2025年美國大學生數學建模競賽D題中英版

1420 預計閱讀需要34分鍾

中文賽題：建設更美好城市的路線圖

背景

交通係統可以幫助或妨礙城市的增長以及居民的生活。成功的交通基礎設施能夠吸引企業(ye) 、學校、遊客和新居民。城市麵臨(lin) 的交通挑戰是複雜且交織在一起的。各個(ge) 利益相關(guan) 方（城市居民、企業(ye) 主、郊區居民、通勤者、通道、遊客等）在這些係統中有不同的需求和優(you) 先事項。通常，交通係統的一個(ge) 元素或組件會(hui) 偏向某個(ge) 利益相關(guan) 方，從(cong) 而幹擾係統中其他需求。高速公路、公交路線和鐵路係統可能會(hui) 幹擾本地城市騎車人和行人的出行，反之亦然，當車輛駕駛員被城市人行道和交通信號燈耽擱時。有時，最有效的交通係統的最大障礙是城市的地理條件——水域（河流、港口、溪流、排水溝）或地形（山丘、溝渠、山穀、斜坡）。甚至土壤成分和氣候條件也可能造成幹擾。

情況

馬裏蘭(lan) 州巴爾的摩市是一個(ge) 受到老化基礎設施和有限交通選擇影響的城市，這些問題影響了人們(men) 的生活並阻礙了經濟增長。除此之外，最近發生了一個(ge) 主要橋梁（弗朗西斯·斯科特·基橋）的坍塌，關(guan) 閉了通過其繁忙港口的主要高速公路。巴爾的摩市一直在製定改進其交通網絡的計劃，包括通過基礎設施改善和提升公共交通來實現其可持續發展目標。這些目標基於(yu) 識別、優(you) 先考慮並實施一些倡議，如利益相關(guan) 方之間的合作、維護或更新物理係統、更有效地使用數據，以及尋求技術進步來提升居民和遊客的生活質量。

巴爾的摩是一個(ge) 繁忙的港口和航運中心，位於(yu) 一條主要的州際高速公路（I-95）上。它的一些過路和通勤高速公路及鐵路線路阻礙或幹擾了街道和社區，使得城市居民很難進入航運行業(ye) 的就業(ye) 機會(hui) ，也讓當地企業(ye) 難以運輸貨物進出社區。通過修複道路、修建繞行道、擴展公共交通選項以及改善港口和機場的通行能力，巴爾的摩希望促進商業(ye) 發展，並讓城市成為(wei) 一個(ge) 更好的生活、工作和旅遊的地方。

最近，借助國家資助和支持，美國一些城市已經製定了基礎設施計劃，旨在拆除那些將社區與(yu) 市中心隔開的高速公路，並尋求以重新連接和振興(xing) 這些區域的方式進行替代。這些高速公路雖然允許郊區居民通勤到市中心或跨城通勤，但在建設這些高速公路的過程中，城市社區被分割或摧毀。巴爾的摩希望重新連接這些社區，並為(wei) 居民提供更多綠色空間、更好的公共住房，以及更多的社區娛樂(le) 和休閑機會(hui) 。

以下是四個(ge) 交通問題的示例：

  1. 重建坍塌的弗朗西斯·斯科特·基橋（位於港口）。[1]
  2. 公共鐵路係統的不足（MARC、輕軌、重軌），這些鐵路連接了已經有多種交通選擇的郊區。這些鐵路的運力不足以讓通勤者和居民輕鬆使用該係統前往工作地點，而市中心的免費巴士主要服務遊客，而不是城市社區的居民。[2]
  3. 通過西巴爾的摩聯合項目（West Baltimore United Project），規劃解決US-40（通往無處之路）高速公路多年來對城市社區造成的破壞。[3]
  4. 巴爾的摩布魯克林社區一位居民的旅行記，記錄了他在參加城市足球比賽後，試圖搭乘公交車回家的經曆。[4]

