2020A题原文

Problem: Funding Biodiversity Conservation

Background: Thousands of species of plants and animals face threats that could result in their extinction, while biodiversity conservation actions that could save them are often available. Conservation managers face difficult decisions when there is limited funding for biodiversity conservation. Managers need to decide which projects they should fund to best achieve their objectives, not the least of which is to save the most species. This is particularly important if the benefits of certain conservation actions vary across projects, the costs of these actions for specific projects differ, and the available funding for these actions is considerably less than is needed to support all proposed projects.

One issue that makes this a more difficult problem is the varying timeline and life cycle of each project. Conservation projects can take years or decades, and the schedule of when costs are incurred during the project can vary significantly depending on the project's scope, location, targeted species, and responsible agency. This means that budgets for conservation projects must provide adequate funds for the entire lifetime of the project. Additionally, managers need to closely monitor their budgets to efficiently allocate funds as demand for resources vary across projects and time. For example, they need to ensure they have adequate resources available for times when some projects require more funding, and take advantage of times when some projects require less.

Objective: Determine how to efficiently invest in biodiversity conservation activities for endangered and threatened species that take place over long time frames, and whose expected costs change over that time.

HiMCM Case: Prioritize Action and Funding for Plant Conservation in Florida (USA)
Florida is one of the hotspots for plant biodiversity conservation, with 20\% of its species imperiled. Only 2\% of these plant species (~64) receive protection under the US Endangered Species Act (ESA), but funding is currently inadequate for protecting even this limited number of species. The Florida Rare Plant Conservation Endowment (FRPCE) (see Attachment A) is a trust fund spearheaded by conservation managers to provide funds over time to support research, protection, and conservation of rare and imperiled plant species found in Florida. This trust fund aims to generate an adequate endowment to pay for both the up-front costs of conservation and the long-term costs that are currently difficult to meet with traditional fundraising campaigns.

Requirements:

1. Given the need to recover imperiled plant species in Florida and manage them into the future, develop a model to advise the FRPCE Board of the minimum fundraising required for "long-term and reliable" funding. For the purposes of this HiMCM problem, we will limit our analysis to the 48 imperiled species included in the attached data set (Attachment B). Note that each row in the database indicates a recovery project for a species.

a. Identify and discuss relevant objectives that the FRPCE Board should consider in their conservation efforts and budgeting decisions. Using these objectives, what measures would you use to evaluate a proposed fundraising plan as being the "best\?"

b. List and address some general characteristics of imperiled plant species. Indicate the factors involved in these species' protection that you will use in your decision model.

c. Develop a model or algorithm (or set of models or algorithms) for the FRPCE Board to use to determine a fundraising schedule (money required with timeline) that will minimize the funds required to be raised, yet still obtain the necessary resources to implement the recovery projects for our 48 species and manage them into the future.

2. Apply your model to recommend to the FRPCE Board a priority order of funding for the recovery projects that will manage balancing the funds available with the spending required on these projects over time. Discuss your recommendation.

3. Write a one-page non-technical memo to the FRPCE Board explaining your results, and make recommendations based on your modeling and analysis.

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

• One-page Summary Sheet.
• Table of Contents.
• Your complete solution.
• One-page Memo.
• References list.

Note: The HiMCM Contest now has a 25 page limit. All aspects of your submission count toward the 25 page limit (Summary Sheet, Table of Contents, Reference List and any Appendices).

Attachments:

Attachment A: A Conservation Endowment For Imperiled Plants In Florida

Attachment B: HiMCM2020ProblemB_ThreatenedPlantsData.xlsx

Data Fields:

unique_id: the unique plant identifier for that species.

Benefit: a measure that indicates the expected relative conservation value of funding one species over another. It takes into account information about how threatened a species is and how easy it would be to perform the conservation actions to recover it.

Taxonomic Uniqueness: a measure of the uniqueness of the species; larger number indicates greater uniqueness.

Feasibility of Success: the probability that the species will be protected from extinction if all of the actions receive funding.

Year "n" cost: the estimated recovery cost in US dollars for each row's species in the "nth" year of that project; n ∈ {1, 2, 3, … 25}.

Glossary:

Biodiversity: the amount of diversity or variety between different plants, animals, and other species in a given habitat at a particular time.

Biodiversity Conservation: the practice of protecting and preserving the great variety of species, habitats, ecosystems, and genetic diversity on the planet.

Imperiled Species: those species whose populations have decreased so dramatically that they are at risk of extinction.

Traditional Fundraising: fundraising efforts or campaigns that occur annually or on a regular schedule that involve requests for donations to attain a specific total monetary goal.

