2017年美国大学生数学建模竞赛F题优秀论文解读

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2017年美赛F题赛题

2017ICM Problem F: Migration to Mars: Utopian Workforce of the 2100 Urban Society

Theinternational agency, Laboratory of Interstellar Financial & ExplorationPolicy (LIFE), has recently (in this year of 2095) completed a series ofshort-term planned living experiments on our neighbor planet, Mars. Newtechnologies, including personalized artificial augmentations units, will soonenable humans to inhabit manufactured cities on Mars by 2100. The first wave ofmigration, called Population Zero, will include 10,000 people.

TheLIFE agency launched project UTOPIA: 2100, with the goal of creating an optimalworkforce for the 22nd century to give all people the greatest quality of lifewith a vision of sustainability for the next 100 years. Over the last 20 years,several planned communities have been designed and built across Earth thattested several planned living conditions. These communities are driven byegalitarian principles in economics, government, workforce, and justicesystems.

LIFEis seeking a set of mathematical and computational models that will inform theInternational Coalition on Mars (ICM) government on how to design aneconomicworkforce-education system that they can implement with PopulationZero. In order to decide what procedure to follow, LIFE has hired the mostqualified policy makers and data scientists with the goal to develop a set ofpolicies to realize the migration to Mars. Your three-person policy modelingteam is part of the group of advisors and policy makers. ICM has asked yourgroup for a policy model and report that will result in a set of policyrecommendations that will create a sustainable life-plan and will make theliving experience on Mars in the year 2100 even better than the Earthly one inthe current year of 2095.

Newtools in network science, systems science, complex systems, organizational& industrial psychology, and other interdisciplinary fields provide newinsights for understanding social and governmental systems, with importantcapabilities to deal with issues of scalability (relevant for both small andlarge populations and effects), modality (multiple layers), and dynamics(changes over time).

PopulationZero aims to have optimal conditions in many workforce and social livingfactors (note that another team is being tasked with health policy, so ICM hasasked that you exclude health care from your analysis). The mission ofPopulation Zero is to create a sustainable society by maximizing both economicoutput (GDP) and happiness in the work place for its citizens. Of course, thesetwo goals can be in opposition, so the policy recommendation has to considerbalancing factors, such as:

●Income: Ensure adequate compensation so that all people can afford fundamentalnecessities (shelter, food, clothes).

●Education: Provide high quality education that prepares citizens for the needsand challenges of the 22nd Century.

●Equality: Improve the retention of women in the workforce, particularly infields where they have been underrepresented or discriminated against on Earth.


YourICM-directed tasks are:

1.Define parameters and specific outcomes related to the three priority factors(income, education, and social equality) in Population Zero. Some issues toconsider are: a) minimum wage and salary distribution (income); b) skillsrequired for an efficient workforce; types of governance and infrastructureneeded to obtain these skills (education); and c) maternity and paternityleave, affordable childcare to ensure people can remain in the workforce(social equality).

a.Identify and define the specific outcomes that would indicate positive resultsacross the three factors for the next decade (years 2100-2110). Consider whatthe goal is for each of these factors; for example, is the objective to improvethe quality of living for all citizens or improve quantity of output of thesystem.

b.What are the major features of the population (eg. demographics, populationsize, and working conditions) that would contribute to these outcomes?

c.Create metrics that you will use to evaluate whether the system is meeting itsobjective by identifying and defining the critical parameters for each of thethree factors.

2.You have been asked to generate a sample population of 10,000 people toemigrate to Mars. Extract data from a census dataset (link to one is providedbelow) or synthesize one.

a.From your data set, identify and analyze the demographic characteristics ofthis simulation of Population Zero. Analyze and describe demographicdistributions, such as gender, ethnicity, age, and education levels.

b.Consider the distribution of citizens in terms of factors that will also helpto meet goals of UTOPIA: 2100 – to build a peaceful, cooperative, Link to PUMSdata (if you desire to use this census data):

PUMS data can be found via following links:

http://www.census.gov/programs-surveys/acs/technicaldocumentation/pums.html

http://www2.census.gov/programs-surveys/acs/data/pums/2015/1- Year/ o

Theselinks show how to extract the data in R:

https://stat.ethz.ch/R-manual/R-devel/library/base/html/sample.html

https://cran.r-project.org/web/packages/sampling/sampling.pdf

This link show how to extract the data in MATLAB:

https://www.mathworks.com/help/stats/datasample.html?requestedDomain=www.mathworks.com

