] “Wordle-The New York Times.” The New York Times, July 21, 2022.
[4] “Wordle Stats.” Twitter, July 20, 2022.

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2023 ICM
Problem D: Prioritizing the UN Sustainability Goals
Unknown author. Public domain via Wikimedia Commons
Background
The United Nations (UN) has set 17 Sustainable Development Goals (SDGs). Achieving these
goals would ultimately lead to an improved life for many people around the world. These goals
are not independent of each other. So, often positive gains in some goals have an impact
(positive or negative and sometimes both) on other goals. This interconnectedness makes the
achievement of all goals a fluid process where funding limitations and other national and
international priorities may take precedence. Additionally, the impact of technological advances,
global pandemics, climate change, regional wars, and refugee movements have had serious
implications on many of the goals.
Requirement
To explore the relationships between the goals:
• Create a network of the relationships between the 17 SDGs.
• Use the individual SDGs, as well as the structure of your network, to set priorities that
can most efficiently move the work of the UN forward. How did you evaluate the
effectiveness of each priority? What could be reasonable to achieve in the next 10 years if
your priorities are initiated?
• If one of the SDGs is achieved (for example, there is no poverty or no hunger), what
would be the structure of the resulting network? How would this achievement impact
your team’s priorities? Are there other goals that should be included or proposed to the
UN for inclusion?
• Discuss the impact of technological advances, global pandemics, climate change,
regional wars, and refugee movements, or other international crises on your team’s
network and your team’s choice of priorities. What are the significant effects on the
progress of the UN from a network perspective?
• Discuss how your network approach may help other companies and organizations set
priorities of their goals. UN Sustainable Development Goals[1]
GOAL 1: No Poverty
GOAL 2: Zero Hunger
GOAL 3: Good Health and Well-being
GOAL 4: Quality Education
GOAL 5: Gender Equality
GOAL 6: Clean Water and Sanitation
GOAL 7: Affordable and Clean Energy
GOAL 8: Decent Work and Economic Growth
GOAL 9: Industry, Innovation and Infrastructure
GOAL 10: Reduced Inequality
GOAL 11: Sustainable Cities and Communities
GOAL 12: Responsible Consumption and Production
GOAL 13: Climate Action
GOAL 14: Life Below Water
GOAL 15: Life on Land
GOAL 16: Peace and Justice Strong Institutions
GOAL 17: Partnerships to achieve the Goal
Your PDF solution of no more than 25 total pages should include:
• One-page Summary Sheet.
• Table of Contents.
• Your complete solution.
• Reference List.
Note: The ICM has a 25-page limit. All aspects of your submission count toward the 25-page
limit (Summary Sheet, Table of Contents, Reference List, and any Appendices). You must cite
the sources for your ideas, images, and any other materials used in your report.
Glossary
United Nations (UN) - The United Nations (UN) is an intergovernmental organization whose
stated purposes are to maintain international peace and security, develop friendly relations
among nations, achieve international cooperation, and be a centre for harmonizing the actions of
nations.
Sustainable Development Goals (SDGs) - The Sustainable Development Goals (SDGs) or
Global Goals are a collection of 17 interlinked objectives designed to serve as a “shared
blueprint for peace and prosperity for people and the planet now and into the future”.
References
[1] Transforming Our World: The 2030 Agenda for Sustainable Development. UN General
Assembly, A/RES/70/1, 2015.

2023 ICM
Problem E: Light Pollution
Photo Credit: K. Blyman
Background
Light pollution is used to describe any excessive or poor use of artificial light. Some of the
phenomena that we refer to as light pollution include light trespass, over-illumination, and
light clutter. These phenomena are most easily observed as a glow in the sky after the sun has
set in large cities; however, they may also occur in more remote regions.
Light pollution alters our view of the night sky, has environmental impacts and affects our health
and safety. For example, plant maturation may be delayed or accelerated, and migration patterns
of wildlife affected. Excessive artificial light may confuse our circadian rhythms, leading to
poor sleep quality and perhaps physical and mental health issues. Glare caused by artificial
lights may contribute to some motor vehicle accidents.
Community officials or local groups may implement intervention strategies to mitigate the
negative effects of light pollution. Artificial light, however, has both positive and negative
effects that impact different locations in different ways. For example, to avoid the negative
impacts of light pollution listed above, some communities opt for low-light neighborhoods which
in turn might lead to increased crime. The impacts of light pollution may depend on factors such
as the location’s level of development, population, biodiversity, geography, and climate.
Therefore, assessing the extent of the effects and the potential impacts of any intervention
strategies must be tailored to a specific location.
Requirement
COMAP’s Illumination Control Mission (ICM) is working to promote awareness of the impacts
of light pollution and develop intervention strategies to mitigate those impacts. In support of this
ICM work, your task is to address measuring and mitigating the effects of light pollution in
various locations, incorporating both human and non-human concerns. Specifically, you should:
 Develop a broadly applicable metric to identify the light pollution risk level of a location.
 Apply your metric and interpret its results on the following four diverse types of
locations:
o a protected land location,
o a rural community,
o a suburban community, and
o an urban community.
| ©2023 by COMAP, Inc. | www.comap.com | www.mathmodels.org | info@comap.com | Describe three possible intervention strategies to address light pollution. Discuss specific
actions to implement each strategy and the potential impacts of these actions on the
effects of light pollution in general.
 Choose two of your locations and use your metric to determine which of your
intervention strategies is most effective for each of them. Discuss how the chosen
intervention strategy impacts the risk level for the location.
 Finally, for one of your identified locations and its most-effective intervention strategy,
produce a 1-page flyer to promote the strategy for that location.
Your PDF solution of no more than 25 total pages should include:
 One-page Summary Sheet.
 Table of Contents.
 Your complete solution.
 One-page promotion flyer.
 Reference List.
Note: The ICM Contest has a 25-page limit. All aspects of your submission count toward the
25-page limit (Summary Sheet, Table of Contents, Report, One-page promotion flyer, Reference
List, and any Appendices). You must cite the sources for your ideas, images, and any other
materials used in your report.
Glossary
Artificial Light: Any non-naturally occurring source of light.
Circadian Rhythms: The natural 24-hour sleep-wake cycle on which humans and other
organisms operate.
Glare: Excessive brightness that decreases one’s ability to see.
Intervention Strategies: Policies and/or actions that could be taken to disrupt the negative
impacts of light pollution.
Light Clutter: Excessive grouping of lights.
Light Trespass: When light enters unintended areas.
Over-Illumination: Lighting at an intensity higher than what is needed for an activity or
location.
Protected Land: Areas that governments or private entities protect from development due to
their ecological, cultural, and/or natural importance.
Rural Community: A community located in one of the least densely populated parts of a
country or region, and not easily accessible from an urban community.
Suburban Community: A community located in a moderately densely populated part of a
country or region, or easily accessible from an urban community.
Urban Community: A community located in one of the most densely populated parts of a
country or region.

