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【真题在线看】2019 ICM问题D：离开卢浮宫的时间到了

问题标题：离开卢浮宫的时间到了

年份：2019
学生等级：本科生
来源：ICM

问题

法国[1]恐怖袭击事件不断增加，因此需要对许多热门目的地的紧急疏散计划进行审查。您的 ICM 团队正在帮助设计法国巴黎卢浮宫的疏散计划。一般来说，疏散的目标是让所有人员尽快安全地离开大楼。收到需要疏散的通知后，人员会从最佳出口撤离，以便尽快清空大楼。

卢浮宫是世界上规模最大、参观人数最多的艺术博物馆之一，2017 年接待了超过 810 万名游客[2]。博物馆的游客数量在一天和一年中都有所不同，这给规划博物馆内的常规流动带来了挑战。游客的多样性——讲各种语言、结伴旅行的团体和残疾游客——使紧急情况下的疏散更加困难。

卢浮宫共有五层，其中两层在地下。

图 1：卢浮宫平面图[3]

这五层楼共设有 38 万件展品，占地面积约为 72,735 平方米，建筑翼长达 480 米或 5 个城市街区[3]。金字塔入口是博物馆的主要和最常用的公共入口。然而，还有另外三个入口通常为拥有博物馆会员资格的团体和个人保留：黎塞留通道入口、卢浮宫旋转木马入口和狮子门入口。卢浮宫有一个在线应用程序“Affluences”（https://www.affluences.com/louvre.php），可以实时更新每个入口的预计等候时间，以方便游客进入博物馆。你的团队可以考虑如何使用技术（包括 Affluences 等应用程序）或其他应用程序来促进你的疏散计划。

只有应急人员和博物馆官员知道实际可用的出口点总数（服务门、员工入口、贵宾入口、紧急出口和君主制建造的旧秘密入口等）。虽然公众对这些出口点的了解可以为疏散计划提供额外的力量，但它们的使用会同时引起安全问题，因为与四个主要入口的安全级别相比，这些出口的安全态势较低或有限。因此，在创建模型时，您的团队应该仔细考虑何时以及如何使用任何额外的出口。

您的主管希望您的 ICM 团队开发一个紧急疏散模型，让博物馆领导探索各种疏散博物馆游客的方案，同时也让应急人员尽快进入大楼。重要的是要确定可能限制向出口移动的潜在瓶颈。博物馆应急规划人员特别感兴趣的是一个可适应的模型，它可以设计用于解决广泛的考虑因素和各种类型的潜在威胁。每种威胁都有可能改变或删除可能的安全路线的片段，这些片段在单一优化路线中可能是必不可少的。一旦开发完成，验证您的模型并讨论卢浮宫如何实现它。

根据你的工作成果，提出卢浮宫应急管理的政策和程序建议。包括你的团队认为对游客安全必要的任何适用的人群管理和控制程序。此外，讨论如何调整和实施你的模型以适应其他大型、拥挤的建筑。

您的提交内容应包括：

单页摘要表，
您的解决方案不得超过 20 页，加上摘要最多可达 21 页。
评委希望获得完整的参考文献列表以及文内引用，但在评审过程中可能不会考虑附录。
注意：参考文献列表和任何附录均不计入 21 页的限制，并且应在完成的解决方案后出现。

题目内容过长，可到文末下载完整版中英文真题

以下是英文版真题

Problem

The increasing number of terror attacks in France^[1] requires a review of the emergency evacuation plans at many popular destinations. Your ICM team is helping to design evacuation plans at the Louvre in Paris, France. In general, the goal of evacuation is to have all occupants leave the building as quickly and safely as possible. Upon notification of a required evacuation, individuals egress to and through an optimal exit in order to empty the building as quickly as possible.

The Louvre is one of the world’s largest and most visited art museum, receiving more than 8.1 million visitors in 2017^[2]. The number of guests in the museum varies throughout the day and year, which provides challenges in planning for regular movement within the museum. The diversity of visitors -- speaking a variety of languages, groups traveling together, and disabled visitors -- makes evacuation in an emergency even more challenging.

The Louvre has five floors, two of which are underground.

Figure 1: Floor plan of Louvre^[3]

The 380,000 exhibits located on these five floors cover approximately 72,735 square meters, with building wings as long as 480 meters or 5 city blocks^[3]. The pyramid entrance is the main and most used public entrance to the museum. However, there are also three other entrances usually reserved for groups and individuals with museum memberships: the Passage Richelieu entrance, the Carrousel du Louvre entrance, and the Portes Des Lions entrance. The Louvre has an online application, “Affluences” (https://www.affluences.com/louvre.php), that provides real-time updates on the estimated waiting time at each of these entrances to help facilitate entry to the museum. Your team might consider how technology, to include apps such as Affluences, or others could be used to facilitate your evacuation plan.

Only emergency personnel and museum officials know the actual number of total available exit points (service doors, employee entrances, VIP entrances, emergency exits, and old secret entrances built by the monarchy, etc.). While public awareness of these exit points could provide additional strength to an evacuation plan, their use would simultaneously cause security concerns due to the lower or limited security postures at these exits compared with level of security at the four main entrances. Thus, when creating your model, your team should consider carefully when and how any additional exits might be utilized.

Your supervisor wants your ICM team to develop an emergency evacuation model that allows the museum leaders to explore a range of options to evacuate visitors from the museum, while also allowing emergency personnel to enter the building as quickly as possible. It is important to identify potential bottlenecks that may limit movement towards the exits. The museum emergency planners are especially interested in an adaptable model that can be designed to address a broad set of considerations and various types of potential threats. Each threat has the potential to alter or remove segments of possible routes to safety that may be essential in a single optimized route. Once developed, validate your model(s) and discuss how the Louvre would implement it.

Based on the results of your work, propose policy and procedural recommendations for emergency management of the Louvre. Include any applicable crowd management and control procedures that your team believes are necessary for the safety of the visitors. Additionally, discuss how you could adapt and implement your model(s) for other large, crowded structures.

Your submission should consist of:

One-page Summary Sheet,
Your solution of no more than 20 pages, for a maximum of 21 pages with your summary.
Judges expect a complete list of references with in-text citations, but may not consider appendices in the judging process.
Note: Reference list and any appendices do not count toward the 21-page limit and should appear after your completed solution.