3.Build a model that includes the three identified factors (income, education,& social equality). Using the parameters that you created in task 1, definethe key elements of a successful society for the next 10 years. Whenintegrating these three factors, what are the critical interdependencies amongthe parameters? Are there additional constraints required to preserve theoutcomes over the 10 year period? How often should the model be evaluated toensure the goals of UTOPIA 2100 continue to be met? What might be economic,social, cultural, and other global factors that might affect the viability ofthe model over that period? Based on these factors and constraints, answer thefollowing:

a.Determine the optimal minimum wage and salary distribution to best manage thetension between wellbeing (higher quality of life) and support for those lessequipped to provide labor services.

b.Identify terms in your model that can be most improved through contribution ofnew ideas. Describe the incentives to motivate contribution of those new ideas.

c.What is the best childcare and paternity/maternity leave strategies?

4.Now that you have created models for the three factors, proceed to merge thesemodels into a global model. In task 3, you designed a model to provide optimaloutcomes for society, at large. Now, consider how the model will function fordifferent groups?

a.Identify the major subgroups of your workforce, and identify their mainpriorities. For example, unskilled labor force might be concerned with workhours, disability care, child care, and minimum wage, while the priorities ofthe professional workforce may be time off, training, and parental leave. Yourmodel will dictate which subgroups you consider. You might have to develop newparameters to adequately evaluate each groups’ priorities.

b.With the understanding that each group will have a different set of needs, perspectives,and criteria for success, analyze how closely their needs are met in terms ofincome, education, and equality. For example, does your model functiondifferently across educational levels? Different ages? Different culturalvalues? Does your model function better for women or men? How are familiesaffected?

c.With the consideration of the subgroups that you have identified, your previousmodel may no longer produce optimal outcomes. Adjust the model by adding newconstraints or parameters to optimize the needs of the different subgroups. Thegoal is to maximize the priority outcomes of the subgroups withoutsignificantly reducing the global outcomes.

5.LIFE has planned additional migration phased over the next 100-years.

a.How sensitive is your model to the population selection for various migrationphases? Does the demographic distribution of this population significantlychange the outcomes? How does your sampling procedure affect your model? Ifmigration and growth in future years will be similar to Population Zero (10,000people in a new manufactured city at a time), how would you change your modelfor the next few migrations? How sustainable are your recruitment and selectionprocesses?

b.Is this long-term plan substantially different than the 10-year plan? Are thereelements in your 10-year vision and recommendations that are not sustainablefor the 100 year vision? Identify any new parameters or constraints that willensure your model continues to be effective for the entire 22nd century.

6.In shocking news, scientists discover a threat of a collision of Earth with aplanet sized comet. We need to evacuate planet Earth and move as many people aspossible to Mars to live in enlarged manufactured cities.

a.Is your model still functional? Would it make a difference if migrationsoccurred in phases?

b.Study the robustness of your model and comment on its general sensitivity to amuch larger scale migration.

c.State the strengths and weaknesses of your model relative to a major migration.

7.Write a policy recommendation addressed to the director of LIFE that includesthe factors of income, education, equality policies based on your model andaccording to the directions of ICM. Will your recommendations change dependingon the composition and size of the Population Zero? Explain the reasoning thatled you to your recommendations and analyze the results you are expecting toachieve.

YourICM submission should consist of a 1 page Summary Sheet, a 1-2 page policyrecommendation, and your solution (not to exceed 20 pages) for a maximum of 23pages. Note: The appendix and references do not count toward the 23 page limit.