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2023 ICM
Problem F: Green GDP
Photo by Towfiqu Barbhuiya on Unsplash
Background
Gross Domestic Product (GDP) is arguably one of the most well-known and commonly used
measures of the health of a nation's economy. It is often used in determining the purchasing
power and access to loans for a country, providing motivation for nations to propose policies and
projects that boost their GDPs. GDP “measures the monetary value of final goods and services
produced in a country in a given time period; it counts all of the output generated within the
borders of a country.”[1] This approach to calculating such an important and often quoted
measure favors production today without any consideration about conserving resources for
tomorrow. For example, a nation with rich forests could boost its current GDP by clear-cutting
the trees and producing large amounts of wooden furniture. This nation could do so without
penalty despite the loss of biodiversity and other negative environmental consequences.
Similarly, a nation can boost its GDP by harvesting more fish now, without penalty for
potentially irreversible harm to the fish stocks.
Because GDP fails to give credit for natural resources, perhaps it is not a good measure of the
true economic health of a nation. If nations change the ways they evaluate and compare their
economies, national governments may change their behaviors, promoting policies and projects
that are better for the environmental health of the planet. Could a “Green” GDP (GGDP), where
“Green” refers to the inclusion of environmental and sustainability perspectives and factors, be a
better measure than the current conventional GDP?
Multilateral changes are extremely challenging. Convincing nations to agree to this new GGDP
over the conventional GDP as the primary measure of economic health would likely be very
difficult. However, if making the shift initiates a global movement of national climate efforts that
makes significant progress towards climate crisis mitigation, then perhaps it is worth the fight.
Requirement
Your task is to consider the world recognizing GGDP as the primary measure of the health of a
nation's economy. What changes should we expect? What would the environmental impact of
those changes be? Specifically, your team should:
 There are many proposed ways to calculate GGDP that have already been developed. Select
one that your team believes could have a measurable impact on climate mitigation if it
replaced GDP as the primary measure of economic health.  Make a simple model that is easily defendable to estimate the expected global impact on
climate mitigation if your selected GGDP is adopted as the primary measure of the
economic health of a nation. It is up to you to decide how to measure global impact.
 Replacing GDP with GGDP could be met with resistance. Determine if your model indicates
that the switch is worthwhile at a global scale, comparing both the potential upside of
climate mitigation impact and the potential downside of the effort required to replace the
status quo. Explain your reasoning and support your answer with your previous global
impact analysis.
 Select a country and provide a more in-depth analysis of how this shift might impact them.
For example, what specific changes would you expect in how they use or save their natural
resources between now (under the current GDP) and after the GGDP is adopted? Would
those changes be beneficial to this specific country, considering both their current economic
status and their ability to support future generations? Be sure that your analysis is explicitly
tied to the changes between how GDP and GGDP are calculated.
 Based on your country-specific analysis, write a one-page non-technical report to the leaders
of that country on whether to support a switch to GGDP or to reject a switch and maintain
GDP as the primary measure of national economic health.
Your PDF solution of no more than 25 total pages should include:
 One-page Summary Sheet that clearly describes your approach to the problem and your
most important conclusions from your analysis in the context of the problem.
 Table of Contents.
 One-page non-technical report.
 Your complete solution.
 Reference List.
Note: The ICM Contest has a 25-page limit. All aspects of your submission count toward the 25-
page limit (Summary Sheet, Table of Contents, Non-technical Report, Solution, Reference List,
and any Appendices). You must cite the sources for your ideas, images, and any other materials
used in your report.
Glossary
Multilateral: Having contributors, supporters, or participants from several groups, especially
several different nations.
References
[1] Callan, T. (2023). Gross Domestic Product: An Economy’s All. International Monetary Fund,
Economics Concepts Explained.