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【真题在线看】2019 MCM问题C：阿片类药物危机

问题标题：阿片类药物危机

年份：2019
学生等级：本科生
来源：MCM

2019 MCM
问题C：阿片类药物危机

背景：

美国正在经历一场关于使用合成和非合成阿片类药物的全国性危机，这些药物用于治疗和管理疼痛(合法、处方使用)或用于娱乐目的(非法、非处方使用)。美国疾病控制中心(CDC)等联邦机构正在努力“挽救生命，防止这种流行病的负面影响，如阿片类药物滥用障碍、肝炎和艾滋病病毒感染，以及新生儿禁欲综合症”。对美国联邦调查局(FBI)和美国卫生部来说，仅仅执行现有的法律是一个复杂的挑战。

禁毒执法局(DEA)等，这对美国经济的重要部门也有影响。例如，如果阿片类药物危机蔓延到美国人口的所有部分(包括受过大学教育和拥有高级学位的人)，需要精确劳动技能、高科技组件组装以及与客户和客户之间敏感的信任或安全关系的企业可能难以填补这些职位。此外，如果老年人中阿片成瘾者的比例增加，保健费用和辅助生活设施的人员配置也将受到影响。

DEA/国家法医实验室信息系统(NFLIS)作为药物管制局(DEA)转用控制办公室的一部分，发布了一份数据量大的年度报告，内容涉及“药物识别结果和联邦、州和地方法医实验室分析的药物案件的相关信息”。NFLIS内的数据库包括来自犯罪实验室的数据，这些实验室处理了美国估计每年120万起国家和地方药物案件中的88%以上。对于这个问题，我们关注位于五个(5)个美国县的个人。州:俄亥俄州、肯塔基州、西弗吉尼亚州、弗吉尼亚和田纳西州。在美国，县是每个拥有税收权的州之下的下一级政府。

为了解决这个问题，我们提供了几个数据集供您使用。第一个文件(MCMNFLIS Data.xlsx)包含2010-2017年这五个州每个县的麻醉镇痛药(合成阿片类药物)和海洛因的药物识别计数，这些数据是由各州犯罪实验室向DEA报告的。当执法机构将证据提交给犯罪实验室作为刑事调查的一部分，而实验室的法医学家对证据进行测试时，就发生了药物识别。通常情况下，当执法机构提交这些样本时，他们会在事件报告中提供位置数据(县)。当证据提交给犯罪实验室，且未提供位置数据时，犯罪实验室会使用提交案件的执法机构所在的市/县/州的地址。为了解决这个问题，你可以假设县的位置数据是正确的。

另外七(7)个文件是压缩文件夹，包含来自美国人口普查局的摘录，代表这五个州的各县在2010-2016年期间收集的一组常见的社会经济因素(ACSxx5YR_DP02.zip)。(注意:2017年的数据不可用。)

每个数据集都包含一个代码表，其中定义了每个已标记的变量。虽然您可以使用其他资源进行研究和背景信息，但提供的每个数据集都包含您应该用于此问题的唯一数据。

题目内容过长，可到文末下载完整版中英文真题

以下是英文版真题

完整版MCM/ICM美赛获奖论文下载⇓

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【真题在线看】2019 MCM问题B：派遣无人机—发展空中救灾系统

问题标题：派遣无人机：开发空中救灾响应系统

年份：2019
学生等级：本科生
来源：MCM

2019 MCM问题B

派遣无人机：发展空中救灾系统

背景:

2017年，有史以来袭击美国领土波多黎各的最严重风(见附件1)给该岛造成了严重破坏，造成2900多人死亡。飓风的涌浪和波浪的破坏力相结合，对建筑物、住宅和道路造成了广泛的破坏，特别是在波多黎各的东海岸和东南海岸。这场风暴伴随着猛烈的风暴和暴雨，摧毁了波多黎各80%的电线杆和所有输电线路，导致岛上340万居民基本失去电力。此外，风暴损坏或摧毁了岛上大部分蜂窝通信网络。电力和蜂窝服务中断在岛上大部分地区持续了数月，在某些地区则持续更长时间。广泛的洪水堵塞和破坏了岛上许多高速公路和道路，使紧急服务车辆几乎无法规划和导航路线。波多黎各的破坏程度在一段时间内仍不清楚;数十个地区被隔离，无法通信。对医疗用品、救生设备和治疗的需求使医疗诊所、医院急诊室和非政府组织的救援行动不堪重负。由于慢性病患者转向医院和临时庇护所寻求治疗，对医疗服务的需求在一段时间内继续激增。

问题:在自然灾害期间或之后，非政府组织(NGOS)经常面临提供充分和及时响应的挑战，例如2017年袭击美国波多黎各领士的飓风。特别是，一家名为HELP，Inc.的非政府组织正在尝试通过设计一个称为“DroneGo”的可运输的灾害响应系统来改善其响应能力。DroneGo将使用旋翼无人机来运送预包装的医疗用品并提供高分辨率的空中视频侦察。选定的无人机应该能够同时或分别执行这两项任务--医疗物资运送和视频侦察，具体取决于救援情况和时间表。HELP公司确定了各种候选的旋翼无人机，希望您的团队考虑将其用于设计其DroneGo机队(见附件2、3)。

DroneGo的预包装医疗用品，称为医疗包，旨在增加而不是取代受灾国家当地医疗援助组织在现场提供的用品。HELP公司计划提供三种不同的医疗包，分别称为MED1、MED2和MED3。无人机将在无人机的货舱内携带这些医疗包，以交付给选定地点(见附件4、5)。根据用于运输医疗用品的具体无人机，多个医疗包可能可以在一个无人机货舱中运输。请注意，无人机必须降落在地面上，以便将医疗用品从无人机货舱卸下。无人机的视频功能将为HELP，Inc.的指挥和控制中心提供受损和可维修的运输道路网络的高分辨率视频，以便进行地面路线规划。

HELP，Inc.将使用国际标准化组织(ISO)标准的干散货集装箱，将完整的DroneGo灾害响应系统快速运输到特定灾区。DroneGo机队中所有无人机的单个运输集装箱，以及所有必要的...

