2023年HIMCM美國中學數學建模競賽B題

文章目錄[隱藏]

中文賽題：推進電動公交車
- 術語表
- 參考資料
Problem: Charging Ahead with E-buses
- Glossary
- References

中文賽題：推進電動公交車

全球各城市電動公交車（簡稱 e-bus）的普及代表了可持續城市交通的重要進展。隨著對空氣汙染和氣候變化擔憂的不斷增加，許多城市被促使重新考慮他們(men) 對傳(chuan) 統柴油公交車的依賴。根據彭博新能源財經最新的一份報告^[1]，預計在2032年前，電動公交車將成為(wei) 全球道路上大多數公交車的主導型號。中國在這一轉變中尤為(wei) 值得關(guan) 注，因為(wei) 中國擁有世界上大多數電動公交車，這在很大程度上是由於(yu) 政府優(you) 先考慮電動車輛和嚴(yan) 格的排放標準的政策所驅動的。

全球各地的城市（例如哥倫(lun) 比亞(ya) 波哥大、美國紐約和德國柏林等）也正在積極努力將電動公交車納入其公交車隊，盡管進展較為(wei) 緩慢。

電動公交車不僅(jin) 環保，而且由於(yu) 電池價(jia) 格下降和運營費用降低，預計從(cong) 長遠來看也將具有成本效益。政府的激勵措施（如美國2023年兩(liang) 黨(dang) 基礎設施法案為(wei) 美國電動公交項目分配了17億(yi) 美元^[1]）進一步推動了電動公交車的普及。然而，電動公交車的推廣也麵臨(lin) 很多挑戰：包括高昂的初始成本、充電基礎設施的建造、漫長的充電時間以及潛在的續航裏程限製。

構建一個(ge) 模型，幫助城市了解過渡到全電動公交車的生態結果。選擇一個(ge) 擁有至少50萬(wan) 人口的大城市，該地區目前的公交車還沒有實現全部電動化。將您的模型應用於(yu) 你所選擇的這個(ge) 城市。
錢很重要。構建一個(ge) 模型，重點關(guan) 注於(yu) 升級為(wei) 電動公交車的相關(guan) 財務影響。您的模型應考慮潛在的外部資金，最多可覆蓋50%的過渡成本。將你的財務模型應用於(yu) 前一個(ge) 問題中你所選取的城市。
城市的交通官員正在探索逐漸將公交車從(cong) 燃油引擎轉變為(wei) 電動引擎的途徑。假設目標是在2033年之前實現全部公交車的電動化，請利用你之前開發的模型製定一個(ge) 10年的路線圖，城市交通主管部門可以利用該路線圖來規劃電動公交車的升級。請將你的模型（或新模型）應用於(yu) 前一個(ge) 問題中所選取的城市。此外，你還需額外選取兩(liang) 個(ge) 大城市，並將模型應用到這兩(liang) 個(ge) 城市。
針對你所選取的其中一個(ge) 城市，給這個(ge) 城市的交通官員寫(xie) 一封一頁的信，在信中詳細說明你們(men) 對他們(men) 升級電動公交車的建議。

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：HiMCM 提交的完整解決(jue) 方案沒有特定的最低頁數要求。您可以使用最多 25 頁的總頁數來展示您所有的解決(jue) 方案工作和任何您想包含的額外信息（例如：圖紙、圖表、計算、表格）。部分解決(jue) 方案也是可以接受的。我們(men) 允許謹慎使用AI，如ChatGPT。如果你選擇使用生成性 AI，就必須遵守 COMAP AI 使用政策：你必須在 PDF 解決(jue) 方案文件的末尾添加一個(ge) 額外的 AI 使用報告，這個(ge) 報告不計入您解決(jue) 方案的 25 頁總頁數限製。

術語表

電動公交車（簡稱 e-bus）是指其推進和附屬係統完全由零排放的電源供電的公交車。

大城市：包含大量人口核心區域，以及與(yu) 該核心區域經濟和社會(hui) 高度整合的相鄰社區。

參考資料

[1]Electric Vehicle Outlook 2023:https://about.bnef.com/electric-vehicle-outlook

[2]Biden-Harris Administration Announces Nearly $1.7 Billion to Help Put Better, Cleaner Buses on the Roads in Communities Across the Country:https://www.transit.dot.gov/about/news/biden-harris-administration-announces-nearly-17-billion-help-put-better-cleaner-buses

Problem: Charging Ahead with E-buses

The proliferation of electronic buses (e-buses) in cities across the globe represents a significant stride toward sustainable urban transport. With the mounting concerns over air pollution and climate change, many cities have been prompted to reconsider their reliance on traditional diesel buses. According to a recent report by Bloomberg New Energy Finance^[1], e-buses are set to dominate the public transit sector, becoming the majority of all buses on the road globally by 2032. China has been particularly noteworthy in this transition, as it is home to most of the world's e-buses, driven in large part by government policies that prioritize electric vehicles and stringent emission standards. Cities throughout the world (e.g., Bogota, Colombia, New York, USA, and Berlin, Germany) are also making concerted efforts to incorporate e-buses into their fleets, albeit at a more gradual pace.

E-buses aren't only environmentally appealing but are also anticipated to be cost-effective in the long run due to falling battery prices and lower operational expenses. Governmental incentives, such as the $1.7 billion allocation from the 2023 Bipartisan Infrastructure Law for e-bus projects in the U.S.^[2], further bolster e-bus adoption. However, challenges include high initial costs, charging infrastructure development, lengthy charging times, and potential range limitations.

Construct a model to aid cities in understanding the ecological consequences of transitioning to an all-electric bus fleet. Identify a metropolitan area with a population of (at least) 500,000 people that does not currently have a fully electric bus fleet. Apply your model to your chosen location.
Money matters. Construct a model that focuses on the financial implications associated with a conversion to e-buses. Your model should factor in potential external funding covering up to 50% of the transition costs. Apply your financial model to the same metropolitan area you used in the previous question.
Transportation officials in metropolitan areas are exploring approaches in which they gradually change their fleet from combustion engines buses to electric. Assuming the goal is to have a fully electric fleet no later than 2033, utilize your previously developed models to craft a 10-year roadmap that urban transport authorities can leverage to plan their e-bus fleet updates. Apply your models (or new model) to the same metropolitan area you used in the previous question and also apply it to two additional metropolitan areas of your choosing.
Write a one-page letter to the transportation officials of one of your chosen metropolitan areas in which you detail your recommendation for their transition to e-buses.

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 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.

Glossary

AnElectric Bus (e-bus)is any bus whose propulsion and accessory systems are powered exclusively by a zero-emissions electricity source.

Metropolitan Area: a core area containing a large population nucleus, together with adjacent communities that have a high degree of economic and social integration with that core.