2015美国大学生数学建模竞赛题目(带中文翻译)
2015年美国数学建模竞赛第二次模拟赛题
Problem A Warmer Days or Sour Grapes ?The high quality of wines（葡萄酒）produced in the Finger Lakes Region（五指湖区）of upstate （北部）New York is widely known. Proximity（接近）to lakes tempers the climate and makes it more suitable for growing several varieties of premium（独特）grapes: R iesling（雷司令）, G ewürztraminer（琼瑶浆）,C hardonnay（霞多丽）, M erlot（梅洛）, P inot Noir（黑比诺）, and CabernetF ranc（品丽珠）. (There are many more, but we will restrict（限制）the discussion to these six to simplify（简化）the modeling.) Each variety has its own preferred “average temperature” range but is also different in its susceptibility（感受性）to diseases and ability to withstand（抵抗）short periods of unusually cold temperature.As our local climate changes, the relative suitability of these varieties will be changing as well. A forward-looking winery（酒厂）has hired your team to help with the long-term planning. You will need to recommenda) the proportion（比例）of the total vineyard（葡萄园）to be used for growing each of the above six varieties;b) and when should these changes be implemented （实施）(based on observed temperatures and/or current market prices for each type of wine).Naturally, the winery is interested in maximizing its annual profit. But since the latter （后者）is weather-dependent, it might vary a lot year-to-year. You are also asked to evaluate the trade-offs （权衡）between optimizing the expected/average case versus the worst(-realistic-)scenario（情景）.Things to keep in mind:Climate modeling is complicated（复杂）and predicting the rate of “global warming” is a hotly debated area. For the purposes of this problem, assume that the annual average temperature in Ithaca（伊萨卡）, NY will increase by no more than 4°C by the end of this century.It is not all about the average temperature – a short snap（临时）of sub- zero（零度）temperature in late Ferburay or early March (after the vines already started getting used to warmer weather) is far more damaging than the same low temperature would be in the middle of the winter.It takes at least 3 years for a newly planted vine to start producing grapes suitable for winemaking.Problem B Outlook of Car-to-Car TechSAN FRANCISCO -- After more than a decade of research into car-to-car communications, U.S. auto safety regulators took a step forward today by unveiling their plan for requiring cars to have wireless gear that will enable them to warn drivers of danger.These vehicle-to-vehicle (V2V) transmitters and software could save thousands of lives and prevent hundreds of thousands of crashes each year by providing cars with information they never will be able to gather simply from cameras and sensors. “Safety is our top priority, and V2V technology represents the next great advance in saving lives,” Transportation Secretary Anthony Foxx said in an announcement. “This technology could move us from helping people survive crashes to helping them avoid crashes altogether.”Requirement 1: Present a mathematical model to discuss the reduction of the number of traffic accidents and road fatalities/injuries in San Francisco by V2V technology. Requirement 2: Determine the maximum number of cars in San Francisco due to the V2V technology.Requirement 3: Discuss the benefits of V2V technology to alleviate road congestion. Requirement 4: Provide your recommendation to the government.Prblem C Forest FiresOne major environmental concern is the occurrence of forest fires (also called wildfires), which affect forest preservation, bring economical and ecological damage and endanger human lives. Such phenomenon is due to multiple causes (e.g. human negligence and lightnings). Despite an increasing of state expenses to control this disaster, each year millions of forest hectares (ha) are destroyed all around the world.Fast detection is an important element for successful firefighting. Traditional human surveillance is expensive and affected by subjective factors, there has been an emphasis to develop automatic solutions, such as satellite-based, infrared/smoke scanners and local sensors (e.g. meteorological). Propagation models try to describe the future evolution of the forest fire given an initial scenario and certain input parameters. Modeling the dynamical behavior of fire propagation in a forest is helpful for creating scheme to control and fight fire.Requirement 1 Describe several different metrics that could be used to evaluate the effectiveness of fire detection. Could you combine your metrics to make them even more useful for measuring quality?Requirement 2 Model the dynamical behavior of fire spread in a forest. Requirement 3 Discuss the factors to