要求

巴爾的摩的所有交通計劃都涉及多個(ge) 利益相關(guan) 方，他們(men) 的觀點各不相同。您團隊的任務是通過推薦改善巴爾的摩交通網絡的方法，來提升城市居民的生活質量。

提供了一個(ge) 包含街道段車輛流量的文件。通過創建巴爾的摩或其某些區域和社區的交通網絡，您將能夠可視化並理解這些問題。因此，您應該為(wei) 巴爾的摩交通係統的某一部分或元素構建一個(ge) 網絡模型。

使用您的模型，考慮與(yu) 以下交通問題相關(guan) 的項目：

  1. 弗朗西斯·斯科特·基橋的坍塌對巴爾的摩交通係統產生了巨大影響。您的網絡模型展示了橋梁坍塌和/或橋梁重建的影響嗎？請確保突出展示對巴爾的摩及周邊地區各利益相關方的影響。
  2. 巴爾的摩市的許多居民步行或乘公交車出行。選擇一個影響公交或人行道係統的項目或潛在項目。您的網絡模型展示了該項目的影響嗎？請確保突出展示對巴爾的摩及周邊地區各利益相關方的影響。
  3. 推薦一個交通網絡項目，該項目能最好地改善巴爾的摩居民的生活。
    1. 這個項目給居民帶來的好處是什麽？
    2. 您的項目如何影響其他利益相關方？
    3. 解釋您的項目如何擾亂其他交通需求和人們的生活。

分享您的見解

  • 安全是巴爾的摩市麵臨的一個重大問題。交通係統如何能最好地解決這一問題？
  • 向巴爾的摩市市長寫一份一頁紙的備忘錄，描述您的兩個項目，包括其對市民安全的好處和缺點。

您的 PDF 解決(jue) 方案總頁數不得超過25頁，包括：

  • 一頁摘要頁。
  • 目錄。
  • 完整解決方案。
  • 一封給交通官員的信（一頁）。
  • 參考文獻列表。
  • AI使用報告（如果使用不計入 25 頁總限製）。

注意：完整的 MCM 提交文件沒有特定的最低頁數要求。您最多可使用 25 頁來包含您的所有解決(jue) 方案內(nei) 容及其他補充信息（例如圖紙、圖表、計算和表格）。允許提交部分解決(jue) 方案。我們(men) 允許謹慎使用 AI 工具（例如 ChatGPT），但完成本問題並不一定需要使用 AI 工具。如果您選擇使用生成式 AI 工具，必須遵循 COMAP 的 AI使用政策。此政策要求您在解決(jue) 方案文件的最後額外添加一份 AI 使用報告，不計入 25 頁的總限製。

全新 MCM/ICM：在線提交流程

本文旨在協助和指導參加 MCM/ICM 的學生和顧問。在文章中，COMAP 提供了有關(guan) 使用新在線提交頁麵的新在線提交流程的信息：

https://forms.comap.org/241335097294056

您需要團隊的控製號、顧問 ID 號和問題選擇才能完成提交。

提供的文件

這些文件用於(yu) 幫助學生找到與(yu) 巴爾的摩相關(guan) 的數據，以便開始此問題，特別是為(wei) 構建網絡模型來研究這些問題。實際數據，如提供的數據集，通常是非常淩亂(luan) 的。例如，巴爾的摩的許多道路不僅(jin) 有路由號碼，還可能有街道名稱，而這些名稱在不同的路段可能會(hui) 發生變化。因此，數據需要處理。關(guan) 於(yu) 如何處理數據的決(jue) 策和假設是建模過程中的重要部分。此外，團隊不隻限於(yu) 使用這些數據。

