2020 MCM Weekend 2
Problem B: The Longest Lasting Sandcastle(s)
Wherever there are recreational sandy ocean beaches in the world, there seem to be children (and adults) creating sandcastles on the seashore. Using tools, toys, and imagination, beach goers create sandcastles that range from simple mounds of sand to complicated replicas of actual castles with walls, towers, moats, and other features that mimic real castles. In all these, one typically forms an initial foundation consisting of a single, nondescript mound of wetted sand, and then proceeds to cut and shape this base into a recognizable 3-dimensional geometric shape upon which to build the more castle-defining features.
Inevitably, the inflow of ocean waves coupled with rising tides erodes sandcastles. It appears, however, that not all sandcastles react the same way to waves and tides, even if built roughly the same size and at roughly the same distance from the water on the same beach. Consequently, one wonders if there exists a best 3-dimensional geometric shape to use for a sandcastle foundation.
Requirements
1. Construct a mathematical model to identify the best 3-dimensional geometric shape to use as a sandcastle foundation that will last the longest period of time on a seashore that experiences waves and tides under the following conditions:
built at roughly the same distance from the water on the same beach, and
built using the same type of sand, roughly the same amount of sand, and the same water-to-sand proportion.
2. Using your model, determine an optimal sand-to-water mixture proportion for the castle foundation, assuming you use no other additives or materials (e.g. plastic or wooden supports, stones, etc.).
3. Adjust your model as needed to determine how the best 3-dimensional sandcastle foundation you identified in requirement 1 is affected by rain, and whether it remains the best 3-dimensional geometric shape to be used as a castle foundation when it is raining.
4. What other strategies, if any, might you use to make your sandcastle last longer?
5. Finally, write an informative, one- to two-page article describing your model and its results for publication in the vacation magazine: Fun in the Sun, whose readers are mainly non-technical.
Your submission should consist of:
One-page Summary Sheet
Table of Contents
One- to Two-page Article
Your solution of no more than 20 pages, for a maximum of 24 pages with your summary, table of contents, and article.
Note: Reference List and any appendices do not count toward the page limit and should appear after your completed solution. You should not make use of unauthorized images and materials whose use is restricted by copyright laws. Ensure you cite the sources for your ideas and the materials used in your report.
2020 MCM Weekend 2
Problem C: A Wealth of Data
In the online marketplace it created, Amazon provides customers with an opportunity to rate and review purchases. Individual ratings - called “star ratings” – allow purchasers to express their level of satisfaction with a product using a scale of 1 (low rated, low satisfaction) to 5 (highly rated, high satisfaction). Additionally, customers can submit text-based messages – called “reviews” – that express further opinions and information about the product. Other customers can submit ratings on these reviews as being helpful or not – called a “helpfulness rating” – towards assisting their own product purchasing decision. Companies use these data to gain insights into the markets in which they participate, the timing of that participation, and the potential success of product design feature choices.
Sunshine Company is planning to introduce and sell three new products in the online marketplace: a microwave oven, a baby pacifier, and a hair dryer. They have hired your team as consultants to identify key patterns, relationships, measures, and parameters in past customer-supplied ratings and reviews associated with other competing products to 1) inform their online sales strategy and 2) identify potentially important design features that would enhance product desirability. Sunshine Company has used data to inform sales strategies in the past, but they have not previously used this particular combination and type of data. Of particular interest to Sunshine Company are time-based patterns in these data, and whether they interact in ways that will help the company craft successful products.
To assist you, Sunshine’s data center has provided you with three data files for this project: hair_dryer.tsv, microwave.tsv, and pacifier.tsv. These data represent customer-supplied ratings and reviews for microwave ovens, baby pacifiers, and hair dryers sold in the Amazon marketplace over the time period(s) indicated in the data. A glossary of data label definitions is provided as well. THE DATA FILES PROVIDED CONTAIN THE ONLY DATA YOU SHOULD USE FOR THIS PROBLEM.
Requirements
1. Analyze the three product data sets provided to identify, describe, and support with mathematical evidence, meaningful quantitative and/or qualitative patterns, relationships, measures, and parameters within and between star ratings, reviews, and helpfulness ratings that will help Sunshine Company succeed in their three new online marketplace product offerings.
2. Use your analysis to address the following specific questions and requests from the Sunshine Company Marketing Director:
a. Identify data measures based on ratings and reviews that are most informative for Sunshine Company to track, once their three products are placed on sale in the online marketplace.
b. Identify and discuss time-based measures and patterns within each data set that might suggest that a product’s reputation is increasing or decreasing in the online marketplace.
c. Determine combinations of text-based measure(s) and ratings-based measures that best indicate a potentially successful or failing product.
d. Do specific star ratings incite more reviews? For example, are customers more likely to write some type of review after seeing a series of low star ratings? e. Are specific quality descriptors of text-based reviews such as ‘enthusiastic’, ‘disappointed’, and others, strongly associated with rating levels?