题目内容过长，可到文末下载完整版中英文真题

以下是英文版真题

完整版MCM/ICM美赛获奖论文下载⇓

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【真题在线看】2019 MCM问题A：生态博弈

问题标题：2019 MCM问题A

年份：2019
学生等级：本科生
来源：MCM

问题

在根据史诗奇幻小说《冰与火之歌》系列改编的虚构电视剧《权力的游戏》中[1]，龙之母丹妮莉丝·坦格利安养育了三条龙。刚孵化出来的龙很小，大约 10 公斤，一年后长到大约 30-40 公斤。它们会根据环境和食物量在一生中不断生长。

为了解决这个问题，假设这三条虚构的龙现在还活着。假设上面描述的龙的基本生物学是准确的。你需要对龙做出一些额外的假设，例如，龙能够飞行很远的距离、喷火和抵抗巨大的创伤。在解决问题要求时，应该清楚你的假设与动物的功能、大小、饮食、变化或其他特征的物理限制之间的关系。
你的团队被指派分析龙的特征、行为、习惯、饮食和与环境的互动。为此，你必须考虑许多问题。至少，要解决以下问题：龙的生态影响和要求是什么？龙的能量消耗是多少，它们的卡路里摄入量要求是多少？养活这三条龙需要多大的面积？需要多大的社区来养活一条龙，才能为龙提供不同程度的援助？在解决这些问题时，要清楚你正在考虑哪些因素。

与其他迁徙动物一样，龙可能会迁徙到气候截然不同的世界不同地区。气候条件对你的分析有多重要？例如，将龙在干旱地区、温带地区和北极地区之间迁移会对维持和培育龙所需的资源产生很大影响吗？

当你完成对龙的分析后，就起草一封两页的信给《冰与火之歌》的作者乔治·RR·马丁，指导如何维护故事的现实生态基础，特别是关于龙从干旱地区向温带地区和北极地区的迁徙。

虽然您的龙分析并不直接适用于真实的物理情况，但数学建模本身利用了建模情况时使用的许多现实特征。除了建模活动本身之外，描述和讨论虚构龙领域之外的情况，您的建模工作可能有助于提供信息和见解？

您的提交内容应包括：

● 一页摘要表，
● 两页信函，
● 您的解决方案不超过 20 页，包括摘要和信函，最多 23 页。
● 注意：参考列表和任何附录不计入 23 页的限制，应出现在您完成的解决方案之后。

注意：您不应使用未经授权的图像和材料，因为版权法限制其使用。请谨慎使用和引用您的想法和报告中所用材料的来源。

题目内容过长，可到文末下载完整版中英文真题

以下是英文版真题

Problem

In the fictional television series Game of Thrones, based on the series of epic fantasy novels A Song of Ice and Fire^[1], three dragons are raised by Daenerys Targaryen, the “Mother of Dragons.” When hatched, the dragons are small, roughly 10 kg, and after a year grow to roughly 30-40 kg. They continue to grow throughout their life depending on the conditions and amount of food available to them.

For the purposes of this problem, consider these three fictional dragons are living today. Assume that the basic biology of dragons described above is accurate. You will need to make some additional assumptions about dragons that might include, for example, that dragons are able to fly great distances, breath fire, and resist tremendous trauma. As you address the problem requirements, it should be clear how your assumptions are related to the physical constraints of the functions, size, diet, changes, or other characteristics associated with the animals.
Your team is assigned to analyze dragon characteristics, behavior, habits, diet, and interaction with their environment. To do so, you will have to consider many questions. At a minimum, address the following: What is the ecological impact and requirements of the dragons? What are the energy expenditures of the dragons, and what are their caloric intake requirements? How much area is required to support the three dragons? How large a community is necessary to support a dragon for varying levels of assistance that can be provided to the dragons? Be clear about what factors you are considering when addressing these questions.

As with other animals that migrate, dragons might travel to different regions of the world with very different climates. How important are the climate conditions to your analysis? For example, would moving a dragon between an arid region, a warm temperate region, and an arctic region make a big difference in the resources required to maintain and grow a dragon?

Once your dragon analysis is complete, draft a two-page letter to the author of A Song of Ice and Fire, George R.R. Martin, to provide guidance about how to maintain the realistic ecological underpinning of the story, especially with respect to the movement of dragons from arid regions to temperate regions and to arctic regions.

While your dragon analysis does not directly apply to a real physical situation, the mathematical modeling itself makes use of many realistic features used in modeling a situation. Aside from the modeling activities themselves, describe and discuss a situation outside of the realm of fictional dragons that your modeling efforts might help inform and provide insight?

Your submission should consist of:

● One-page Summary Sheet,
● Two-page letter,
● Your solution of no more than 20 pages, for a maximum of 23 pages with your summary and letter.
● Note: Reference list and any appendices do not count toward the 23-page limit and should appear after your completed solution.

NOTE: You should not make use of unauthorized images and materials whose use is restricted by copyright laws. Please be careful in how you use and cite the sources for your ideas and the materials used in your report.

Reference

完整版MCM/ICM美赛获奖论文下载⇓

备赛的同学可扫码试听辅导课程

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【真题在线看】2020 ICM 问题：我称之为家的地方……

问题标题：我称之为家的地方……

年份：2020
学生等级：本科生
来源：ICM

问题

研究人员发现，马尔代夫、图瓦卢、基里巴斯和马绍尔群岛等多个岛国因海平面上升而面临彻底消失的风险。当一个国家的土地消失时，岛上的人口会发生什么或应该发生什么？这些因环境而流离失所的人(EDP) 不仅需要搬迁，而且还面临失去独特文化、语言和生活方式的风险。

在这个问题中，我们要求您更仔细地研究这个问题，既要考虑人口搬迁的需要，又要考虑文化的保护。有许多考虑和问题需要解决，包括：这些 EDP 将去哪里？哪些国家会接收他们？鉴于各国在历史上和现在对温室气体的贡献不成比例，加速了与海平面上升有关的气候变化，最严重的违规者是否应该有更大的义务来解决这些问题？那么，谁有权决定这些无国籍的 EDP 在哪里安家落户——是个人、联合国 (UN) 等政府间组织，还是接收这些人员的各国政府？问题论文对这些问题进行了更详细的解释。

由于联合国最近的一项裁决为从理论上承认 EDP 为难民打开了大门，国际气候移民基金会（ICM- F）聘请您为联合国提供建议，开发一个模型并使用它来分析这个多方面的问题，即联合国何时、为何和如何介入解决 EDP 日益增加的挑战。ICM-F 计划向联合国简要介绍联合国应如何针对 EDP 制定系统性应对措施的指导，特别是考虑到保护文化遗产的愿望。

