2024年HIMCM美國中學數學建模競賽A題

中文賽題：舍去還是保留，未來奧運會項目建模

國際奧林匹克委員會(hui) （IOC）正在籌備2032年澳大利亞(ya) 布裏斯班夏季奧運會(hui) 。為(wei) 使奧運會(hui) 保持相關(guan) 性和影響力，IOC致力於(yu) 增加符合現代價(jia) 值觀且吸引全球觀眾(zhong) 的運動、分項或比賽（SDEs）。奧運曆史上，為(wei) 了反映時代變化，SDEs 時有增減。例如，2020年空手道、運動攀岩、衝(chong) 浪和滑板首次成為(wei) 奧運項目，但空手道未入選2024年巴黎奧運會(hui) ，取而代之的是霹靂舞。展望2028年洛杉磯奧運會(hui) ，美式橄欖球、長曲棍球和近海賽艇將被加入，棒球和壘球也將在缺席20年後重新回歸。

為(wei) 了指導這些決(jue) 策，IOC的奧運項目委員會(hui) 製定了一套標準以確保每項運動符合奧林匹克精神^[1]。IOC列出的運動入選標準如下：

• 受歡迎度和可達性：提升奧運會的吸引力和全球關注度，同時不顯著增加成本或後勤需求。
• 性別平等：確保男女運動員有平等的參賽機會。
• 可持續性：促進環境和社會責任。
• 包容性：代表多元文化，促進全球參與（至少有四大洲的75個國家在實踐該運動）。
• 相關性與創新：吸引年輕觀眾，反映現代趨勢，引入創新（如體感虛擬運動），同時尊重奧運傳統。
• 安全與公平競爭：確保運動員保護和反興奮劑的高標準。

IOC 雇傭(yong) 了你們(men) 團隊——HiMCM奧運顧問團隊（HOC）來協助評估應在2032年夏季奧運會(hui) 中加入（或可能移除）的 SDEs 。你的任務是創建一個(ge) 數學模型，根據這些標準評估 SDEs ，以提供有依據的推薦。該模型將用於(yu) 根據定量信息判斷哪些 SDEs 最符合奧運會(hui) 的發展願景。

任務

1. 根據 IOC 標準，列出並描述需要考慮的各種因素。注意這些因素可能是定量或定性、恒定或變量、確定性或概率性的。務必對選擇的因素加以解釋並在適當情況下附上單位。
2. 使用確定的因素構建一個或多個模型，以幫助 IOC 評估哪些 SDEs 最符合奧運標準。
3. 選擇至少三個在2020年、 2024年和2028年奧運會中新增或移除的 SDEs，以及至少三個自1988年或更早以來持續存在的 SDEs，對模型進行測試。HiMCM 提供的奧運數據表（HiMCM_Olympic_Data.xlsx）包括自現代奧運會開始以來的項目、分項及賽事數據信息。選擇多樣化的 SDEs 來評估，討論模型在不同 SDEs 上的適用性，驗證其當前奧運地位。
4. 識別三個可能在2032年布裏斯班奧運會上新增或重新引入的 SDEs ，並確定優先推薦的順序（第一、第二、第三）。此外，是否有潛力在2036年或更晚的奧運會上加入的 SDEs ？
5. 評估模型的穩健性，分析在模型中使 SDEs 得分較高的因素，並討論這些因素在決策工具中的優劣。
6. 向 IOC 提交 1-2 頁的總結信，通俗易懂地說明模型的理論依據及其對 SDEs 的評估結果。包括建議的新增或移除的 SDEs ，以及模型支持這些結論的理由。

你的PDF解決(jue) 方案最多 25 頁，包括：

• 一頁的總結
• 目錄
• 完整解決方案
• 1-2 頁的 IOC 總結信
• 參考文獻
• AI 使用報告（如使用，不計入 25 頁限製）

注意：沒有特定的最低頁數要求，可以使用最多 25 頁完成所有解決(jue) 方案工作和任何附加信息（如圖畫、圖表、計算、表格）。接受部分解決(jue) 方案。允許謹慎使用生成式 AI 工具（如ChatGPT），但非必須使用。如使用生成式 AI，需遵循 COMAP 的 AI 使用政策，並將 AI 使用報告附加在 PDF 的最後部分，不計入 25 頁限製。