affect fire occurrence. Which factors are the most critical in causing fires. Build mathematical models to predict the burned area of fires using Meteorological Data.Requirement 4 Give y our suggestion for preventing from forest fire and fighting against it.Problem D Wearable Activity RecognitionThe percentage of EU citizens aged 65 years or over is projected to increase from 17.1% in 2008 to 30.0% in 2060. In particular, the number of 65 years old is projected to rise from 84.6 million to 151.5 million, while the number of people aged 80 or over is projected to almost triple from 21.8 million to 61.4 million (EUROSTAT: New European Population projections 2008–2060). It has been calculated that the purely demographic effect of an ageing population will push up health-care spending by between 1% and 2% of the gross domestic product (GDP) of most member states. At first sight this may not appear to be very much when extended over several decades, but on average it would in fact amount to approximately a 25% increase in spending on health care, as a share of GDP, in the next 50 years (European Economy Commission, 2006). The effective incorporation of technology into health-care systems could therefore be decisive in helping to decrease overall public spending on health. One of these emerging health-care systems is daily living physical activity recognition.Daily living physical activity recognition is currently being applied in chronic disease management (Amft & Troter, 2008; Zwartjes, Heida, van Vugt, Geelen, & Veltink, 2010), rehabilitation systems (Sazonov, Fulk, Sazonova, & Schuckers, 2009) and disease prevention (Sazonov, Fulk, Hill, Schutz, & Browning, 2011; Warren et al., 2010), as well as being a personal indicator to health status (Arcelus et al., 2009). One of the principal subjects of the health related applications being mooted is the monitoring of the elderly. For example, falls represent one of the major risks and obstacles to old people’s independence (Najafi, Aminian, Loew, Blanc, & Robert, 2002; Yu, 2008). This risk is increased when some kind of degenerative disease affects them. Most Alzheimer’s patients, for exa mple, spend a long time every day either sitting or lying down since they would otherwise need continuous vigilance and attention to avoid a fall.The registration of daily events, an important task in anticipating and/or detecting anomalous behavior patterns and a primary step towards carrying out proactive management and personalized treatment, is normally poorly accomplished by patients’ families, healthcare units or auxiliary assistants because of limitations in time and resources. Automatic activity-recognition systems could allow us to conduct a completely detailed monitoring and assessment of the individual, thus significantly reducing current human supervision requirements.Most wearable activity recognition systems assume a predefined sensor deployment that remains unchanged during runtime. However, this assumption does not reflect real-life conditions. During the normal use of such systems, users may place the sensors in a position different from the predefined sensor placement. Also, sensors may move from their original location to a different one, due to a loose attachment. Activity recognition systems trained on activity patterns characteristic of a given sensor deployment may likely fail due to sensor displacements.Your task is as follows.(1) Build models to recognize daily living activities.(2) Explore the effects of sensor displacement induced by both the intentionalmisplacement of sensors and self-placement by the user.(3) Verify your recognition models’ toleranc e to sensor displacement.Data Set Information:The REALDISP (REAListic sensor DISPlacement) dataset has been originally collected to investigate the effects of sensor displacement in the activity recognition process in real-world settings. It builds on the concept of ideal-placement, self-placement and induced- displacement. The ideal and mutual-displacement conditions represent extreme displacement variants and thus could represent boundary conditions for recognition algorithms. In contrast, self-placement reflects a users perception of how sensors could be attached, e.g., in a sports or lifestyle application. The dataset includes a wide range of physical activities (warm up, cool down and fitness exercises), sensor modalities (acceleration, rate of turn, magnetic field and quaternions) and participants (17 subjects). Apart from investigating sensor displacement, the dataset lend itself for benchmarking activity recognition techniques in ideal