2025_Problem_D_Data.zip：此壓縮文件包含下列9個(ge) 數據文件：

  1. Bus_Routes.csv：[5] 該數據集表示2022年巴爾的摩市內MTA公交路線的位置。
  2. Bus_Stops.csv：[6] 該數據集表示2022年巴爾的摩市內MTA公交車站的位置。
  3. nodes_all.csv：[7] 該數據集表示通過OpenStreetMaps[8]標記的地理屬性位置，提供巴爾的摩的交通數據點。通常，這些是兩個交通路徑（道路、高速公路、自行車道、人行道等）交匯的地點。
  4. nodes_drive.csv：[7] 該數據集表示通過OpenStreetMaps[8]標記的地理屬性位置，適用於汽車行駛。通常，這些是兩個道路或高速公路交匯的地點。
  5. edges_all.csv：[7] 該數據集表示兩個節點之間的交通路徑，數據來源於nodes_all.csv數據集。
  6. edges_drive.csv：[7] 該數據集表示兩個節點之間的道路，數據來源於nodes_drive.csv數據集。
  7. MDOT_SHA_Annual_Average_Daily_Traffic_Baltimore.csv：[9] 該數據集包含馬裏蘭州交通部（MDOT SHA）年均日交通（AADT）數據，涵蓋了馬裏蘭州各地的道路及交通流量信息。
  8. Edge_Names_With_Nodes.csv：[7] 該數據集將nodes_all.csv數據集中的信息與edges_all.csv數據集中的信息相匹配，提供帶節點的街道名稱。
  9. DataDictionary.csv：該數據文件描述了提供的每個數據集中的特征。

有許多有價(jia) 值的數據集可從(cong) 以下網址獲取：

https://baltometro.org/about-us/data-maps/regional-gis-data-center

和

https://opendata.baltimorecountymd.gov/

術語表

通道：旅行者到達目的地必須經過的地方。

基礎設施：用於(yu) 支持或進行人員或貨物運輸的結構或設施

街道段：數據集或地圖中街道或道路部分位置（通常具有起點和終點）的虛擬邊緣。

Problem: A Roadmap to a Better City

Background

Transportation systems can help or harm a city’s growth and the lives of its residents. Asuccessful transportation infrastructure can attract businesses, schools, tourists, and new residents. The transportation challenges that cities face are complex and intertwined. The various stakeholders (city residents, business owners, suburban residents, commuters, passthrough travelers, tourists, etc.) have different needs and priorities within those systems. Often one element or component of a transportation system favors one stakeholder over others therefore creating an interference with other needs of the system. Highways, bus routes, and rail systems can interfere with local city bikers and pedestrians and vice versa when vehicle drivers are delayed by city walkways and traffic lights. Sometimes, the biggest obstacle to effective transportation systems is the city’s geography – water (rivers, harbors, streams, drainage runoff) or landforms (hills, ditches, valleys, slopes). Even soil composition and weather conditions can be disruptive.

Situation

Baltimore, Maryland, USA is a city affected by aging infrastructure and limited transportation options that impact people’s lives and hinder its economic growth. Adding to that is the recent collapse of a major bridge (Francis Scott Key Bridge) closing a major highway across its busy harbor. Baltimore has been making plans to improve its transportation network through infrastructure improvement and enhancing its public transportation as a part ofits sustainability goals. These goals are based upon identifying, prioritizing, and implementing initiatives such as collaboration between stakeholders, maintaining or updating its physical systems, using data more effectively, and seeking technological advancements that enhance the lives of its residents and visitors.

Baltimore has a bustling port and shipping center along with being located on a major interstate highway (I-95). Several of its passthrough and commuter highways and rail lines block or interfere with streets and neighborhoods making it difficult for city residents to access job opportunities in the shipping industries and for local businesses to transport goods into and around neighborhoods. Through planning initiatives to repair roads, build bypasses, expand public transit options, and improve access to ports and airports, Baltimore hopes to facilitate commerce and make the city a better place to live, work, and visit.