HiMCM/MidMCM最新：在線提交流程

本文旨在幫助和指導參與(yu) HiMCM/MidMCM 的學生和指導老師。COMAP 在文中提供了關(guan) 於(yu) 新的在線提交流程的信息，需使用新的在線提交頁麵（提交鏈接）。完成提交時，你需要準備好團隊控製編號、指導老師ID和所選問題編號。

數據

HiMCM_Olympic_Data.xlsx - 包含當前和已取消的夏季奧運會(hui) 項目數據集。

• 運動和分項：數據集中列出了夏季奧運會正式項目和已取消項目，按IOC使用的名稱字母順序排列。
• 代碼：每個分項由 IOC 分配一個唯一的三字符標識代碼。
• 體育管理機構：列出了與奧運項目相關的體育管理機構。
• 年份（1896 - 2028）：每列的四位數字代表相關奧運會的年份。每個項目（或分項）在相應奧運會上舉行的賽事數量標注在對應年份下；帶“•”的項目為示範或非正式比賽。

術語表

• 確定性：指隻有一個（預定）結果的過程。
• 國際奧林匹克委員會（IOC）：是奧運會和奧林匹克運動的國際非政府體育管理機構，負責組織夏季和冬季奧運會。
• IOC奧運項目委員會：除其他職責外，負責分析夏季和冬季奧運會的項目安排。
• 體感虛擬運動：指結合物理活動和虛擬或數字元素的運動，通常通過增強現實（AR）、虛擬現實（VR）或電競平台實現。這類運動將現實中的身體活動與虛擬場景或比賽相結合，例如 Zwift 騎行，選手使用配備速度和阻力傳感器的動感單車在虛擬環境中騎行，與其他線上選手進行比賽。
• 概率性：基於概率理論或依賴隨機性來預測未來事件的過程。
• 奧運會項目：IOC 為每屆奧運會設立的所有運動比賽項目。
• SDE：運動（S）、分項（D）、賽事定義（E）
  • 運動：IOC 定義的奧運會項目是由一個國際體育聯合會（IF）管理的項目。一個運動項目可能包含一個或多個分項，每個分項有一個或多個賽事。
  • 分項：一個運動項目的分支，包含一個或多個賽事。
  • 賽事：一個分項下的比賽，結果會產生排名並頒獎（例如：獎牌）。項目、分項、賽事的關係示例（以2024年巴黎奧運會為例）：
    • 由世界遊泳聯合會（World Aquatics）管理。
    • 水上運動包含多個分項——藝術遊泳、跳水、馬拉鬆遊泳、遊泳和水球。
    • 例如，在跳水分項中包含八個獎牌賽事：
      • 男子與女子3米跳板
      • 男子與女子10米跳台
      • 男子與女子同步3米跳板
      • 男子與女子同步10米跳台
• 體育管理機構：負責監督和製裁某項運動的體育組織，具有不同的管理範圍和紀律職能，包括處理違規行為及決定規則變更。國際體育聯合會（IFs）是 IOC 認可的非政府國際組織，負責在全球範圍內管理一項或多項運動。

免責聲明

COMAP 是一個(ge) 致力於(yu) 提升數學教育的非營利組織，專(zhuan) 注於(yu) 提高學生的數學建模能力。本競賽問題引用了國際奧林匹克委員會(hui) （IOC）的材料，用於(yu) 教育和非商業(ye) 用途，以豐(feng) 富參賽者的學習(xi) 體(ti) 驗。此內(nei) 容並未獲得 IOC 的認可或與(yu) IOC 有任何關(guan) 聯。

Problem: To Play or not to Play: Modeling Future Olympic Games

The International Olympic Committee (IOC) is planning the 2032 Summer Olympics in Brisbane, Australia. As the Olympics evolve, the IOC aims to keep the Games both relevant and impactful by adding sports, disciplines, or events (SDEs) that resonate with modern values and appeal to a global audience. Throughout Olympic history, SDEs have been introduced, removed, or even reintroduced to reflect the times. For example, in 2020, Karate, Sport Climbing, Surfing, and Skateboarding made their Olympic debut. However, Karate was no longer included in the 2024 Paris Olympics, while Breaking (also known as breakdancing) was introduced. Looking forward to the 2028 Los Angeles Olympics, Flag Football, Lacrosse, and Coastal Rowing will be added, while Baseball and Softball will return to be contested in the 2028 Games after a 20-year absence.