conditions.Dataset summary:#Activities: 33#Sensors: 9#Subjects: 17#Scenarios: 3ACTIVITY SET:A1: WalkingA2: JoggingA3: RunningA4: Jump upA5: Jump front & backA6: Jump sidewaysA7: Jump leg/arms open/closedA8: Jump ropeA9: Trunk twist (arms outstretched)A10: Trunk twist (elbows bent)A11: Waist bends forwardA12: Waist rotationA13: Waist bends (reach foot with opposite hand)A14: Reach heels backwardsA15: Lateral bend (10_ to the left + 10_ to the right)A16: Lateral bend with arm up (10_ to the left + 10_ to the right)A17: Repetitive forward stretchingA18: Upper trunk and lower body opposite twistA19: Lateral elevation of armsA20: Frontal elevation of armsA21: Frontal hand clapsA22: Frontal crossing of armsA23: Shoulders high-amplitude rotationA24: Shoulders low-amplitude rotationA25: Arms inner rotationA26: Knees (alternating) to the breastA27: Heels (alternating) to the backsideA28: Knees bending (crouching)A29: Knees (alternating) bending forwardA30: Rotation on the kneesA31: RowingA32: Elliptical bikeA33: CyclingSENSOR SETUP:Each sensor provides 3D acceleration (accX,accY,accZ), 3D gyro (gyrX,gyrY,gyrZ), 3D magnetic field orientation (magX,magY,magZ) and 4D quaternions (Q1,Q2,Q3,Q4). The sensors are identified according to the body part on which is placed respectively:。
(最新整理)数学建模美赛试题
2015数学建模美赛试题编辑整理：尊敬的读者朋友们：这里是精品文档编辑中心，本文档内容是由我和我的同事精心编辑整理后发布的，发布之前我们对文中内容进行仔细校对，但是难免会有疏漏的地方，但是任然希望（2015数学建模美赛试题）的内容能够给您的工作和学习带来便利。
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地球资源的消耗速度快,越来越多的人关注人类社会的未来.自1960年以来，已经有许多专家研究可持续发展.然而大多数人的研究对象是整个世界，一个国家或一个地区。
几乎没有人选择48个最不发达国家(LDC)在联合国为研究对象列表。
然而,LDC国家集团共享许多相同的点。
他们的发展道路也有法律的内涵。
本文选择这些国家为研究对象针对发现常规的可持续发展道路。
本文组织如下.第二部分介绍研究的背景和本研究的意义。
第三节描述了我们对可持续发展的理解细节和显示我们的评估系统的建立过程和原理，那么我们估计每一个国家的LDC和获得可持续发展的能力和等级。
第四节提供了一个最糟糕的国家毛里塔尼亚计划指数在第三节。
第五节演示了在第四节的合理性和可用性计划。
最后在第六节总结本文的主要结论和讨论的力量和潜在的弱点。
地球上的资源是有限的。
三大能源石油、天然气和煤炭可再生。
如何避免人类的发展了资源枯竭和实现可持续发展目标是现在的一个热门话题.在过去的两个世纪,发达国家已经路上,先污染，再控制和达到高水平的可持续发展。
发展中国家希望发展和丰富。
然而,因为他们的技术力量和低水平的经济基础薄弱,浪费和低效率的发展在这些国家是正常的.所以本文主要关注如何帮助发展中国家特别是48在联合国最不发达国家实现可持续发展是列表可持续发展的理解是解决问题的关键.可持续发展的定义经历了一个长期发展的过程.在这里，布伦特兰可持续发展委员会的简短定义的"能力发展可持续- — - — - -以确保它既满足现代人的需求又不损害未来的能力代来满足自己的需求"［1]无疑是最被广泛接受的一个在各种内吗定义.这个定义方面发挥了重要作用在很多国家的政策制定的过程.然而，为了证明一个国家的现状是否可持续不可持续的,更具体的定义是必要的更具体的概念,我们认为,如果一个国家的发展是可持续的,它应该有一个基本的目前的发展水平，一个平衡的国家结构和一个光明的未来。
2015年美国数学建模竞赛B题一等奖
Team# 39600
Page 1 of 53
Controlling Epidemic Situation of Ebola
Contents
1 Introduction .................................................................................................................................... 3 2 Model Overview ............................................................................................................................ 4 3 Common Assumptions ................................................................................................................... 5 4 Model ............................................................................................................................................. 6 4.1 Improved SIR Model .......................................................................................................... 6 4.1
2015美国大学生数学建模竞赛D题
1.2 Our work
We tackle four main sub problems: Factors affecting the evaluation of sustainable development of a country are analyzed based on the theory of sustainable development. Develop a model for the sustainability of a country. This model should provide a measure to distinguish more sustainable countries and policies from less sustainable ones. Choose from forty-eight poorest countries LDC country, according to the model of a task1 has been established for the selected countries to create a more sustainable development plan in the next 20 years in the development process, so that the country toward a more sustainable future. Evaluate the effect our 20-year sustainability plan has on our country’s sustainability measure created in Task 1. And predicted under the evaluation system to implement our plan will happen the change over the next 20 years. According to the selected country, we should consider the environmental factors, Climate change, development aid, foreign investment, natural disasters, and the instability of the regime, etc. We determine which project or policy for the sustainable development measures of the state will have the greatest effect. Write a report to explain the established model, including sustainable development, sustainable development plans, according to the model and the national environmental situation, analysis the effect of the plan. For the ICM provides a sustainable development of intervention strategy about investment in LDC countries.