3. Write a one- to two-page letter to the Marketing Director of Sunshine Company summarizing your team’s analysis and results. Include specific justification(s) for the result that your team most confidently recommends to the Marketing Director.
Your submission should consist of:
One-page Summary Sheet
Table of Contents
One- to Two-page Letter
Your solution of no more than 20 pages, for a maximum of 24 pages with your summary sheet, table of contents, and two-page letter.
Note: Reference List and any appendices do not count toward the page limit and should appear after your completed solution. You should not make use of unauthorized images and materials whose use is restricted by copyright laws. Ensure you cite the sources for your ideas and the materials used in your report.
Glossary
Helpfulness Rating: an indication of how valuable a particular product review is when making a decision whether or not to purchase that product.
Pacifier: a rubber or plastic soothing device, often nipple shaped, given to a baby to suck or bite on.
Review: a written evaluation of a product.
Star Rating: a score given in a system that allows people to rate a product with a number of stars.
Attachments: The Problem Datasets
Problem_C_Data.zip
The three data sets provided contain product user ratings and reviews extracted from the Amazon Customer Reviews Dataset thru Amazon Simple Storage Service (Amazon S3).
hair_dryer.tsv
microwave.tsv
pacifier.tsv
Data Set Definitions: Each row represents data partitioned into the following columns.
● marketplace (string): 2 letter country code of the marketplace where the review was written.
● customer_id (string): Random identifier that can be used to aggregate reviews written by a single author.
● review_id (string): The unique ID of the review.
● product_id (string): The unique Product ID the review pertains to.
● product_parent (string): Random identifier that can be used to aggregate reviews for the same product.
● product_title (string): Title of the product.
● product_category (string): The major consumer category for the product.
● star_rating (int): The 1-5 star rating of the review.
● helpful_votes (int): Number of helpful votes.
● total_votes (int): Number of total votes the review received.
● vine (string): Customers are invited to become Amazon Vine Voices based on the trust that they have earned in the Amazon community for writing accurate and insightful reviews. Amazon provides Amazon Vine members with free copies of products that have been submitted to the program by vendors. Amazon doesn't influence the opinions of Amazon Vine members, nor do they modify or edit reviews.
● verified_purchase (string): A “Y” indicates Amazon verified that the person writing the review purchased the product at Amazon and didn't receive the product at a deep discount.
● review_headline (string): The title of the review.
● review_body (string): The review text.
● review_date (bigint): The date the review was written.
2020 ICM Weekend 2
Problem F: The Place I Called Home…
Researchers have identified several island nations, such as The Maldives, Tuvalu, Kiribati, and The Marshall Islands, as being at risk of completely disappearing due to rising sea levels. What happens, or what should happen, to an island’s population when its nation’s land disappears? Not only do these environmentally displaced persons (EDPs) need to relocate, but there is also risk of losing a unique culture, language, and way of life. In this problem, we ask you to look more closely at this issue, in terms of both the need to relocate people and the protection of culture. There are many considerations and questions to address, to include: Where will these EDPs go? What countries will take them? Given various nations’ disproportionate contributions to the green-house gasses both historically and currently that have accelerated climate change linked to the rising seas, should the worst offenders have a higher obligation to address these issues? And, who gets a say in deciding where these nationless EDPs make a new home – the individuals, an intergovernmental organization like the United Nations (UN), or the individual governments of the states absorbing these persons? A more detailed explanation of these issues is given in the Issue Paper beginning on page 3.
As a result of a recent UN ruling that opened the door to the theoretical recognition of EDPs as refugees, the International Climate Migration Foundation (ICM-F) has hired you to advise the UN by developing a model and using it to analyze this multifaceted issue of when, why, and how the UN should step into a role of addressing the increasing challenge of EDPs. The ICM-F plans to brief the UN on guidance for how the UN should generate a systemized response for EDPs, especially in consideration of the desire to preserve cultural heritage. Your assignment is to develop a model (or set of models) and use your model(s) to provide the analysis to support this briefing. The ICM-F is especially interested in understanding the scope of the issue of EDPs. For example, how many people are currently at risk of becoming EDPs[1]; what is the value of the cultures of at-risk nations; how are those answers likely to change over time? Furthermore, how should the world respond with an international policy that specifically focuses on protecting the rights of persons whose nations have disappeared in the face of climate change while also aiming to preserve culture? Based on your analysis, what recommendations can you offer on this matter, and what are the implications of accepting or rejecting your recommendations?