To guide these decisions, the IOC’s Olympic Programme Commission has developed a set of criteria to help ensure that each sport aligns with Olympic values.^[1] IOC Criteria for Sports Inclusion is summarized below:

• Popularity and Accessibility: Enhances the Olympic Games’ appeal and global interestwithout excessively increasing costs or logistical demands.
• Gender Equity: Ensures that both men and women athletes have equal opportunity toparticipate.
• Sustainability: Promotes environmental and social responsibility.
• Inclusivity: Represents diverse cultures and promotes global participation (at least 75countries across four continents practicing the sport).
• Relevance and Innovation: The sport must appeal to younger audiences, reflect moderntrends, and incorporate innovations including physical virtual sports where appropriatewhile respecting Olympic traditions.
• Safety and Fair Play: Maintains high standards for athlete protection and anti-doping.

The IOC has hired your team, HiMCM Olympic Consultants (HOC), to assist in evaluating which SDEs should be added (or potentially removed) from the 2032 Summer Games. Your task is to create a mathematical model that evaluates SDEs against these criteria to provide well-reasoned recommendations. This model will be used to make quantitatively informed decisions about which SDEs best fit the Olympics’evolving vision.

Your Tasks

1. What factors need to be considered when addressing the IOC criteria? List and describe the various factors your team identifies. Note that factors may be quantitative or qualitative, constant or variable, and deterministic or probabilistic. Be sure to justify your choices and to include units where appropriate.
2. Use your factors to build a model (or set of models) to help the IOC evaluate which SDEs align best with Olympic criteria.
3. Test your model on at least three SDEs that have been added or removed from recent Olympics, namely Olympic years 2020, 2024, and 2028 and at least three SDEs that have continuously been in the Olympic programme since the 1988 games or earlier. The supplied data HiMCM_Olympic_Data.xlsx provides information about which sports and disciplines, and number of events, have appeared in each Olympics since their modern formation. Be sure to highlight the general applicability of your model by choosing a diverse collection of SDEs to evaluate. Discuss how your model affirms these SDEs’ current Olympic status.
4. Identify three SDEs that could be new additions or reintroductions for the 2032 Olympics in Brisbane. Make sure to identify which SDE should be considered first, second and third for inclusion in the Brisbane games. Are there any SDEs that you believe have potential for inclusion in an Olympic games in 2036 or beyond?
5. Perform sensitivity analysis to address the robustness of your model. Identify what aspects of your model make an SDE score well and discuss if these represent a strength or weakness of your model, especially in light of it being used as a decision-making tool.
6. Draft a one- to two-page letter addressed to the IOC summarizing your findings in a non-technical way. Explain your model’s rationale and its results for the evaluated SDEs. Include your recommendations for which SDEs to add or remove and why your model supports these conclusions.

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 IOC letter
• References list.
• AI Use Report (If used does not count toward the 25-page limit.)

Note: There is no specific required minimum page length for a complete HiMCM submission. You may use up to 25 total pages for all your solution work and any additional information you want to include (for example: drawings, diagrams, calculations, tables). Partial solutions are accepted. We permit the careful use of AI such as ChatGPT, although it is not necessary to create a solution to this problem. If you choose to utilize a generative AI, you must follow the COMAP AI use policy. This will result in an additional AI use report that you must add to the end of your PDF solution file and does not count toward the 25 total page limit for your solution.

NEW HiMCM/MidMCM: Online Submission Process The purpose of this article is to assist and guide students and advisors participating in HiMCM/MidMCM. In the article, COMAP, provides information about the new online submission process using the new online submission page https://forms.comap.org/242386224483964. You will need your team's control number, advisor id number and your problem choice to complete your submission.