您的任务是开发一个模型（或一组模型），并使用您的模型提供分析以支持此简报。

ICM-F 特别有兴趣了解 EDP 问题的范围。例如，目前有多少人面临成为 EDP 的风险[1]；处于危险中的国家的文化价值是什么；这些答案可能会如何随着时间的推移而变化？此外，世界应该如何应对，制定国际政策，专门保护因气候变化而消失的国家人民的权利，同时又致力于保护文化？根据您的分析，您能就此事提出哪些建议？接受或拒绝您的建议意味着什么？

这个问题极其复杂。我们理解您的提交内容无法充分考虑第 3 页开始的问题文件中描述的所有方面。但是，考虑到您解决的方面，请将您的工作综合成对 ICM-F 的连贯回答，因为他们会向联合国提供建议。您的团队的论文至少应包括：

从面临风险的人数和文化丧失的风险两个方面对问题的范围进行分析；

针对 EDP 问题提出的政策建议，涉及人权（能够在新家园重新定居并充分参与生活）和文化保护两个方面；

用于衡量拟议政策的潜在影响的模型的开发描述；

解释如何使用您的模型来设计和/或改进您提出的政策；

通过您的分析来解释实施您所提议的政策的重要性。

ICM-F 由数学家、气候科学家和难民移民专家等跨学科评委组成，负责审查您的论文。因此，您的论文应面向科学素养高、受众多样化的读者。

您的提交内容应包括：

单页摘要表
目录
您的解决方案不超过 20 页，包括摘要和目录，最多 22 页。
注意：参考文献列表和任何附录不计入页数限制，应在完成解决方案后显示。您不应使用未经授权的图像和材料，这些图像和材料的使用受版权法限制。确保您引用了您的想法和报告中使用的材料的来源。

词汇表

环境流离失所者 (EDP)：由于气候变化事件导致家园变得无法居住而必须搬迁的人

文化遗产：一个群体或社会世代传承的生活方式，包括风俗、习俗、艺术和价值观。

[1]现有文献中对当前和预测的气候难民数量有多种估计，但差异很大。因此，您需要根据自己的模型进行分析来支持您的结论，这些分析可以基于现有分析，也可以基于新的独立分析。

题目内容过长，可到文末下载完整版中英文真题

以下是英文版真题

Problem

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 鈥� 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.

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;
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.

[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.

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【真题在线看】2020 ICM问题F：淹没在塑料中

问题标题：淹没在塑料中

年份：2020
学生等级：本科生
来源：ICM

问题

自 1950 年代以来，塑料的用途广泛，例如食品包装、消费品、医疗设备和建筑，其制造业呈指数级增长。虽然塑料有显著的好处，但增加塑料产量所带来的负面影响令人担忧。塑料制品不易分解，难以处理，而且只有大约 9% 的塑料被回收利用[1] 。每年大约有 400 万至 1200 万吨塑料垃圾进入海洋，这便是其影响[1,2]。塑料垃圾对环境造成了严重后果，预计如果目前的趋势继续下去，到 2050 年，海洋中的塑料将比鱼还多[2]。人们已经研究了塑料对海洋生物的影响[3]，但其对人类健康的影响尚未完全了解[4] 。一次性和一次性塑料制品的兴起导致整个行业都致力于制造塑料垃圾。这也表明，产品的使用时间明显短于适当缓解塑料垃圾所需的时间。因此，要解决塑料垃圾问题，我们需要减缓塑料生产的流动并改善塑料垃圾的管理方式。

您的团队已受雇于国际塑料废物管理委员会( ICM )，以应对这一日益严重的环境危机。您必须制定一项计划，以大幅减少（甚至消除）一次性塑料产品垃圾。

开发一个模型来估算一次性或一次性塑料产品废弃物的最大水平，这些废弃物可以安全地减少而不会造成进一步的环境损害。您可能需要考虑许多因素，包括这些废弃物的来源、当前废弃物问题的严重程度以及处理这些废弃物的资源的可用性。

讨论塑料垃圾可以减少到何种程度以达到对环境安全的水平。这可能涉及考虑影响塑料垃圾水平的因素，包括但不限于一次性塑料的来源和用途、塑料替代品的可用性、对公民生活的影响，或城市、地区、国家和大陆减少一次性塑料的政策及其有效性。这些因素可能因地区而异，因此考虑特定地区的限制可能会使某些政策比其他政策更有效。

利用您的模型和讨论，为一次性或一次性塑料产品的全球废弃物设定最低可实现水平的目标，并讨论实现这一水平的影响。您可以考虑人类生活发生的变化、环境影响或对价值数万亿美元的塑料行业的影响。

虽然这是一个全球性问题，但其原因和影响在各个国家或地区并不均等。讨论全球危机引发的公平问题以及您打算采取的解决方案。您建议 ICM 如何解决这些问题？

向 ICM 写一份两页的备忘录，描述全球一次性或一次性塑料产品废弃物的现实目标最低可实现水平、达到该水平的时间表，以及任何可能加速或阻碍实现目标和时间表的情况。

您的提交内容应包括：

单页摘要表
目录
两页备忘录
您的解决方案不超过 20 页，最多 24 页，包括摘要、目录和两页备忘录。
注意：参考文献列表和任何附录不计入页数限制，应在完成解决方案后显示。您不应使用未经授权的图像和材料，这些图像和材料的使用受版权法限制。确保您引用了您的想法和报告中使用的材料的来源。

词汇表

一次性塑料制品：不可回收而成为垃圾的塑料材料或制品。

减轻：使严重程度降低、缓和、缓解。

塑料废物：未经妥善回收或无法回收的塑料物品；由塑料制成的碎片。

一次性塑料制品：由塑料制成，一次性使用后丢弃的产品。

可到文末下载完整版中英文真题

以下是英文版真题

Problem

Since the 1950s, the manufacturing of plastics has grown exponentially because of its variety of uses, such as food packaging, consumer products, medical devices, and construction. While there are significant benefits, the negative implications associated with increased production of plastics are concerning. Plastic products do not readily break down, are difficult to dispose of, and only about 9% of plastics are recycled^[1].聽 Effects can be seen by the approximately 4-12 million tons of plastic waste that enter the oceans each year^[1,2]. Plastic waste has severe environmental consequences and it is predicted that if our current trends continue, the oceans will be filled with more plastic than fish by 2050^[2]. The effect on marine life has been studied^[3], but the effects on human health are not yet completely understood^[4]. The rise of single-use and disposable plastic products results in entire industries dedicated to creating plastic waste. It also suggests that the amount of time the product is useful is significantly shorter than the time it takes to properly mitigate the plastic waste. Consequently, to solve the plastic waste problem, we need to slow down the flow of plastic production and improve how we manage plastic waste.