This problem is extremely complex. We understand that your submission will not be able to fully consider all of the aspects described in the Issue Paper beginning on page 3. However, considering the aspects that you address, synthesize your work into a cohesive answer to the ICM-F as they advise the UN. At a minimum, your team’s paper should include:
An analysis of the scope of the issue in terms of both the number of people at risk and the risk of loss of culture;
Proposed policies to address EDPs in terms of both human rights (being able to resettle and participate fully in life in their new home) and cultural preservation;
A description of the development of a model used to measure the potential impact of proposed policies;
[1] There are multiple estimates for the current and predicted number of climate refugees in the existing literature, but they are vastly different. Therefore, you need to support your conclusions with analysis based on your own model(s), either building off of existing analysis or with a new and independent analysis.
An explanation of how your model was used to design and/or improve your proposed policies;
An explanation, backed by your analysis, of the importance of implementing your proposed policies.
The ICM-F consists of interdisciplinary judges including mathematicians, climate scientists, and experts in refugee migration to review your work. Therefore, your paper should be written for a scientifically literate yet diverse audience.
Your submission should consist of:
One-page Summary Sheet
Table of Contents
Your solution of no more than 20 pages, for a maximum of 22 pages with your summary and table of contents.
NOTE: Reference List and any appendices do not count toward the page limit and should appear after your completed solution. You should not make use of unauthorized images and materials whose use is restricted by copyright laws. Ensure you cite the sources for your ideas and the materials used in your report.
Glossary
Environmentally displaced persons (EDPs): people who must relocate as their homeland becomes uninhabitable due to climate change events
Cultural heritage: the ways of living of a group or society passed through generations to include customs, practices, art, and values.
ICM Problem F Issue Paper
As noted in the problem statement, several island nations are at risk of completely disappearing due to rising sea levels.[1] The issue is quite complex. It is not simply a matter of identifying how to move a certain number of people around the globe – it is also about recognizing that these people are human beings who have rights and who are the last living representatives of their unique culture. In this Issue Paper, we highlight three of the essential ideas that frame this problem: relocation decisions as they relate to human rights, nation-state responsibility, and individual choice; the tension between assimilation and accommodation as part of resettlement and cultural preservation; and time factors such as the rate of the nation disappearing, the timing of these losses aligning with a global rise in nationalism, and the difficulty in making sound predictions about the size of this issue.
Relocation Decisions: Human Rights, Nation-State Responsibility, and Individual Choice
Considering the relocation issue, you might think that such EDPs would have similar rights as other UN-recognized refugees, but the United Nations High Commission on Refugees (UNHCR) and the widely adopted 1967 protocol has historically only afforded rights to those who are displaced due to politically related security issues, such as ethnic or religious persecution. However, in a very recent ruling, the UN has acknowledged this issue and recognized that some EDPs might qualify as refugees.[2] Although a ruling has now been made, there is not yet a vision on how the international community should respond as these situations increase in magnitude and frequency.[3]
Rights awarded to these refugees include right to work, freedom of movement, and protection by host governments. Additionally, the UNHCR, in collaboration with other aid organizations, work to provide aid and assistance to refugees until they are resettled in another country, become naturalized by their host state, or repatriate to their country of origin. Now, with this new ruling, the former inhabitants of the disappeared nation may be eligible for some of those rights or aid, but there is no hope of repatriation as the land itself is gone.
Even if EDPs are eligible for rights somewhere else, it is not clear where this new home would be or who would be responsible for making that decision. There are individual and international considerations related to whether the selection of a new long-term residence is made by individuals or if the choices are made or swayed by immigration policies developed by nations in isolation or as part of a cooperative effort coordinated by the United Nations. Possible migration policies could consider the financial ability of the new nation to absorb these new individuals, but there is also discussion of setting up burden-sharing based on nations’ relative contributions (pollution) to the environmental conditions that is leading to the loss of these nations. In other words, the international community may press nations with high pollution records to contribute more to the resettlement of EDPs in some equitable manner.
Resettlement and Cultural Preservation: Assimilation versus Accommodation
In terms of the cultural preservation issues, the nations that are most at risk are arguably some of the most culturally distinct in the world with languages, music, art, dances, social norms, and ways of life that can be different from island to island even within the same island chain. As a result, the loss of one of these nations could represent a significant cultural loss. While the displaced inhabitants may be able to preserve some aspects of their culture, some are geographically specific. For example, traditional ocean fishing techniques used in The Marshall
Islands are unlikely to continue to be practiced by families who settle in the Alps. As another example, perhaps the language could be preserved, but this would require host nations to be more accommodating and less strict on the assimilation requirements of these special new residents who may be trying to preserve their culture in a new land. For example, France current requires refugees who resettle there to learn French, but if there were international pressure, perhaps France would waive this requirement for groups of EDPs who are trying to preserve a lost culture.