Recently, through national funding and support, US cities have developed infrastructure plans to remove highways that divide neighborhoods into their downtown areas and seek to replace them in ways that reconnect and revitalize those areas. While the highways allow suburban residents to commute downtown or across the city to their jobs, urban neighborhoods were separated or destroyed in the construction of these highways. Baltimore hopes to reconnect these communities and provide more sustainable communities with more green spaces, better public housing, and opportunities for community entertainment and recreation.

As examples, four transportation issues are outlined in these references:

  1. The rebuilding of a collapsed bridge (Francis Scott Key Bridge) in the Harbor.[1]
  2. The inadequacy of the minimal public rail systems (MARC, light rail, heavy rail), which connect suburbs that already have several transportation options. The rail transits are not substantial enough to enable commuters and residents to easily use the system to get to the workplace and the downtown free buses primarily help tourists and not the residents of intercity communities.[2]
  3. Planning for fixing the disruption over decades on urban communities by US-40 (Highway to Nowhere) through the collaborative West Baltimore United Project.[3]
  4. A travelogue of a resident of Brooklyn (community in Baltimore) and his ordeal of trying to use buses to get home after attending a football game in the city.[4]

Requirements

All of Baltimore’s transportation plans affect multiple stakeholders with differing perspectives. Your team’s assignment is to improve the lives of the city’s residents by recommending ways to improve Baltimore’s transportation network.

A file with vehicle counts on street segments is provided. Creating transportation networks for Baltimore or one of its areas and communities will help you visualize and understand the issues. Therefore, you should build a network model(s) for some part or element of Baltimore’s transportation system. Using your model, consider projects related to these transportation issues:

  1. The collapse of the Francis Scott Key Bridge had a large impact on the transportation system of Baltimore. What does your network model(s) show is the impact of the bridge collapse and/or the reconstruction of the bridge? Be sure to highlight the impacts on the various stakeholders in and around Baltimore.
  2. Many residents of the City of Baltimore walk or travel by bus. Select a project or potential project that impacts the bus or pedestrian walkway systems. What does your network model(s) show is the impact of this project? Be sure to highlight the impacts on the various stakeholders in and around Baltimore.
  3. Recommend a project for the transportation network that best improves the lives of the residents of Baltimore.
    • What are the benefits to residents of this project?
    • How does your project impact other stakeholders?
    • Explain the ways that your project disrupts other transportation needs and people’s lives.

Share Your Insights

  • Safety is a significant issue facing the City of Baltimore. How can the transportation system be used to best address this issue?
  • Write a one-page memo to the Mayor of Baltimore describing two of your projects, including the benefits and drawbacks on the people and their safety in the city.

Your PDF solution of no more than 25 total pages should include:

  • One-page Summary Sheet.
  • Table of Contents.
  • Your complete solution.
  • One-page letter to the transportation officials.
  • 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 MCM 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 MCM/ICM: Online Submission Process

The purpose of this article is to assist and guide students and advisors participating in MCM/ICM. In the article, COMAP, provides information about the new online submission process using the new online submission page:

https://forms.comap.org/241335097294056

You will need your team's control number, advisor id number and your problem choice to complete your submission.

Files provided

These files are provided to assist students with finding data relevant for Baltimore to begin this problem, particularly to build a network model to study these problems. Real data, like that in the sets provided, is often quite messy. For example, many roads in Baltimore not only have a route number identifying them, but also a street name that may change from one section to another. Therefore, the data will require manipulation. Decisions and assumptions about how to manipulate the data are an important part of the modeling process. Moreover, teams are not limited to these data.

2025_Problem_D_Data.zip: This zip file contains all 9 of the data files listed below.