问题提出与分析

问题提出

2020年B题相较于A题更加学术化一些，研究的是如何制定最优的濒危植物保护计划。从赛题后说明的“命题”信息中也可以看到，该题目获得了亚利桑那州和佛罗里达州相关研究者的支持。

COMAP thanks researchers from Arizona and Florida for their assistance in developing this project. Upon completion of HiMCM, COMAP will recognize these researchers and their institutions on the HiMCM webpage and in our spring Consortium publication.

虽然很多同学可能都没接触过濒危植物的保护计划（笔者也是），但对于类似的学术命题，我们一定可以通过学术期刊来获取更多信息。可以确认的是“保护濒危植物”是一项有社会意义的课题，一定有研究者做过类似研究，而且预估会有很多研究。

我们这里先抛开其他学者的研究，从题目介绍的背景信息我们可以梳理得到：

• 保护计划往往资金有限；
• 决策者需要确立好目标以判断哪些项目需要做，哪些项目要优先做；
• 项目的实施受到资金、时间跨度、物种本身的特点等诸多因素影响。

简而言之，**如何在有限资金情况下，制定最优的保护计划？**

问题分析

题目所提供的信息

2020年B题提供的信息本身就是很丰富的，主要包括：

• 问题目标、限制条件、建模方向等。这些可以通过问题123来进行仔细体会和梳理；
• 数据资源。要解决问题本身附带数据信息，并不需要额外去寻找数据来建模；
• 资源链接。提供了相关网站、论文进行参考。

重述问题123：

1. 利用题目提供的数据集(附件B) a. 确立濒危植物保护计划的目标 b. 列出濒危植物物种的一般特征 c. 建立模型或算法以最小化整个保护时间内筹集所需的资金。
2. 应用模型，确定保护计划的优先顺序，以便平衡这段时间的收支。
3. 向FRPCE委员会写一页非技术备忘录，解释你的结果，并提出建议。

重述问题后我们大概可以理出解决问题的大致顺序：

1. 确定优化目标及相关因素（哪些因素影响保护计划“优劣”，将其综合成一个目标函数）；
2. 建立模型确定何时资助哪些项目（项目开始的时间是要决定的首要决策变量）；
3. 将模型用于数据集获得具体时间表；
4. 撰写备忘录及论文。

数据给我们提供了更多信息： 数据共有48个样本，29列特征，我这里仅展示前4行前7列数据： 每一个样本都有ID('unique_id'),益处('Benefit'),独特性('Taxonomic Uniqueness'),成功率('Feasibility of Success'), 第n年的花费('Year #n cost'，这里最长的花费年限是25年）。
通过数据，我们可以获得保护濒危植物要考虑的重要因素（问题1b），不过这还不够，仅靠数据中提供的指标名称和题目中给的名词解释

unique_id: the unique plant identifier for that species.

Benefit: a measure that indicates the expected relative conservation value of funding one species over another. It takes into account information about how threatened a species is and how easy it would be to perform the conservation actions to recover it.

Taxonomic Uniqueness: a measure of the uniqueness of the species; larger number indicates greater uniqueness.

Feasibility of Success: the probability that the species will be protected from extinction if all of the actions receive funding.

Year "n" cost: the estimated recovery cost in US dollars for each row's species in the "nth" year of that project; n ∈ {1, 2, 3, … 25}.

对于一个不熟悉该领域的同学而言也是很抽象的，我们需要更多的信息和知识来支撑我们对上述数据的使用。接下来我们结合题目中给的资源信息（A Conservation Endowment For Imperiled Plants In Florida），同时进一步检索相关文献（使用google scholar谷歌学术搜索关键词或问题。 这里我以检索词“efficiently invest in biodiversity conservation activities for endangered and threatened species" 进行文献检索： 检索的结果还是比较理想的，至少从圈出的红框的标题来看，我们要解决的问题还是贴近的，甚至从题目上我们也可以获得一些建模思路的启发，如：

• maximizing return on investment
• Evaluating the effectiveness and efficiency of biodiversity conservation spending

调整检索关键词，并对于感兴趣的文章标题和摘要(abstract)进行筛选，先下载10-20篇论文进行阅读和思路梳理，获得一个相对丰富的文献视野，然后再具体进行下一步的模型构建。

从我个人的阅读收获来看，已有的学术论文已经探讨过诸如问题1a，1b类似的问题，也给出过不同的规划模型，但肯定没有针对这份具体数据的研究。我们同学可以充分站在前人的肩膀上，然后给出针对本题的合适的模型。

---

import pandas as pd

data = pd.read_excel('data/HiMCM2020ProblemB_ThreatenedPlantsData.xlsx')

data.iloc[:4,:7].columns

Index(['unique_id', 'Benefit', 'Taxonomic Uniqueness',
       'Feasibility of Success', 'Year 1 cost', 'Year 2 cost', 'Year 3 cost'],
      dtype='object')