References:

https://www.kansascityfed.org/publications/community/transformworkforce

https://www.kansascityfed.org/~/media/files/publicat/community/workforce/transformingworkforcedevelopment/book/transformingworkforcedevelopmentpolicies.pdf

http://www.economist.com/blogs/freeexchange/2012/01/chinas-labour-force

  2017年美赛F题赛题翻译

2017年ICM问题F:向火星迁移:2100城市社会的乌托邦劳动力

国际机构,星际金融与勘探政策实验室(LIFE)最近(在今年的2095年)完成了对我们的邻居星球火星的一系列短期计划生活实验。包括个性化人工增强装置在内的新技术将很快使人类能够在2100年之前居住在火星上的制造城市。第一波迁移,称为人口零,将包括10,000人。

LIFE机构启动了项目UTOPIA:2100,其目标是为22世纪创造最佳劳动力,为所有人提供最佳生活质量,并在未来100年内实现可持续发展愿景。在过去的20年中,在地球上设计和建造了几个规划的社区,测试了几个计划的生活条件。这些社区由经济学,政府,劳动力和司法系统中的平等主义原则驱动。

LIFE正在寻求一套数学和计算模型,这将为国际火星联盟(ICM)政府提供如何设计一个他们可以与人口零度实施的经济劳动力教育系统的信息。为了确定要遵循的程序,LIFE聘请了最合格的决策者和数据科学家,目标是制定一套政策来实现向火星的迁移。您的三人政策建模团队是顾问和决策者团队的一部分。 ICM已经向您的小组询问了一个政策模型和报告,这将产生一系列政策建议,这些建议将创建一个可持续的生活计划,并将使2100年火星上的生活体验甚至比当年的地球生活体验更好。

网络科学,系统科学,复杂系统,组织和工业心理学以及其他跨学科领域的新工具为理解社会和政府系统提供了新的见解,具有处理可扩展性问题的重要能力(与小型和大型人群及影响相关)),模态(多层)和动态(随时间变化)。

人口零度旨在为许多劳动力和社会生活因素提供最佳条件(请注意,另一个团队正在执行健康政策,因此ICM要求您从分析中排除医疗保健)。人口零的使命是通过最大限度地提高公民的工作场所的经济产出(GDP)和幸福来创造一个可持续发展的社会。当然,这两个目标可能是对立的,因此政策建议必须考虑平衡因素,例如:

●收入:确保适当的补偿,以便所有人都能负担得起基本必需品(住所,食物,衣服)。

●教育:提供高质量的教育,使公民为22世纪的需求和挑战做好准备。

●平等:提高妇女在劳动力中的保留率,特别是在地球上代表性不足或受到歧视的领域。

您的ICM指导任务是:

1.确定人口零点中与三个优先因素(收入,教育和社会平等)相关的参数和具体结果。需要考虑的一些问题是:a)最低工资和工资分配(收入); b)高效劳动力所需的技能; 获得这些技能所需的治理类型和基础设施(教育); c)产假和陪产假,负担得起的儿童保育,以确保人们能够留在劳动力队伍中(社会平等)。

a)确定并确定具体结果,这些结果将表明未来十年(2100-2110年)三个因素的积极结果。考虑每个因素的目标是什么; 例如,目标是改善所有公民的生活质量或提高系统的产出量。

b)人口的主要特征(如人口统计,人口规模和工作条件)会对这些结果产生什么影响?

c)通过识别和定义三个因素中每个因素的关键参数,创建用于评估系统是否满足其目标的度量标准。

2.您被要求生成10,000人的样本人口以移民到火星。从人口普查数据集中提取数据(下面提供了一个链接)或合成一个数据集。

a)从您的数据集中,识别并分析此人口零模拟的人口统计特征。分析和描述人口统计分布,例如性别,种族,年龄和教育水平。

b)考虑公民在有助于实现UTOPIA目标的因素方面的分布:2100  - 建立和平,合作,PUMS数据链接(如果您希望使用此人口普查数据):

PUMS数据可通过以下链接找到:

http://www.census.gov/programs-surveys/acs/technicaldocumentation/pums.html

http://www2.census.gov/programs-surveys/acs/data/pums/2015/1- Year/ o

这些链接显示了如何在R中提取数据:

https://stat.ethz.ch/R-manual/R-devel/library/base/html/sample.html

https://cran.r-project.org/web/packages/sampling/sampling.pdf

此链接显示如何在MATLAB中提取数据:

https://www.mathworks.com/help/stats/datasample.htmlrequestedDomain=www.mathworks.com

3.建立一个包含三个已确定因素(收入,教育和社会平等)的模型。使用您在任务1中创建的参数,定义未来10年成功社会的关键要素。在整合这三个因素时,参数之间的关键相互依赖性是什么?是否需要额外的限制来保持10年期间的结果?应该多久评估一次模型,以确保继续满足UTOPIA2100的目标?可能影响该时期模型可行性的经济,社会,文化和其他全球因素是什么?基于这些因素和约束,请回答以下问题:

a)确定最佳的最低工资和工资分配,以最好地管理福利(更高的生活质量)与支持那些设施较差的人提供劳务服务之间的紧张关系。

b)通过新想法的贡献,确定模型中可以最大程度改进的术语。描述激励这些新想法的贡献的动机。

c)什么是最好的托儿和陪产假/产假策略?