Data

HiMCM_Olympic_Data.xlsx – Data set of current and discontinued summer program.

• Sport and Discipline: The sports (and disciplines) make up the current and discontinued Summer Olympic Games official program and are listed alphabetically according to the name used by the IOC.
• Code: Each discipline is marked with a unique 3-character identifier code by the IOC. Sports Governing Body: A listing of the sports governing bodies associated with Olympic sports.
• 1896 – 2028: The four number code in each column represents the year of the associated Olympic Games. Figures in each cell of the associated column indicate the number of events for each sport contested at the respective Games; a bullet (•) denotes that the sport was contested as a demonstration or unofficial sport.

Glossary

• Deterministic: processes that have only one (predetermined) outcome.
• International Olympic Committee (IOC): is the international, non-governmental, sports governing body of the Olympic Games and the Olympic Movement. The IOC is best known as the organization responsible for organizing the Summer and Winter Olympics.
• IOC’s Olympic Programme Commission: has, among other duties, the responsibility for analyzing the programmes for the Summer and Winter Olympic Games.
• Physical virtual sport: refers to a sport that integrates physical activity with virtual or digital elements, often through advanced technology like augmented reality (AR), virtual reality (VR), or esports platforms. These sports combine real-world physical exertion or skill with virtual settings or competitions, bridging traditional physical sports and digital interaction. One example of a physical virtual sport is Zwift cycling, where athletes use stationary bikes equipped with sensors to track their speed and resistance. The data is then streamed into a virtual environment where cyclists "ride" through various digital courses, competing with other participants online. This type of setup blends real physical cycling with a virtual competition, allowing for both athletic performance and digital engagement.
• Probabilistic: processes based on the theory of probability or that randomness plays a role in predicting future events.
• Programme: of the Olympic Games is the programme of all sports competitions established by the IOC for each edition of the Olympic Games.
• SDE: Sport, Discipline, or Event
  • Sport: The IOC defines an Olympic sport as a discipline that is governed by a single international sports federation (IF). A single sport may contain one or more disciplines, each of which is the focus of one or more events.
  • Discipline: A branch of a sport that includes one or more events.
  • Event: A competition within a discipline that results in a ranking and awards (e.g. medals).Example of the relationship between sport, discipline, and event in the Olympic programme from the 2024 Paris Olympics:
    • World Aquatics is the IF that governs the sport of aquatics
    • Within the sport of aquatics are multiple disciplines – artistic swimming, diving, marathon swimming, swimming, and water polo.
    • Within the discipline of diving are eight medal events:
      • Individual 3m springboard - men & women
      • Individual 10m platform - men & women
      • Synchronized 3m springboard - men & women
      • Synchronized 10m platform - men & women
• Sports governing body: A sports governing body is a sports organization that has a regulatory or sanctioning function. Sports governing bodies come in various forms and have a variety of regulatory functions, including disciplinary action for rule infractions and deciding on rule changes in the sport that they govern. Governing bodies have different scopes. They may cover a range of sports at an internationally acceptable level. An example of a sports governing body is an International Federation. International Sports Federations (IFs): are international non-governmental organizations recognized by the (IOC) as administering one or more sports at the world level. Recognized IFs must ensure that their statutes, practice and activities conform with the Olympic Charter, ultimately, they are responsible for the integrity of their sport on the international level.

Disclaimer

COMAP is a non-profit organization dedicated to improving mathematics education with an emphasis on increasing student proficiency in mathematical modeling. This contest problem references material from the International Olympic Committee (IOC). We acknowledge and respect the IOC’s ownership of this material, and it is used here solely for educational, non-commercial purposes to enrich learning experiences for participants. This content is not endorsed by or affiliated with the IOC.

Reference

[1]

Factsheet: The programme of the Games of the Olympiad. DInternational Olympic Committee, 2024: https://stillmed.olympics.com/media/Documents/Olympic-Games/Factsheets/The-programme-of-the-Games-of-the-Olympiad.pdf