全国大学生数学建模竞赛通讯

CUMCM Newsletter

全国大学生数学建模 竞赛组织委员会主办

创新意识团队精神重在参与公平竞争

目 录

2009年美国大学生数学建模竞赛(MCM)

和交叉学科建模竞赛(ICM)赛题 (1)

我国学生参加2009年美国大学生数学建模竞赛(MCM)

和交叉学科建模竞赛(ICM)情况简介 (11)

赛区通讯

第十七届数模竞赛北京地区颁奖会暨赛后继续研讨会 (19)

2009年湘、赣、鄂、闽、豫五省数学建模骨干教师培训班 (20)

数模竞赛赛题摘选 (21)

“2009高教社杯全国大学生数学建模竞赛MATLAB创新奖”的通知 (25)

迈斯沃克公司广告………………………………………………………(封底)

《全国大学生数学建模竞赛通讯》征稿启事 《全国大学生数学建模竞赛通讯》主要面向全国各赛区组委会、参赛院校教育行政部门、指导教师和学生。征稿内容为：

z赛区组委会在组织报名、培训、竞赛巡视、评阅等方面的经验和具体作法；

z参赛院校和指导教师在组织报名、培训等方面的经验和具体作法；

z参赛学生的体会；

z竞赛在培养创新人才、推动教学改革中的典型事例；

z争取社会各界支持竞赛的成功经验和作法，及社会各界对竞赛的理解；

z国内外有关信息。

来稿请寄：100084北京清华大学数学科学系胡明娅，注明“数学建模竞赛通讯稿件”。

欢迎以电子邮件方式投稿：mhu@https://www.wendangku.net/doc/c81983600.html,

《全国大学生数学建模竞赛通讯》2009年第2期 (2009年6月, 总第30期）

主办：全国大学生数学建模竞赛组织委员会

地址：北京清华大学数学科学系（邮编：100084）网址：https://www.wendangku.net/doc/c81983600.html,

电话：010-******** 传真：010-******** 责任编辑：孟大志

2009年美国大学生数学建模竞赛(MCM)

和交叉学科建模竞赛(ICM)赛题

PROBLEM A: Designing a Traffic Circle

Many cities and communities have traffic circles—from large ones with many lanes in the circle (such as at the Arc de Triomphe in Paris and the Victory Monument in Bangkok) to small ones with one or two lanes in the circle. Some of these traffic circles position a stop sign or a yield sign on every incoming road that gives priority to traffic already in the circle; some position a yield sign in the circle at each incoming road to give priority to incoming traffic; and some position a traffic light on each incoming road (with no right turn allowed on a red light). Other designs may also be possible.

The goal of this problem is to use a model to determine how best to control traffic flow in, around, and out of a circle. State clearly the objective(s) you use in your model for making the optimal choice as well as the factors that affect this choice. Include a Technical Summary of not more than two double-spaced pages that explains to a Traffic Engineer how to use your model to help choose the appropriate flow-control method for any specific traffic circle. That is, summarize the conditions under which each type of traffic-control method should be used. When traffic lights are recommended, explain a method for determining how many seconds each light should remain green (which may vary according to the time of day and other factors). Illustrate how your model works with specific examples.

A题: 设计环岛1

许多城市和社区都设有交通环岛 — 从有几条行车道的(诸如法国巴黎的凯旋门和泰国曼谷的胜利纪念碑处)大型环岛到只有一或两条行车道的小型环岛. 有些环岛在每条进入环岛的车道路口设置停车标志或让行标志, 给已经驶入环岛的车辆以行车优先权; 有的在每条进入环岛的车道路口设置让行标志, 给正在驶入环岛的车辆以行车优先权. 还有一些在每条进入环岛的车道路口设置交通信号灯(红绿灯, 红灯时不能右转弯). 还可能有其他的设计.

本问题的目的就是要你们用模型来确定进入环岛、环岛内以及从环岛出去的交通流的最优控制. 你们要清楚地叙述为了做出最优选择而在你的模型中用到的目标函数以及影响这种选择的因素. 你们的论文还应包括不超过2页2倍行距打印的技术报告, 向交通工程师解释这样用你们的模型对任何特定的环岛选择适当的交通流控制方法. 即, 说明应用每种交通流控制方法的条件. 如果推荐使用红绿灯的话, 则要说明确定绿灯要亮几秒钟(可以按照每天不同的时间以及其他因素而变化)的方法. 说明你们的模型怎样能用来解决一些特殊的环岛实例.