Your team has been hired by the International Council of Plastic Waste Management (ICM) to address this escalating environmental crisis. You must develop a plan to significantly reduce, if not eliminate, single-use and disposable plastic product waste.

Develop a model to estimate the maximum levels of single-use or disposable plastic product waste that can safely be mitigated without further environmental damage. You may need to consider, among many factors, the source of this waste, the extent of the current waste problem, and the availability of resources to process the waste.

Discuss to what extent plastic waste can be reduced to reach an environmentally safe level. This may involve considering factors impacting the levels of plastic waste to include, but not limited to, sources and uses of single-use or disposable plastics, the availability of alternatives to plastics, the impact on the lives of citizens, or policies of cities, regions, countries, and continents to decrease single-use or disposable plastic and the effectiveness of such policies. These can vary between regions, so considering regional-specific constraints may make some policies more effective than others.

Using your model and discussion, set a target for the minimal achievable level of global waste of single-use or disposable plastic products and discuss the impacts for achieving such levels. You may consider ways in which human life is altered, the environmental impacts, or the effects on the multi-trillion-dollar plastic industry.

While this is a global problem, the causes and effects are not equally distributed across nations or regions. Discuss the equity issues that arise from the global crisis and your intended solutions. How do you suggest ICM address these issues?

Write a two-page memo to the ICM describing a realistic global target minimum achievable level of global single-use or disposable plastic product waste, a timeline to reach this level, and any circumstances that may accelerate or hinder the achievement of your target and timeline.

Your submission should consist of:

One-page Summary Sheet
Table of Contents
Two-page Memo
Your solution of no more than 20 pages, for a maximum of 24 pages with your summary, table of contents, and two-page memo.

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

Disposable Plastic Products: plastic materials or products that are not recyclable and become trash.

Mitigate: To make less severe, to moderate, to alleviate.

Plastic Waste: plastic objects that have not been recycled properly or cannot be recycled; debris made of plastic.

Single-Use Plastic Products: products made of plastic intended for one time use before being discarded.

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【真题在线看】2020ICM问题D：团队策略

问题标题：团队策略

年份：2020
学生等级：本科生
来源：ICM

问题

随着社会联系越来越紧密，社会面临的挑战也变得越来越复杂。我们依靠拥有不同专业知识和不同观点的跨学科团队来解决许多最具挑战性的问题。在过去 50 多年里，我们对团队成功的概念理解有了显著的进步，这使得更好的科学、创意或物理团队能够解决这些复杂的问题。研究人员已经报告了组建团队的最佳策略、队友之间的最佳互动以及理想的领导风格。所有部门和领域的强大团队都能够完成复杂的任务，而这些任务是无法通过个人努力或队友的一系列附加贡献来实现的。

探索团队过程最具启发性的场景之一是竞技团队运动。团队运动必须遵守严格的规则，这些规则可能包括但不限于球员人数、他们的角色、球员之间允许的接触、他们的位置和动作、获得的分数以及违规的后果。团队的成功不仅仅是单个球员能力的总和。相反，它取决于许多其他因素，包括队友之间的配合程度。这些因素可能包括团队是否拥有多样化的技能（一个人可能速度快，而另一个人则精准）、团队在个人表现和集体表现之间的平衡程度（明星球员可能有助于利用所有队友的技能）以及团队在一段时间内有效协调的能力（当一名球员从对手手中抢球时，另一名球员准备进攻）。

鉴于您的建模技能，您家乡的足球队（在欧洲和其他地方称为 football）哈士奇队的教练请您的公司I ntrepid C hampion M odeling (ICM) 帮助了解球队的动态。具体来说，教练请您探索场上球员之间的复杂互动如何影响他们的成功。目标不仅是研究直接导致得分的互动，而且要探索整场比赛和整个赛季的球队动态，以帮助确定可在下个赛季改善团队合作的具体策略。教练要求 ICM 量化和形式化球队成功（和失败）的结构和动态特征。哈士奇队提供了详细数据[1]，包括他们与 19 个对手进行的全部 38 场比赛（与每个对手球队交手两次）。总体而言，数据涵盖 366 名球员（30 名哈士奇队球员和 336 名对方球队球员）之间的 23,429 次传球，以及 59,271 场比赛。

为了响应 Huskie 教练的请求，您的 ICM 团队应该使用提供的数据来解决以下问题：
为球员之间的传球创建一个网络，其中每个球员都是一个节点，每次传球都构成球员之间的联系。使用传球网络来识别网络模式，例如二元和三元配置以及团队阵型。还要考虑比赛中的其他结构指标和网络属性。在观察互动时，您应该探索多个尺度，例如（但不限于）微观（成对）到宏观（所有球员），以及时间，例如短时间（每分钟）到长时间（整场比赛或整个赛季）。

确定反映成功团队合作的绩效指标（除了得分或胜利之外），例如比赛类型的多样性、球员之间的协调或贡献的分配。您还可以考虑其他团队级别的流程，例如适应性、灵活性、节奏或流程。澄清策略是否普遍有效或取决于对手的反击策略可能很重要。使用您确定的绩效指标和团队级别流程创建一个模型，以捕捉团队合作的结构、配置和动态方面。

利用从团队合作模式中获得的见解，告知教练哪些结构策略对哈士奇队有效。建议教练根据网络分析结果，在下个赛季应做出哪些改变来提高团队成功率。

通过对哈士奇队的分析，你能够在团队运动的受控环境中考虑群体动态。了解导致某些群体表现优于其他群体的复杂因素对于社会的发展和创新至关重要。随着我们的社会越来越多地解决涉及团队的问题，你能否概括你的研究结果，说明如何设计更有效的团队？为了开发团队绩效的通用模型，还需要捕捉团队合作的哪些其他方面？

