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2017美赛B题中文翻译
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Math Modeling（8）
2017 MCM Problem A: Managing The Zambezi River
The Kariba Dam on the Zambezi River is one of the larger dams in Africa. Its construction was controversial, and a 2015 report by the Institute of Risk Management of South Africa included a warning that the dam is in dire need of maintenance. A number of options are available to the Zambezi River Authority (ZRA) that might address the situation. Three options in particular are of interest to ZRA:
(Option 1) Repairing the existing Kariba Dam,
(Option 2) Rebuilding the existing Kariba Dam, or
(Option 3) Removing the Kariba Dam and replacing it with a series of ten to twenty smaller dams along the Zambezi River.
There are two main requirements for this problem:
Requirement 1 ZRA management requires a brief assessment of the three options listed, with sufficient detail to provide an overview of potential costs and benefits associated with each option. This requirement should not exceed two pages in length, and must be provided in addition to your main report.
Requirement 2 Provide a detailed analysis of Option (3) - removing the Kariba Dam and replacing it with a series of ten to twenty smaller dams along the Zambezi river. This new system of dams should have the same overall water management capabilities as the existing Kariba Dam while providing the same or greater levels of protection and water management options for Lake Kariba that are in place with the existing dam. Your analysis must support a recommendation as to the number and placement of the new dams along the Zambezi River.
In your report for Requirement 2, you should include a strategy for modulating the water flow through your new multiple dam system that provides a reasonable balance between safety and costs. In addition to addressing known or predicted normal water cycles, your strategy should provide guidance to the ZRA managers that explains and justifies the actions that should be taken to properly handle emergency water flow situations (i.e. flooding and/or prolonged low water conditions). Your strategy should provide specific guidance for extreme water flows ranging from maximum expected discharges to minimum expected discharges. Finally, your recommended strategy should include information addressing any restrictions regarding the locations and lengths of time that different areas of the Zambezi River should be exposed to the most detrimental effects of the extreme conditions.
Translation：
Problem A：管理赞比西河
赞比西河上的卡里巴水坝是非洲较大的水坝之一。它的建设是有争议的，南非风险管理研究所的2015年报告包括一个警告-大坝是急需维护。赞比西河管理局（ZRA）可提供若干选择，以解决这一问题。 ZRA特别感兴趣的有三个选项：
选项1 修复现有的Kariba水坝
选项2 重建现有的Kariba水坝
选项3 拆除Kariba水坝，并更换为沿赞比西河的一系列十到二十个较小的水坝。
这个问题有两个主要要求：
要求1 ZRA管理要求对所列出的三个选项进行简要评估，并提供足够的详细信息，以提供与每个选项相关的潜在成本和收益的概述。此要求的长度不应超过两页，除了主要报告之外，还必须提供此页面。
要求2对选项（3）进行详细分析 - 删除Kariba水坝，并用赞比西河沿岸一系列十至二十个较小的水坝替代。这个新的水坝系统应该与现有的Kariba水坝具有相同的整体水管理能力，同时为现有的水坝提供与卡里巴湖相同或更高水平的保护和水管理选择。您的分析必须支持关于沿赞比西河新坝的数量和位置的建议。
在您的要求2报告中，您应该包括一个策略，用于调节通过您的新多坝系统的水流，从而在安全和成本之间提供合理的平衡。除了解决已知或预测的正常水循环，您的战略应为ZRA经理提供指导，解释和证明应当采取的行动，以正确处理应急水流情况（即洪水和/或长期低水位状况）。您的策略应为从最大预期排放到最小预期排放的极端水流提供具体指导。最后，您的建议战略应包括解决对赞比西河不同地区暴露于极端条件最有害影响的位置和时间长度的任何限制的信息。
个人思路 仅供参考
a warning that the dam is in dire need of maintenance
考虑到题目说明是需要maintenance，保养，那么成本consideration 是一定的。
其实题目已经给了我们一些参考信息，给出了三种可行的方案。我们要做的，就是评估，预测成本和收益的关系，那么答案自然而出。
1. 构建Cost-benefit Prediction model 成本效益预测模型
2. 考虑 k-NN ，或者Random forest
关于 water management
providing the same or greater levels of protection and water management options
大概的输出类似下图，需要做一定的研究与分析：
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(1)(5)(3)(1)(4)(4)(4)(6)(7)(2)(2)(11)(18)(8)(6)(10)(19)(4)(1)(1)[转载]2017美国数学建模MCM B题（离散型）翻译 收费后合并