(译注: 本题的作者为位于美国俄亥俄州克利夫兰的凯斯西部保留地大学(Case Western Reserve University, Cleveland, OH) 的 Danny Solow.)

1道路的圆形交叉路口. —译注

PROBLEM B: Energy and the Cell Phone

This question involves the “energy” consequences of the cell phone revolution. Cell phone usage is mushrooming, and many people are using cell phones and giving up their landline telephones. What is the consequence of this in terms of electricity use? Every cell phone comes with a battery and a recharger.

Requirement 1

Consider the current US, a country of about 300 million people. Estimate from available data the number H of households, with m members each, that in the past were serviced by landlines. Now, suppose that all the landlines are replaced by cell phones; that is, each of the m members of the household has a cell phone. Model the consequences of this change for electricity utilization in the current US, both during the transition and during the steady state. The analysis should take into account the need for charging the batteries of the cell phones, as well as the fact that cell phones do not last as long as landline phones (for example, the cell phones get lost and break). Requirement 2

Consider a second “Pseudo US”—a country of about 300 million people with about the same economic status as the current US. However, this emerging country has neither landlines nor cell phones. What is the optimal way of providing phone service to this country from an energy perspective? Of course, cell phones have many social consequences and uses that landline phones do not allow. A discussion of the broad and hidden consequences of having only landlines, only cell phones, or a mixture of the two is welcomed.

Requirement 3

Cell phones periodically need to be recharged. However, many people always keep their recharger plugged in. Additionally, many people charge their phones every night, whether they need to be recharged or not. Model the energy costs of this wasteful practice for a Pseudo US based upon your answer to Requirement 2. Assume that the Pseudo US supplies electricity from oil. Interpret your results in terms of barrels of oil.

Requirement 4

Estimates vary on the amount of energy that is used by various recharger types (TV, DVR, computer peripherals, and so forth) when left plugged in but not charging the device. Use accurate data to model the energy wasted by the current US in terms of barrels of oil per day. Requirement 5

Now consider population and economic growth over the next 50 years. How might a typical Pseudo US grow? For each 10 years for the next 50 years, predict the energy needs for providing phone service based upon your analysis in the first three requirements. Again, assume electricity is provided from oil. Interpret your predictions in term of barrels of oil.

B题：能源和手机

本问题与手机革命对“能源”会造成什么后果有关. 手机的使用正在迅速扩大, 而且许多人正在使用手机而放弃了他们的固网电话(座机). 就所用的电力而言这样做的后果是什么? 每部手机都伴随有一个电池和一个充电器.

要求1：考虑当前约有3亿人口的美国的情况. 从可以获得的数据来估计过去有座机服务的每户人家有m口人的户数H. 现在, 假设所有的座机都被手机替代了; 即, 每户人家的m口人每人都有了手机. 就这种改变 — 无论是在转移的过程中或者是已经达到了稳定的状态 — 对当前美国的电力

使用所造成的后果进行建模. 建模分析应该考虑手机电池充电所需要的电力, 以及手机不会像座机那样使用长久(例如手机丢失或者毁坏).

要求2：考虑一个与当前约有3亿人口以及同样经济状况的美国类似的第二个“虚拟美国”. 这个新兴国家既没有座机也没有手机.从能量的角度看, 什么是向这个国家提供电话服务的最佳方式. 当然, 手机有许多座机没有的社会影响和用途. 讨论只使用座机、只使用手机, 或者两者混合使用会带来的广泛的和潜在的后果.

要求3：手机需要定期充电. 但是许多人总是把充电器插在电源上. 此外, 许多人不管他们的手机是否需要充电, 每天晚上都对他们的手机进行充电. 基于你们对要求2的回答, 对这个虚拟美国的这种浪费的做法的能量费用进行建模. 假设该虚拟美国是用石油来提供电力的. 用所消耗的原油桶数来解释你们的结果.

要求4：估计由各种充电器类型(电视、DVR2、计算机外围设备, 等等) — 当它们插在电源上, 但是没有对仪器充电时 — 所消耗的能源多少的差异. 利用准确的数据对当前美国浪费掉的这种能源进行建模, 用每天消耗的原油桶数来表示.

要求5：现在来考虑今后50年的人口和经济增长. 典型的虚拟美国可能会有怎样的增长. 根据你们在前三个要求中的回答对今后50年里每隔10年预测一下提供电话服务所需要的能源量. 再次假设电力是由原油提供的. 用原油桶数来解释你们的预测.