您的提交内容应包括：

2020_Problem_D_DATA.zip
fullevents.csv
matches.csv
passingevents.csv
README.txt

该数据集是从一个更大的数据集处理而来的，涵盖了欧洲五大国家足球比赛以及 2018 年世界杯的近 2000 场比赛。

词汇表

二元配置：涉及成对玩家的关系。

三元配置：涉及三名玩家组成的群体的关系。
引用的参考文献

[1] Pappalardo, L.、Cintia, P.、Rossi, A.等人。足球比赛中时空比赛事件的公共数据集。科学数据6, 236 (2019)。

可选资源

对足球网络的研究已经产生了许多讨论相关主题的文章。下面列出了一些文章。您不需要在解决方案中使用任何这些示例文章，这也不是一份完整的列表。我们鼓励团队利用任何支持他们解决问题方法的期刊文章。

可到文末下载完整版中英文真题

以下是英文版真题

Problem

As societies become more interconnected, the set of challenges they face have become increasingly complex. We rely on interdisciplinary teams of people with diverse expertise and varied perspectives to address many of the most challenging problems. Our conceptual understanding of team success has advanced significantly over the past 50+ years allowing for better scientific, creative, or physical teams to address these complex issues. Researchers have reported on best strategies for assembling teams, optimal interactions among teammates, and ideal leadership styles. Strong teams across all sectors and domains are able to perform complex tasks unattainable through either individual efforts or a sequence of additive contributions of teammates.

One of the most informative settings to explore team processes is in competitive team sports. Team sports must conform to strict rules that may include, but are not limited to, the number of players, their roles, allowable contact between players, their location and movement, points earned, and consequences of violations. Team success is much more than the sum of the abilities of individual players. Rather, it is based on many other factors that involve how well the teammates play together. Such factors may include whether the team has a diversity of skills (one person may be fast, while another is precise), how well the team balances between individual versus collective performance (star players may help leverage the skills of all their teammates), and the team's ability to effectively coordinate over time (as one player steals the ball from an opponent, another player is poised for offense).

In light of your modeling skills, the coach of the Huskies, your home soccer (known in Europe and other places as football) team, has asked your company, Intrepid Champion Modeling (ICM), to help understand the team's dynamics. In particular, the coach has asked you to explore how the complex interactions among the players on the field impacts their success. The goal is not only to examine the interactions that lead directly to a score, but to explore team dynamics throughout the game and over the entire season, to help identify specific strategies that can improve teamwork next season. The coach has asked ICM to quantify and formalize the structural and dynamical features that have been successful (and unsuccessful) for the team. The Huskies have provided data[1] detailing information from last season, including all 38 games they played against their 19 opponents (they played each opposing team twice). Overall, the data covers 23,429 passes between 366 players (30 Huskies players, and 336 players from opposing teams), and 59,271 game events.

To respond to the Huskie coach's requests, your team from ICM should use the provided data to address the following:

Create a network for the ball passing between players, where each player is a node and each pass constitutes a link between players. Use your passing network to identify network patterns, such as dyadic and triadic configurations and team formations. Also consider other structural indicators and network properties across the games. You should explore multiple scales such as, but not limited to, micro (pairwise) to macro (all players) when looking at interactions, and time such as short (minute-to-minute) to long (entire game or entire season).

Identify performance indicators that reflect successful teamwork (in addition to points or wins) such as diversity in the types of plays, coordination among players or distribution of contributions. You also may consider other team level processes, such as adaptability, flexibility, tempo, or flow. It may be important to clarify whether strategies are universally effective or dependent on opponents' counter-strategies. Use the performance indicators and team level processes that you have identified to create a model that captures structural, configurational, and dynamical aspects of teamwork.

Use the insights gained from your teamwork model to inform the coach about what kinds of structural strategies have been effective for the Huskies. Advise the coach on what changes the network analysis indicates that they should make next season to improve team success.

Your analysis of the Huskies has allowed you to consider group dynamics in a controlled setting of a team sport. Understanding the complex set of factors that make some groups perform better than others is critical for how societies develop and innovate. As our societies increasingly solve problems involving teams, can you generalize your findings to say something about how to design more effective teams? What other aspects of teamwork would need to be captured to develop generalized models of team performance?

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.

Attachment

2020_Problem_D_DATA.zip
fullevents.csv
matches.csv
passingevents.csv
README.txt

This data set was processed from a much larger dataset covering nearly 2000 matches from five European national soccer competitions, as well as the 2018 World Cup.

Glossary

Dyadic Configurations: relationships involving pairs of players.

Triadic Configurations: relationships involving groups of three players.

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【真题在线看】2020 MCM问题C：丰富的数据

问题标题：丰富的数据

年份：2020
学生等级：本科生
来源：MCM

问题

在其创建的在线市场中，亚马逊为客户提供了对购买的商品进行评级和评论的机会。个人评级（称为“星级评定”）允许购买者使用 1（评级低，满意度低）到 5（评级高，满意度高）的等级来表达他们对产品的满意程度。此外，客户可以提交基于文本的消息（称为“评论”），以表达对产品的进一步意见和信息。其他客户可以对这些评论提交评级，看它们是否有用（称为“有用性评级”），以帮助他们做出自己的产品购买决定。公司使用这些数据来深入了解他们参与的市场、参与的时机以及产品设计功能选择的潜在成功率。

Sunshine 公司计划在网上市场推出和销售三种新产品：微波炉、婴儿奶嘴和吹风机。他们聘请了您的团队作为顾问，以识别过去客户提供的与其他竞争产品相关的评级和评论中的关键模式、关系、度量和参数，以 1) 为他们的在线销售策略提供信息，以及 2) 识别可能提高产品吸引力的重要设计特征。Sunshine 公司过去曾使用数据来指导销售策略，但他们之前从未使用过这种特定的组合和类型的数据。Sunshine 公司特别感兴趣这些数据中是否存在基于时间的模式，以及它们是否以有助于公司打造成功产品的方式进行交互。

为了帮助您，Sunshine 的数据中心为您提供了该项目的三个数据文件：hair_dryer.tsv、microwave.tsv和pacifier.tsv。这些数据代表了客户在数据中指定的时间段内对在亚马逊市场上销售的微波炉、婴儿奶嘴和吹风机提供的评级和评论。还提供了数据标签定义词汇表。提供的数据文件包含您应该用于解决此问题的唯一数据。

要求

1. 分析提供的三个产品数据集，以识别、描述和支持数学证据、有意义的定量和/或定性模式、关系、度量和参数，这些模式、关系、度量和参数在星级评定、评论和有用性评级之内和之间，这将有助于 Sunshine Company 在其三个新的在线市场产品中取得成功。