2015 ICM C翻译(全美数学建模C题)
2015 ICM Problem CManaging Human Capital in Organizations组织中的人力资本管理Building an organization filled with good, talented, well-trained people is one of the keys to success. But to do this, an organization needs to do more than recruit and hire the best candidates – they also need to retain good people, keep them properly trained and placed in proper positions, and eventually target new hires to replace those leaving the organization. Individuals play unique roles within their organizations, both formally and informally. Thus, the departure of individuals from an organization leaves important informational and functional components missing that need to be replaced. This is true for sports teams, commercial companies, schools and universities, governments, and almost any formal group or organization of people.构建一个组织填充好，有才华的，训练有素的人是成功的关键之一。
2015年美国(国际)大学生数学建模竞赛
比赛时间：美国东部时间：2015年2月5日（星期四）下午8点-2月9日下午8点（共4天）北京时间：2015年2月6日（星期五）上午9点-2月10日上午9点农历：十二月十八～十二月廿二重要说明：●COMAP是所有的规则和政策的最后仲裁者，对不遵循竞赛规则和程序的任何队伍，拥有唯一的自由裁量权，取消参赛资格或拒绝登记。
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比赛之前注册报名1.报名截至时间：2015年2月5日下午2：00 EST。
截止日期后，注册系统将自动关闭，不再接受任何新的注册，没有例外。
2.每支参赛队伍都必须有一位来自参赛机构（institute）的教师担任导师（faculty advisor），不允许学生担任导师。
由指导老师负责为其指导队伍注册报名，每位指导老师可注册的队伍数目没有限制。
2015数模美赛A题翻译
PROBLEM A: Eradicating EbolaThe world medical association has announced that their new medication could stop Ebola and cure patients whose diseases not advanced. Build a realistic, sensible, and useful model that considers not only the spread of the disease, the quantity of the medicine needed, possible feasible delivery systems, locations of delivery, speed of manufacturing of the vaccine or drug, but also any other critical factors your team considers necessary as part of the model to optimize the eradication of Ebola, or at least its current strain. In addition to your modeling approach for the contest, prepare a 1-2 page non-technical letter for the world medical association to use in their announcement.A消除埃博拉病毒世界医学协会已经宣布他们的新疗法可以阻止埃博拉疫情和治愈非晚期患者。
构建一个现实的、合理的和有用的模型,不仅要考虑疾病的传播,所需药物的数量,可能且可行的给药系统,给药地点,生产疫苗或药物的速度,而且还要考虑其他关键因素（你的团队认为有必要要考虑的）作为模型的一部分以优化消除埃博拉病毒，或至少是现行毒株。
数学建模美赛题目及翻译
PROBLEM A: The Keep-Right-Except-To-Pass Rule The Keep-Right-Except-To-Pass RuleIn countries where driving automobiles on the right is the rule (that is, USA, China and most other countries except for Great Britain, Australia, and some former British colonies), multi-lane freeways often employ a rule that requires drivers to drive in the right-most lane unless they are passing another vehicle, in which case they move one lane to the left, pass, and return to their former travel lane.Build and analyze a mathematical model to analyze the performance of this rule in light and heavy traffic. You may wish to examine tradeoffs between traffic flow and safety, the role of under- or over-posted speed limits (that is, speed limits that are too low or too high), and/or other factors that may not be explicitly called out in this problem statement. Is this rule effective in promoting better traffic flow? If not, suggest and analyze alternatives (to include possibly no rule of this kind at all) that might promote greater traffic flow, safety, and/or other factors that you deem important.In countries where driving automobiles on the left is the norm, argue whether or not your solution can be carried over with a simple change of orientation, or would additional requirementsbe needed.Lastly, the rule as stated above relies upon human judgment for compliance. If vehicle transportation on the same roadway was fully under the control of an intelligent system – either part ofthe road network or imbedded in the design of all vehicles using the roadway – to what extent would this change the results ofyour earlier analysis?问题A ：除非超车否则靠右行驶的交通规则在一些汽车靠右行驶的国家（比如美国，中国等等），多车道的高速公路常常遵循以下原则：司机必须在最右侧驾驶，除非他们正在超车，超车时必须先移到左侧车道在超车后再返回。
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Teams (Student or Advisor) are now required to submit an electronic copy (summary sheet and solution) of their solution paper by email too solutions@ as a Word or PDF attachment. Your email MUST be received at COMAP by the submission deadline of 8:00 PM EST, February 9, 2015. Note you will not receive an auto response.