This leads to a tension between accommodation and assimilation as other nations volunteer to absorb the populations of the former nations. It is important to note that it is the lack of a UN protocol for dealing with EDPs that forces other nations to volunteer to settle and naturalize those affected. In fact, the loss of a nation falls into the no-man’s land between several UN charges – the care of refugees (UNHCR), the protection of world culture (United Nations Educational, Scientific, and Cultural Organization (UNESCO)), and emergency aid response (United Nations Office for the Coordination of Humanitarian Affairs (UNOCHA)). And while the residents of a handful of small island nations might be absorbed relatively easily by volunteer nations, the fact is that climate change has been ushering a literal wave of more frequent and more intense environmental disasters. Imagine a major tsunami taking out a nuclear power plant and causing enough other significant damage that a more heavily inhabited nation may become uninhabitable; or a place being hit by so many repeated severe storms that rebuilding was deemed unwise; or a place where climate change is making it impossible for a nation that was formerly flush with crops to provide for its people. At what point should the UN step in, and in what role?
Time Factors: Raging Waves, Rising Seas, and Rising Nationalism
If a nation is wiped out as a result of a rapid catastrophic event, such as a tsunami or hurricane, then there is no time to prepare, even if the country knew they were at risk of such an event. When a nation is sinking as a result of slowly rising sea levels, then there are issues about how a migration could be coordinated and planned, or even how the loss could be mitigated through land-preserving measures taken by the at-risk nation with or without international support. It is not clear how the timescale of the loss would impact, or should impact, the ultimate decisions that need to be made concerning the resettlement of a population, the protection of their human rights, and the preservation of their culture.
Additionally, as the urgency to address this issue is literally rising with the sea level, the world is also experiencing a rise of nationalism, so the global response today may be very different than it would have been at other periods in history where globalism may have been more in favor than nationalism. If policies, or a lack of policies, end up pushing EDPs towards a subset of welcoming nations, then those countries may get overwhelmed and become less welcoming in response. Therefore, the changing global political climate may also be an important factor to consider.
Lastly, all of these challenges make the size of this problem extremely difficult to predict. Credible studies have predicted anywhere from 140 million to one billion EDPs by 2050.[4,5]
Summary:
In summary, as a nation disappears, it is not clear if an international cooperative and coordinated effort should be adopted to address the loss of homes, the need to resettle, and the preservation of culture. This issue is complex, and no model or report would be able to adequately address every
aspect in detail, but excellent reports need to be aware of these different aspects and how they are interrelated. There is the aspect of human rights, which are now recognized in theory, but have never been applied in practice. There is the balance of individual choice versus policy-driven migration. Another aspect is defining equitable burden sharing which could be driven by the capacity for nations to absorb new residents and/or obligations due to contributions to climate change; specifically, whether the nations with the largest contributions to climate change have any ethical obligations to take on a higher burden in assisting climate refugees. Yet another aspect is a balance between assimilation and accommodation, as new residents preserve their culture and/or blend into their new home. Some nations may disappear slowly, such as sinking under rising sea levels or loss of the ability to produce food, while other nations may be wiped out in a catastrophic disaster; and the immediate needs and ability to plan for the long-term needs in these situations are different. Furthermore, the situation is evolving over time as climate change advances and as we see a global rise in nationalism. Lastly, all of this complexity has made it difficult to even measure the problem or predict how quickly it will escalate.
Cited References Note that these are provided as citations to support claims in the Issue Paper. We have already pulled the important ideas from these resources for you, so although your team may use these sources, access to these is not required. Instead your team is encouraged to look for other sources to support your claims.
[1] Letman, J. (2018, November 19). Rising seas give island nation a stark choice: relocate or elevate. National Geographic. Retrieved from https://www.nationalgeographic.com/environment/2018/11/rising-seas-force-marshall-islands-relocate-elevate-artificial-islands/.
[2] Young, M. (2019, December 9). Climate Refugees Refused UN Protection & Denied Rights Under International Law. Retrieved from http://www.ipsnews.net/2019/12/climate-refugees-refused-un-protection-denied-rights-international-law/.
[3] Su, Y. (2020, January 29). UN ruling on climate refugees could be gamechanger for climate action. Retrieved from https://www.climatechangenews.com/2020/01/29/un-ruling-climate-refugees-gamechanger-climate-action/.
[4] The World Bank Report. (2018, March 19). Climate Change Could Force Over 140-Million to Migration Within Countries by 2050. Retrieved from https://www.worldbank.org/en/news/press-release/2018/03/19/climate-change-could-force-over-140-million-to-migrate-within-countries-by-2050-world-bank-report.
[5] Kamal, B. (2017, August 21). Climate Migrants Might Reach One Billion by 2050. Retrieved from http://www.ipsnews.net/2017/08/climate-migrants-might-reach-one-billion-by-2050/.
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