4.现在您已经为这三个因子创建了模型,继续将这些模型合并到一个全局模型中。在任务3中,您设计了一个模型,为整个社会提供最佳结果。现在,考虑一下该模型如何适用于不同的群体?

a)确定您的员工的主要子群,并确定他们的主要优先事项。例如,非熟练劳动力可能与工作时间,残疾护理,儿童保育和最低工资有关,而专业劳动力的优先事项可能是休假,培训和育儿假。您的模型将决定您考虑的子组。您可能必须开发新参数以充分评估每个组的优先级。

b)了解每个小组将有不同的需求,观点和成功标准,分析他们在收入,教育和平等方面的需求有多接近。例如,您的模型在教育水平上的功能是否不同?不同年龄段?不同的文化价值?您的模型对女性或男性有效吗?家庭如何受到影响?

c)考虑到您已识别的子组,您之前的模型可能不再产生最佳结果。通过添加新约束或参数来调整模型,以优化不同子组的需求。目标是在不显着降低全球结果的情况下最大化子组的优先结果。

5.LIFE计划在未来100年内逐步实施额外迁移。

a)您的模型对各种迁移阶段的人口选择有多敏感?这一人口的人口分布是否会显着改变结果?您的抽样程序如何影响您的模型?如果未来几年的迁移和增长与人口零度(一次新制造城市中的10,000人)相似,那么您将如何更改下一次迁移的模型?您的招聘和选拔流程有多可持续?

b)这个长期计划与10年计划有很大不同吗?您的10年愿景和建议中是否存在不可持续的100年愿景?确定任何新的参数或约束,以确保您的模型在整个22世纪继续有效。

6.令人震惊的消息是,科学家发现了地球与行星大小的彗星碰撞的威胁。我们需要撤离地球,让尽可能多的人迁移到火星,以便生活在扩大的制造城市中。

a)你的模型还能运作吗?如果迁移分阶段发生会有所不同吗?

b)研究模型的稳健性,并评论其对更大规模迁移的一般敏感性。

d)说明模型相对于主要迁移的优缺点。

7.撰写针对LIFE主任的政策建议,其中包括基于您的模型和ICM方向的收入,教育,平等政策等因素。您的建议会根据人口零点的构成和大小而改变吗?解释导致您提出建议并分析您期望实现的结果的原因。

您的ICM提交应包含1页摘要表,1-2页政策建议和您的解决方案(不超过20页),最多23页。注意:附录和参考文献不计入23页限制。

参考文献:

https://www.kansascityfed.org/publications/community/transformworkforce

https://www.kansascityfed.org/~/media/files/publicat/community/workforce/transformingworkforcedevelopment/book/transformingworkforcedevelopmentpolicies.pdf

http://www.economist.com/blogs/freeexchange/2012/01/chinas-labour-force

 2017年美赛F题优秀论文解读

2017年美国大学生数学建模竞赛有800支队伍选择了F题,其中有4支队伍获得了特等奖。他们分别是64486、68940、72197、72283,我们对这4篇特等奖论文进行了简单的分析,结果如下:

(1)64486队伍提出了一种在可持续性范围内最大限度地提高劳动力经济产出和工作满意度的模型。建立了一个自适应系统,并对其动力学进行了定义.而且用真实世界的人口普查数据(PAMS2015[1])对该系统进行模拟,以找到最优可行的解决方案。首先,他们构建了一个参数框架,其中包含了三个方面的变量:收入、教育和社会平等。从普查数据库中存在的基本参数得出了揭示社会特征的指标。