(译注: 本题的作者为位于美国纽约州牙买加市的约克学院(York College in Jamaica, NY) 的Joe Malkevitch.) PROBLEM C: Creating Food Systems: Re-Balancing Human-Influenced Ecosystems

Background

Less than 1% of the ocean floor is covered by coral. Yet, 25% of the ocean's biodiversity is supported in these areas. Thus, conservationists are concerned when coral disappears, since the biodiversity of the region disappears shortly thereafter.

Consider an area in the Philippines located in a narrow channel between Luzon Island and Santiago Island in Bolinao, Pangasinan, that used to be filled with coral reef and supported a wide range of species (Figure 1). The once plentiful biodiversity of the area has been dramatically reduced with the introduction of commercial milkfish (Chanos chanos) farming in the mid 1990's. It's now mostly muddy bottom, the once living corals are long since buried, and there are few wild fish remaining due to over fishing and loss of habitat. While it is important to provide enough food for the human inhabitants of the area, it is equally important to find innovative ways of doing so that allow the natural ecosystem to continue thriving; that is, establishing a desirable polyculture system that could replace the current milkfish monoculture. The ultimate goal is to develop a set of aquaculture practices that would not only support the human inhabitants financially and nutritionally, but simultaneously improve the local water quality to a point where reef- building corals could recolonize the ocean floor and co-exist with the farms.

A desirable polyculture is a scenario where multiple economically valuable species are farmed together and the waste of one species is the food for another. For example, the waste of a fin-fish can be eaten by filter feeders and excess nutrients from both fish and filter feeders can be absorbed by algae which can also be sold, either as food or commercially useful by-products. Not only does this reduce the amount of nutrient input from the fish farming into the surrounding waters, it also increases the amount of profit a farmer can make by using the fish waste to generate a 2数字视频录像机也叫数字硬盘录像机 (Digital Video Recorder). —译注

greater quantity of usable products (mussels, seaweed, etc.)

For modeling purposes, the primary animal organisms involved in these biodiverse environments can be partitioned into predatory fish (phylum Chordata, subphylum Vertebrata); herbivorous fish (phylum Chordata, subphylum Vertebrata); molluscs (such as mussels, oysters, clams, snails, etc., phylum Mollusca); crustaceans (such as crabs, lobsters, barnacles, shrimp, etc., phylum Arthropoda, subphylum Crustacea); echinoderms (such as star fish, sea cucumbers, sea urchins, etc.; phylum Echinodermata); and algae. By feeding types, there are primary producers (photosynthesizers—these can be single cell phytoplankton, cyanobacteria, or multicellular algae); filter feeders (strain plankton, organic particles, and sometimes bacteria out of the water); deposit feeders (that eat mud and digest the organic molecules and nutrients out of it); herbivores (eat primary producers); and predators (carnivores). Just as on land, most of the carnivores eat herbivores or smaller carnivores, but in the ocean they can also eat many of the filter feeders and deposit feeders. Most animals have growth efficiencies of 10-20%, so 80-90% of what they ingest ends up as waste in one form or another (some dissipated heat, some physical waste, etc.). The role of coral in this biodiverse environment is largely to partition the space and allow species to condense and coexist by giving a large number of species

each its own chance at a livable environment in a relatively small space—the aquatic analogue of high-rise urbanization. Coral also provides some amount of filter feeding, which helps clean the water. The ability of an area to support coral depends on many factors, the most important of which is water quality. For example, corals in Bolinao are able to live and reproduce in waters that contain half a million to a million bacteria per milliliter and 0.25ug chlorophyll per liter (a proxy for phytoplankton biomass). The fish pen channel currently sees levels upwards of ten million bacteria per milliliter and 15ug chlorophyll per liter. Excess nutrients from the milkfish farms encourage fast-growing algae to choke out coral growth, and particulate influx from the milkfish farms reduces corals ability to photosynthesize. Therefore, before coral larvae can begin to grow, acceptable water quality must be established. Other threats to coral include degradation from increasing ocean acidity due to increased atmospheric CO2, and degradation from increasing ocean temperature due to global warming. These can be considered second order threats which we will not specifically address in this problem.

Problem Statement

The challenge for this problem is to come up with viable polyculture systems to replace the current monoculture farming of milkfish that would improve water quality sufficiently that coral larvae could begin settling and recolonizing the area. Your polyculture scenario should be economically interesting and environmentally friendly both in the short and long term.