2. 利用你的分析来解决阳光公司营销总监提出的以下具体问题和要求：

一旦阳光公司的三种产品在网上市场上销售，就根据评级和评论确定最有助于阳光公司跟踪的数据指标。
识别并讨论每个数据集内基于时间的测量值和模式，这些测量值和模式可能表明产品在在线市场上的声誉是上升还是下降。
确定最能表明潜在成功或失败产品的基于文本的度量和基于评级的度量的组合。
特定星级评分是否会引发更多评论？例如，客户在看到一系列低星级评分后是否更有可能撰写某种类型的评论？
基于文本的评论的特定质量描述（例如“热情”，“失望”等）是否与评级水平密切相关？

3. 写一封一至两页的信给阳光公司的营销总监，总结您团队的分析和结果。包括您的团队最有信心向营销总监推荐的结果的具体理由。

您的提交内容应包括：

单页摘要表
目录
一至两页的信函
您的解决方案不超过 20 页，最多 24 页，包括摘要表、目录和两页信件。
注意：参考文献列表和任何附录不计入页数限制，应在完成解决方案后显示。您不应使用未经授权的图像和材料，这些图像和材料的使用受版权法限制。确保您引用了您的想法和报告中使用的材料的来源。

词汇表

有用性评级：表明特定产品评论在决定是否购买该产品时的价值。

安抚奶嘴：一种橡胶或塑料的安抚装置，通常为乳头形状，供婴儿吸吮或咬住。

评论：对产品的书面评价。

星级评定：系统给出的分数，允许人们用星级来对产品进行评级。

附件：问题数据集

Problem_C_Data.zip
提供的三个数据集包含通过 Amazon Simple Storage Service (Amazon S3) 从 Amazon 客户评论数据集中提取的产品用户评分和评论
。hair_dryer.tsv
microphone.tsv
pacifier.tsv

数据集定义：每行代表分为以下列的数据。

市场（字符串）：撰写评论的市场的 2 个字母的国家代码。
customer_id（字符串）：可用于汇总单个作者撰写的评论的随机标识符。
review_id（字符串）：评论的唯一 ID。
product_id（字符串）：与评论相关的唯一产品 ID。
product_parent（字符串）：可用于汇总同一产品的评论的随机标识符。
product_title（字符串）：产品标题。
product_category（字符串）：产品的主要消费者类别。
star_rating（int）：评论的 1-5 星评级。
helpful_votes (int)：有帮助的投票数。
total_votes (int)：该评论收到的总投票数。
vine（字符串）：客户被邀请成为 Amazon Vine Voices，基于他们在 Amazon 社区中因撰写准确且有见地的评论而赢得的信任。Amazon 为 Amazon Vine 成员提供供应商提交给该计划的产品的免费副本。Amazon 不会影响 Amazon Vine 成员的意见，也不会修改或编辑评论。
verified_purchase（字符串）：“Y”表示亚马逊已验证撰写评论的人在亚马逊购买了该产品，但并未以大幅折扣购买该产品。
review_headline（字符串）：评论的标题。
review_body（字符串）：评论文本。
review_date (bigint)：撰写评论的日期。

可到文末下载完整版中英文真题

以下是英文版真题

Problem

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 Companyare 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:

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.
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.
Determine combinations of text-based measure(s) and ratings-based measures that best indicate a potentially successful or failing product.
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?
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.

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.

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【真题在线看】2020 MCM问题B：最持久的沙堡

问题标题：最持久的沙堡

年份：2020
学生等级：本科生
来源：MCM

问题

世界上任何有休闲沙滩的地方，似乎都有孩子（和成人）在海边堆沙堡。沙滩游客利用工具、玩具和想象力，堆起的沙堡从简单的沙堆到复杂的真实城堡复制品，带有墙壁、塔楼、护城河和其他模仿真实城堡的特征。在所有这些沙堡中，人们通常先形成一个由单一、不起眼的湿沙堆组成的初始地基，然后继续切割和塑造这个底座，使其成为可识别的三维几何形状，在此基础上建造更具城堡特色的特征。

不可避免的是，海浪的涌入和潮汐的上涨会侵蚀沙堡。然而，看起来并不是所有的沙堡对海浪和潮汐的反应都一样，即使它们建在同一片海滩上，大小大致相同，距离水面的距离也大致相同。因此，人们不禁想知道，是否存在一个最适合沙堡地基的三维几何形状。

要求

1. 建立一个数学模型，确定最适合用作沙堡地基的三维几何形状，该形状将在以下条件下在经历海浪和潮汐的海岸上持续最长时间：

建在同一片海滩上，距离水面的距离大致相同，
使用相同类型的沙子、大致相同的沙子数量以及相同的水与沙子的比例建造。

2. 使用您的模型，确定城堡地基的最佳沙水混合比例，假设您不使用其他添加剂或材料（例如塑料或木质支架、石头等）。

3. 根据需要调整模型，以确定您在要求 1 中确定的最佳 3 维沙堡地基如何受到雨水的影响，以及它在下雨时是否仍然是用作城堡地基的最佳 3 维几何形状。

4. 如果有的话，您还可以使用哪些其他策略来让您的沙堡保存更长时间？

5. 最后，撰写一篇一到两页的内容丰富的文章，描述您的模型及其结果，并在度假杂志《阳光下的乐趣》上发表，该杂志的读者主要是非技术人员。

您的提交内容应包括：

单页摘要表
目录
一至两页的文章
您的解决方案不超过 20 页，最多 24 页，包括摘要、目录和文章。

注意：参考文献列表和任何附录不计入页数限制，应在完成解决方案后显示。您不应使用未经授权的图像和材料，这些图像和材料的使用受版权法限制。确保您引用了您的想法和报告中使用的材料的来源。

可到文末下载完整版中英文真题

以下是英文版真题

Problem

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.