Subject line
COMAP your control number
Example: COMAP 11111
Click here to download a PDF of the complete contest instructions.
Click here to download a copy of the Summary Sheet in Microsoft Word format.
*Be sure to change the control number and problem selected before printing out the page. You must still login to the website and choose your problem.
Teams are free to choose between MCM Problem A, MCM Problem B, ICM Problem C or ICM Problem D.
COMAP Mirror Site: For more in:
/undergraduate/contests/mcm/
MCM: The Mathematical Contest in Modeling
ICM: The Interdisciplinary Contest in Modeling
2015 Contest Problems
MCM PROBLEMS
PROBLEM A: Eradicating Ebola
The world medical association has announced that their new medication could stop Ebola and cure patients whose disease is not advanced. Build a realistic, sensible, and useful model that considers not only the spread of the disease, the quantity of the medicine needed, possible feasible delivery systems, locations of delivery, speed of manufacturing of the vaccine or drug, but also any other critical factors your team considers necessary as part of the model to optimize the eradication of Ebola, or at least its current strain. In addition to your modeling approach for the contest, prepare a 1-2 page non-technical letter for the world medical association to use in their announcement. PROBLEM B: Searching for a lost plane
Recall the lost Malaysian flight MH370. Build a generic mathematical model that could assist "searchers" in planning a useful search for a lost plane feared to have crashed in open water such as the Atlantic, Pacific, Indian, Southern, or Arctic Ocean while flying from Point A to Point B. Assume that there are no signals from the downed plane. Your model should recognize that there are many different types of planes for which we might be searching and that there are many different types of search planes, often using different electronics or sensors. Additionally, prepare a 1-2 page non-technical paper for the airlines to use in their press conferences concerning their plan for future searches.
ICM PROBLEMS
PROBLEM C: Managing Human Capital in Organizations
Click the title below to download a PDF of the 2015 ICM Problem C.
Your ICM submission should consist of a 1 page Summary Sheet and your solution cannot exceed 20 pages for a maximum of 21 pages.
Managing Human Capital in Organizations
PROBLEM D: Is it sustainable?
Click the title below to download a PDF of the 2015 ICM Problem D.
Your ICM submission should consist of a 1 page Summary Sheet and your solution cannot exceed 20 pages for a maximum of 21 pages.
Is it sustainable?
© 2015 COMAP, The Consortium for Mathematics and Its Applications
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问题一：根除病毒
世界医学协会已经宣布他们的新药物能阻止埃博拉病毒和治愈患者的疾病不先进。
建立一个现实的，明智的，和有用的模型，不仅考虑了疾病的蔓延，需要药物的量，可能可行的输送系统，输送的位置，疫苗或药物的生产速度，但也有其他重要因素，你的团队认为有必要作为模型的一部分来优化埃博拉病毒根除，或者至少目前的应变。
除了你的建模方法的较量，准备为世界医学协会使用在其公告1-2页的非技术性的信。
问题B：寻找失踪的飞机
回忆失去的马来西亚mh370飞行。
建立一个通用的数学模型，可以帮助“搜索”规划的一个有用的寻找失踪的飞机可能坠毁在开放水域如大西洋，太平洋，印度，南，或北冰洋而从A点到B点飞行假设有从坠落的飞机没有信号。
你的模型应该认识到有许多不同类型的飞机，我们可以搜索，有许多不同类型的搜索飞机，经常使用不同的电子或传感器。
另外，准备一个1-2页的非技术对航空公司的使用在他们的新闻发布会，关于他们未来的搜索计划。