1. MODEL THE ORIGINAL BOLINAO CORAL REEF ECOSYSTEM BEFORE FISHFARM INTRODUCTION: Develop a model of an intact coral reef foodweb containing the milkfish as the only predatory fish species, one particular herbivorous fish (of your choice), one mollusc species, one crustacean species, one echinoderm species, and one algae species. Specify the numbers of each species present in a way you find reasonable; cite the sources you use or show the estimates you make in arriving at these population numbers. In articulating your model, specify how each species interacts with the others Show how your model predicts a steady state level of water quality sufficient for the continued healthy growth of your coral species. If your model does not yield a high enough level of water quality, then adjust your number of each species in a way you find most reasonable until you do achieve a satisfactory quality level, and describe clearly which species numbers you adjusted and why your changes were reasonable.

2. MODEL THE CURRENT BOLINAO MONOCULTURE MILKFISH:

a. First examine the impact if milkfish farming were to suppress other animal species. Do this by removing (setting the population to zero of) all herbivorous fish, all molluscs, all crustaceans, and all echinoderms. Set all other populations to be the same as in your full model above. Since you have removed the milkfish's natural food supply, you will need to introduce a constant term that models farmer feeding of the penned milkfish; choose this term to keep your model in equilibrium. What steady state level of water quality does your model now predict? Is water quality sufficient for the continued healthy growth of your coral species? Compare and describe how your result

compares to observations.

b. Milkfish farming does not totally suppress all other animal species and water quality is probably not as bad as your results from part 2a suggest, so use your model to simulate the current Bolinao situation by reintroducing all deleted species and adjust only those populations until water quality matches that currently observed in Bolinao. Compare your populations with those currently observed in Bolinao and discuss what changes to your model could bring your population predictions into closer agreement with observations.

3. MODEL THE REMEDIATION OF BOLINAO VIA POLYCULTURE: You now strive to replace the current monoculture with a polyculture industry, seeking to make the water clear enough that the original reef ecosystem that you modeled in part 1 can re-establish itself without any help from humans. The idea is to introduce an interdependent set of species such that, whatever feed the milkfish farmer puts in, the combination of all of his/her "livestock" will use it entirely so that there are no (or only minimal) leftover trients and particles (feed and feces) falling onto the newly growing reef habitat below. Additionally, you seek to commercially harvest edible biomass from this polyculture in order to feed humans and increase value.

a. Develop a commercial polyculture to remediate Bolinao. Do this by starting with your "current" penned model from part 2b, and introduce into it additional species that both help clean the water and yield valuable, harvestable biomass. For example, you could line the pens with mussels, oysters, clams or other economically valuable filter feeder to remove some of the waste from the milkfish. Economically valuable algae could be grown on the sides of the pens near the surface (where they get enough light), and some of these could feed the small herbivorous fish that feed the milkfish. Clearly present your model and its steady state populations.

b. Report on the outputs of your model. What did you optimize, what constraints did you enforce, and why? What water quality does your model yield? How much harvest does your model yield, and what is its economic value? How much does it cost you to further improve water quality? In other words, from your optimal scenario, how many dollars of harvest does it cost you to improve water quality by one unit?

4. SCIENCE: Discuss the harvesting of each species for human consumption. How do we use your model for predicting or understanding harvesting for human consumption? Does a harvested pound of carnivorous fish count the same as a harvested pound of seaweed so that we seek to maximize total weight harvested, or do we differentiate by value (as measured by price of each harvested species) so that we seek to maximize the value of the harvest? Or do we seek to maximize the total value of harvest minus cost of milkfish feed? Should we define the value of edible biomass as the sum of the values of each species harvested, minus the cost of milkfish feed?

5. MAXIMIZE THE VALUE OF THE TOTAL HARVEST: We now wish to maintain an cceptable (maximal) level of water quality while harvesting a high (maximal) value of marketable (because edible and sell-able for byproducts are equally legitimate ways to maximize value) biomass from all living species in the model for human consumption. Change your model to harvest a constant amount from each species. What is the total value of biomass (as defined above) you can harvest and the corresponding water quality? Try different harvesting strategies and different levels of milkfish feeding (always choosing values that will keep your model in equilibrium), and graph water quality as a function harvest value. What strategy is optimal and what is the optimal harvest?

6. CALL TO ACTION: Write an information paper to the director of the Pacific Marine Fisheries Council summarizing your findings on the relationship between biodiversity and water quality for coral growth. Include a strategy for remediating an area like Bolinao and how long it will take to remediate. Present your optimal harvesting/feeding strategy from part 5 above along with persuasive justification, and present suggested fishing/harvest quotas that will implement your plan. Show the leverage of your strategy by presenting the ratio of the harvest value under your plan to the harvest value under the current Bolinao scenario. Discuss the pros and cons from an ecological perspective of implementing your polyculture system.