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【真题在线看】2020MCM 问题A：向北移动

问题标题：向北移动

年份：2020
学生等级：本科生
来源：MCM 问题A

问题

全球海洋温度影响某些海洋生物栖息地的质量。当温度变化太大而无法继续繁衍生息时，这些物种就会迁徙，寻找更适合其现在和未来生活和繁殖的其他栖息地。美国缅因州的龙虾种群就是一个例子，它们正在缓慢向北迁徙到加拿大，那里较低的海洋温度提供了更合适的栖息地。这种地理上的种群转移可能会严重扰乱依赖海洋生物稳定生存的公司的生计。

您的团队已被苏格兰北大西洋渔业管理联盟聘为顾问。该联盟希望更好地了解当全球海洋温度升高时，苏格兰鲱鱼和鲭鱼可能从其目前苏格兰附近的栖息地迁徙的问题。这两种鱼类对苏格兰渔业做出了重大的经济贡献。鲱鱼和鲭鱼种群位置的变化可能会使苏格兰规模较小的渔业公司无法使用没有船上冷藏设备的渔船捕捞鲜鱼并将其运送到苏格兰渔港的市场，这在经济上是不切实际的。

要求

1. 建立一个数学模型来确定未来 50 年内这两种鱼类最有可能的栖息地，假设水温发生足够的变化导致种群迁移。

2. 根据海水温度变化的速度，使用你的模型来预测最佳情况、最坏情况以及最可能经过的时间，如果小型渔业公司继续在当前地点经营，这些种群将距离小型渔业公司太远而无法捕捞。

3. 根据您的预测分析，这些小型渔业公司是否应该改变其运营方式？

a. 如果答案是肯定的，请使用您的模型来识别和评估适合小型渔业公司的实用且经济上有吸引力的策略。您的策略应考虑（但不限于）现实的选择，包括：

- 将渔业公司的部分或全部资产从苏格兰港口的当前位置迁移到更靠近两种鱼类种群迁徙的地方；
- 使用一定比例的小型渔船，这些渔船可以在一段时间内无需陆基支持即可作业，同时仍能确保捕捞物的新鲜度和高质量。
- 您的团队可能确定和模仿的其他选项。

b. 如果您的团队拒绝进行任何更改，请根据您的建模结果与您的团队所做的假设相关地说明拒绝的理由。

4. 使用您的模型来解决如果部分渔业转移到另一个国家的领海（海域）时您的提案会受到怎样的影响。

5. 除了技术报告之外，还要为《Hook Line and Sinker》杂志准备一篇一到两页的文章，帮助渔民了解问题的严重性以及您提出的解决方案将如何改善他们未来的业务前景。

您的提交内容应包括：

单页摘要表
目录
一至两页的文章
您的解决方案不超过 20 页，最多 24 页，包括摘要、目录和文章。
注意：参考文献列表和任何附录不计入页数限制，应在完成解决方案后显示。您不应使用未经授权的图像和材料，这些图像和材料的使用受版权法限制。确保您引用了您的想法和报告中使用的材料的来源。

词汇表

渔业：特定物种的鱼类及其栖息区域的集合。

栖息地：生物或群体通常生活或出现的环境类型。

小型渔业公司：从事商业捕鱼的公司，其用于投资新设备/船只的资金有限或非常有限。

领海（海）：“根据 1982 年《联合国海洋法公约》的定义，领海是指从沿海国家基线（通常是平均低水位线）延伸至多 12 海里（22.2 公里；13.8 英里）的沿海水域带。领海被视为国家的主权领土，但外国船只（军用和民用）可以无害通行，或过境海峡；这种主权也延伸到领海上方的空域和下方的海床。” [领海。（nd）。维基百科。2020 年 1 月 28 日检索自 https://en.wikipedia.org/wiki/Territorial_waters。]

可到文末下载完整版中英文真题

以下是英文版真题

Problem

Global ocean temperatures affect the quality of habitats for certain ocean-dwelling species. When temperature changes are too great for their continued thriving, these species move to seek other habitats better suited to their present and future living and reproductive success. One example of this is seen in the lobster population of Maine, USA that is slowly migrating north to Canada where the lower ocean temperatures provide a more suitable habitat. This geographic population shift can significantly disrupt the livelihood of companies who depend on the stability of ocean-dwelling species.

Your team has been hired as consultants by a Scottish North Atlantic fishery management consortium. The consortium wants to gain a better understanding of issues related to the potential migration of Scottish herring and mackerel from their current habitats near Scotland if and when global ocean temperatures increase. These two fish species represent a significant economic contribution to the Scottish fishing industry. Changes in population locations of herring and mackerel could make it economically impractical for smaller Scotland-based fishing companies, who use fishing vessels without on-board refrigeration, to harvest and deliver fresh fish to markets in Scotland fishing ports.

Requirements

1. Build a mathematical model to identify the most likely locations for these two fish species over the next 50 years, assuming that water temperatures are going to change enough to cause the populations to move.

2. Based upon how rapidly the ocean water temperature change occurs, use your model to predict best case, worst case, and most likely elapsed time(s) until these populations will be too far away for small fishing companies to harvest if the small fishing companies continue to operate out of their current locations.

3. In light of your predictive analysis, should these small fishing companies make changes to their operations?

a. If yes, use your model to identify and assess practical and economically attractive strategies for small fishing companies. Your strategies should consider, but not be limited to, realistic options that include:

- Relocating some or all of a fishing company’s assets from a current location in a Scottish port to closer to where both fish populations are moving;
- Using some proportion of small fishing vessels capable of operating without land-based support for a period of time while still ensuring the freshness and high quality of the catch.
- Other options that your team may identify and model.

b. If your team rejects the need for any changes, justify reasons for your rejection based on your modeling results as they relate to the assumptions your team has made.

4. Use your model to address how your proposal is affected if some proportion of the fishery moves into the territorial waters (sea) of another country.

5. In addition to your technical report, prepare a one- to two-page article for Hook Line and Sinker magazine to help fishermen understand the seriousness of the problem and how your proposed solution(s) will improve their future business prospects.

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.

Glossary

Fishery: The collection of fish of a given species and the area that they inhabit.

Habitat: The type of environment in which an organism or group normally lives or occurs.

Small Fishing Company: A company engaged in commercial fishing with limited or very limited financial resources to invest in new equipment/vessels.

Territorial Waters (sea): "as defined by the 1982 United Nations Convention on the Law of the Sea, is a belt of coastal waters extending at most 12 nautical miles (22.2 km; 13.8 mi) from the baseline (usually the mean low-water mark) of a coastal state. The territorial sea is regarded as the sovereign territory of the state, although foreign ships (military and civilian) are allowed innocent passage through it, or transit passage for straits; this sovereignty also extends to the airspace over and seabed below." [Territorial Waters. (n.d.). In Wikipedia. Retrieved January 28, 2020, from https://en.wikipedia.org/wiki/Territorial_waters.]

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