  1. Bus_Routes.csv:[5] This dataset represents the locations of MTA bus routes within the City of Baltimore as of 2022.
  2. Bus_Stops.csv:[6] This dataset represents the locations of MTA Bus Stops as of 2022 within the City of Baltimore.
  3. nodes_all.csv:[7] This dataset represents the locations of tagged geographic attributes by OpenStreetMaps[8] that provide transportation data points in Baltimore. Generally, these are locations where two transportation paths (road, highway, bikeway, walkway, etc.) intersect.
  4. nodes_drive.csv:[7] This dataset represents the locations of tagged geographic attributes by OpenStreetMaps[8] for car travel. Generally, these are locations where two roads or highways intersect.
  5. edges_all.csv:[7] This dataset represents the transportation paths between two nodes from the nodes_all.csv dataset.
  6. edges_drive.csv:[7] This dataset represents the roadways between two nodes from the nodes_drive.csv dataset.
  7. MDOT_SHA_Annual_Average_Daily_Traffic_Baltimore.csv:[9] MDOT SHA Annual Average Daily Traffic (AADT) data consists of linear & point geometric features which represent the geographic locations & segments of roadway throughout the State of Maryland that include traffic volume information. Traffic volume information is produced from traffic counts used to calculate annual average daily traffic (AADT), annual average weekday traffic (AAWDT), AADT based on vehicle class (current year only) for roadways throughout the State.
  8. Edge_Names_With_Nodes.csv:[7] This dataset pairs the information from the nodes_all.csv dataset with information from the edges_all.csv dataset to provide street names with nodes.
  9. DataDictionary.csv: This data file describes the features in each of the data sets provided for this question.

There are many valuable data sets available at:

https://baltometro.org/about-us/data-maps/regional-gis-data-center

and

https://opendata.baltimorecountymd.gov/

Glossary

Passthrough: A place that travelers have to go through to get to their destinations.

Infrastructure: A structure or facility that is used to support or conduct transportation of people or goods

Street segments: virtual edges in a dataset or map of locations of parts (usually with a start point and end point) of a street or road.

參考資料[1]

Rebuild of Baltimore’s Key Bridge to start ConstructConnect. Rebuild of Baltimore's key bridge to start. ConstructConnect. 2024 Jan 18: https://www.constructconnect.com/construction-economic-news/rebuild-of-baltimores-key-bridge-to-start

[2]

Reconnecting communities in West Baltimore SCIRP. Reconnecting communities in West Baltimore. SCIRP. 2023 Dec 10.: https://www.scirp.org/journal/paperinformation?paperid=138654

[3]

Reconnecting communities in West Baltimore Streets of Baltimore. Reconnecting communities in West Baltimore. Streets of Baltimore. 2024 Jan 15: https://streetsofbaltimore.com/reconnecting-communities-in-west-baltimore

[4]

Transportation equity problems in Baltimore WYPR. With the national spotlight on Baltimore, transportation equity problems shine through. WYPR. 2024 Feb 26.: https://streetsofbaltimore.com/reconnecting-communities-in-west-baltimore

[5]

City of Baltimore. Baltimore Transit Data: Bus Routes [Internet]. Baltimore, MD: City of Baltimore; 2025 [cited 2025 Jan 7]. : https://data.baltimorecity.gov/datasets/d17c836e96324823b989378735b52249_0/about

[6]

City of Baltimore. Baltimore Transit Data: Bus Stops [Internet]. Baltimore, MD: City of Baltimore; 2025 [cited 2025 Jan 7].: https://www.google.com

[7]

Boeing, G. 2024. “Modeling and Analyzing Urban Networks and Amenities with OSMnx.” Working paper: https://geoffboeing.com/publications/osmnx-paper/

[8]

OpenStreetMap contributors. OpenStreetMap [Internet]. [place of publication unknown]: OpenStreetMap Foundation; 2025 [cited 2025 Jan 10]: https://www.google.com

[9]Maryland Department of Transportation. MDOT SHA Annual Average Daily Traffic (AADT) Locations [Internet]. Baltimore, MD: Maryland Department of Transportation; 2025 [cited 2025 Jan 10]: https://data.imap.maryland.gov/datasets/maryland::mdot-sha-annual-average-daily-traffic-aadt-locations/explore

 

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