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PROBLEM B: Merge After TollMulti-lane divided limited-access toll highways use “ramp tolls” and “barrier tolls” to collect tolls from motorists. A ramp toll is a collection mechanism at an entrance or exit ramp to the highway and these do not concern us here. A barrier toll is a row of tollbooths placed across the highway, perpendicular to the direction of traffic flow. There are usually (always) more tollbooths than there are incoming lanes of traffic (see former 2005 MCM Problem B). So when exiting the tollbooths in a barrier toll, vehicles must “fan in” from the larger number of tollbooth egress lanes to the smaller number of regular travel lanes. A toll plaza is the area of the highway needed to facilitate the barrier toll, consisting of the fan-out area before the barrier toll, the toll barrier itself, and the fan-in area after the toll barrier. For example, a three-lane highway (one direction) may use 8 tollbooths in a barrier toll. After paying toll, the vehicles continue on their journey on a highway having the same number of lanes as had entered the toll plaza (three, in this example).Consider a toll highway having L lanes of travel in each direction and a barrier toll containing B tollbooths (B & L) in each direction. Determine the shape, size, and merging pattern of the area following the toll barrier in which vehicles fan in from B tollbooth egress lanes down to L lanes of traffic. Important considerations to incorporate in your model include accident prevention, throughput (number of vehicles per hour passing the point where the end of the plaza joins the L outgoing traffic lanes), and cost (land and road construction are expensive). In particular, this problem does not ask for merely a performance analysis of any particular toll plaza design that may already be implemented. The point is to determine if there are better solutions (shape, size, and merging pattern) than any in common use.Determine the performance of your solution in light and heavy traffic. How does your solution change as more autonomous (self-driving) vehicles are added to the traffic mix? How is your solution affected by the proportions of conventional (human-staffed) tollbooths, exact-change (automated) tollbooths, and electronic toll collection booths (such as electronic toll collection via a transponder in the vehicle)?Your MCM submission should consist of a 1 page Summary Sheet, a 1-2 page letter to the New Jersey Turnpike Authority, and your solution (not to exceed 20 pages) for a maximum of 23 pages. Note: The appendix and references do not count toward the 23 page limit.B题中文翻译：问题B：收费后合并高速路的收费站会通过&匝道收费&和&过卡收费&两种方式来收取驾驶员的高速费。匣道收费是一种在入口和出口的回道处设立的收费站，但是今天这个不在我们的讨论范围之列。过卡收费是一排垂直高速路行驶方向设立的的许多收费窗口。而这些收费窗口通常都会比车道条数要多(详情参见2005 年MCM的B题)。因此，当汽车驶出收费站之后，车流必须从较宽的收费站出口呈扇形快速并入车道较少的常规机动车道。收费广场是为改善过卡之后的拥堵状况建立的，包括收费站之前多车道区域，收费站本身以及经过收费站之后的扇入区域。举个例子，一条单向的三车道高速路需要8个收费窗口，在支付过桥费后，驾驶员可以继续保持与自己进收费广场之前的相同数量的车道（在该示例中为三个）的高速公路上继续行驶。试考虑一个收费高速公路上两个方向都有L条车道，每个方向上有B个收费站(B&L), 请确定你设计的收费区域的形状，大小以及当汽车从驶出B时如何将车道进行合并至L条车道。在你的设计中请注明一些重要事项如事故预防， 吞吐量(即每小时有多少车辆从收费广场驶出，驶入L条车道。)成本(土地和公路建设的费用很昂贵) ，重点在于并非只是对现有的收费广场进行性能分析，请试着探索是否有比现今采用的更好的收费解决方案(包括形状，大小以及收费方式)。请确定你的解决方案在小车流量和大车流量下的性能表现。随着更多的私家(自驾)车进入其中，你的解决方案会有什么改变昵?你的解决方案会如何影响常规收费站(需要人员进行收费) ，不找零(自动化的)收费站以及电于收费站的比例(比如通过车内的发射器应答器来收取费用) ?您的MCM提交应包括1页摘要表，1-2页给新泽西州收费公路管理局的信件，以及您的解决方案（不超过20页），最多23页。注意：附录和参考文献不计入23页的限制。© 2017 COMAP, The Consortium for Mathematics and Its ApplicationsMay be reproduced for academic/research purposesFor More information on COMAP and this project visit 更多美赛赛题资料、参考文献见数学建模与统计建模论坛Mathematical Modelling and Statistical Modelling Forum美赛板块
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