通过层次分析法,他们确定了关键参数,其中幸福指数是评价公民幸福状况的重要综合指标。第二,他们制定了选择10000名移民的标准。第三,他们建立了一个模型来模拟种群零的动态演化。并用人口学、经济学和幸福指数详细地讨论了一个样本结果。此外,还利用这个模型找到了经济更快发展和社会福利更好这两个矛盾目标之间的平衡点。通过对人口数据进行主成分分析,他们将成功社会的关键要素定义为高平均家庭收入、高最低工资和低标准差。并采用遗传算法求解三目标优化问题.接下来,他们将收入、教育和社会平等的模型合并成一个全球模型,并在不同的社会群体中进行检验。他们将这些子组划分为专业工人和非熟练工人。建立了一个非线性规划模型,确定了不同子组之间的资源分配策略。最后从复杂网络理论的角度研究移民潮的影响。他们建立了一个无标度的复杂网络,用拥有小型的世界财产以代表包括火星居民和新移民在内的所有个人之间的人际关系。

(2)68940队伍建立了一个agent-based的模型,利用美国人口普查局的职业收入数据,模拟火星上1万名代理商的真实世界数据。为了最大限度地提高社会福利和生产力,他们选择了监测经济状况,并制定衡量基于代理的因素对社区福祉的影响的指标。测量了这些代理产生的社区的多个参数,这使得我们能够评估经济状况。根据这些参数,我们生成了三个度量指标:收入度量I、教育度量E和平等度量Q。此外,他们的模型还包括几个经济指标和特性,如通货膨胀率、累进税制、总投资和政府债务等。利用他们的模型,他们发现最佳初始人口的平均年龄为37岁,创新者与生产者的比例为1:10。对他们的指标的分析表明,假设存在基础设施,火星社会可以支持1万多人从地球上紧急迁移。事实证明,政府控制通货膨胀对维持人民的购买力至关重要。

(3)72197队伍发现地球上的人类文明日益受到收入不平等、非生产性教育系统和基于性别的歧视的困扰。在了解了这一问题的复杂性之后,他们的模型侧重于改进这三个缺点。在收入模式中,他们的目标是通过实施北欧社会模式来减少收入不平等。因此,他们的最低工资是20,000元,而累进税率则会随入息而增加,直至上限达到50%为止。他们用基尼系数来衡量不平等,把它从0.58降到0.33,这接近北欧的水平。在教育模式中,他们使用加权决策矩阵,根据不同学科对社会所支持的价值观和经济应用领域的贡献,对不同学科进行排序。在社会平等模型中,利用机会成本分析方法,根据托儿费用和其他人口数据,模拟男女劳动力的保留率。从这里,确定了7,500美元的标准托儿费用以及同等长度的产假和陪产假。他们将教育和社会平等模式与所得税模式结合起来,以验证其政策在经济上是可行的。在尝试建立一个乌托邦社会时,他们也考虑到他们的模式在其范围上的局限性。

(4)72283队伍创建一组定量支持的模型,以评估人口零度火星上的殖民地的各种属性和结果。首先,他们为三个优先级因素中的收入,教育和平等定义了重要的指标和评估标准。将收入分解为经济效率和经济平等,他们决定将GDP,基尼系数和社会最低工资作为主要指标。最后,从性别和文化角度考虑了平等,使用了一种称为不相似的度量。当被要求分析人口统计数据和人口因素零对火星上殖民地的结构和目标至关重要时,他们通过维度分析确定了火星上的农民生产力与基本的人类消费需求,大约25%的零人口将是农民。此外,准马尔可夫链模型使他们能够确定年龄的最佳初始分布,并且通过逻辑,我们将人口平均分为男性和女性。接下来,他们通过为每个优先领域开发模型,将先前确定的指标应用于收入,教育和平等。他们基于不同的模拟揭示了收入平等和社会平等之间的权衡,我们发现了一个合理长度的育儿假。随后,他们将三个模型整合为一个模型,以评估不同子群体在社会中的满意度,作为我们主要优先领域的一个功能。在他们的每个关键参数(如GDP和不相似性)上开发并应用基于数据的权重,他们发现关键参数的值是强值。他们意识到移民可以通过多种方式进行,我们分析了三种截然不同的移民方法/政策对年龄分布和经济影响的影响,以便了解哪些移民方法/政策相对可持续。继而发现,逐渐迁移是将新种群引入原始殖民地的最佳形式。


        

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