Getting Started References

https://www.wendangku.net/doc/c81983600.html,/wiki/Integrated_Multi-trophic_Aquaculture https://www.wendangku.net/doc/c81983600.html,/wiki/Coral_reef

https://www.wendangku.net/doc/c81983600.html,/infobooks/Coral/home.html

Supplementary Information Figure 1. Map of the Bolinao area and the sites sampled for water quality data listed in Tables 1 and 2. Sites A and B have fairly healthy coral reefs while Site C has fairly degraded reefs, Site D has a few corals still holding on but is mostly dead coral and algae at this point in time, and the area under the fish pens no longer has live coral at all. In the fish pen channel, farmers employ nets measuring roughly 10m x 10m x 8m with stocking densities of ~ 50,000 fish per pen and 10 pens per hectare. (Fig. from Garren et al. 2008)

The following tables are representative of the data you

will be able to find through public searches. These data may not be complete for your purposes and are intended only to help give you ideas on how to get started. You should use the best-suited and most complete data that you find. Characteristics of Site Water

Table 1. Water characteristics of Bolinao sites. (from Garren et al. 2008)

Site

Dissolved Organic Carbon

(DOC) (uM) Total

Nitrogen (Dissolved, uM ) Chl a (ug/L)

Particulate

Organic Carbon

(POC) (ug/L) Total

Nitrogen (Particulate, ug/L) A 69.7± 1.3 7.4±0.4 0.25± 0.03 106± 4 9±15 B 80.4± 2.9 8.0± 0.2 0.28± 0.03 196± 57 39± 15 C 89.6± 1.7 14.2± 0.7 0.38± 0.03 662± 68 54± 17 D 141± 2.9 30.5± 1.3 4.5± 0.2 832± 338 86± 45 Fish Pens

162± 18.5

39.8± 2.7

10.3± 0.2

641± 60

86± 18

Microbial Abundances and Particle Characteristics of Site Water

Table 2. Bacteria and particle abundances in Bolinao. (from Garren et al 2008) Organism Information

References for Information found in the Table（略）

C题:创建食物系统 — 重建受到人类影响的生态系统

背景

只有不到1%的海底是由珊瑚覆盖的. 然而, 这些海域却支持了25%的海洋生物多样性. 环保工作者非常关心珊瑚的消失, 因为从此该地区的生物多样性也将很快消失.

考虑在菲律宾的位于Pangasinan(邦阿西楠)的Bolinao(波里纳奥)的Luzon(吕宋)岛和Santiago(圣地亚哥)岛之间的狭窄的通道区域, 那里过去曾经布满了珊瑚礁并支持着大量物种的生存(图1). 由于1990年代中期引进的商业性的虱目鱼(Chanos Chanos)养殖, 该海域曾经有过的丰富的生物多样性大大降低了. 现在那里大部分都变成了浑浊多泥的海底, 曾经活着的珊瑚早就被埋葬了, 由于过度的捕捞和鱼类栖息地的丧失只剩下很少的野生鱼种了. 尽管对于哪个地区的居民来说提供足够的食物是重要的, 但是同样重要的是要寻找一种能使自然的生态系统能够继续欣欣向荣的革新的方法; 即建立一种能够代替目前的虱目鱼单一养殖的令人满意的混养体制. 最终目标是研发一套水产养殖的做法使得不仅能够支持人类居民经济上和营养上的需求, 而且能够同时改善当地的水质到一定的水平使得在暗礁上建立起来的珊瑚能重新拓展到海底并和养殖场共存.

令人满意的混养体制应该展现这样一种情景: 多个有经济价值的物种养殖在一起, 而一个物种的排泄物正好是另一个物种的食物. 例如, 有鳍鱼的排泄物可供滤食性动物食用而且有鳍鱼和滤食性动物的过量的营养物质可以被海藻吸收, 海藻既可以作为食物也可以作为商业上有用的副产品. 这不仅减少了从鱼类养殖输入到周围水体的营养物质, 也由于利用鱼的排泄物生成大量的有用的产品(贻贝、海藻等)而使渔民增加了收益.

为了建模的目的, 在这种生物多样性的环境里主要的动物生物体可以分为捕食鱼类(脊索动物门、脊椎动物亚门); 食草鱼类(脊索动物门、脊椎动物亚门); 软体动物(诸如贻贝、牡蛎、蛤蜊、蜗牛等, 软体动物门); 甲壳类动物(诸如蟹、龙虾、藤壶、河虾等, 节肢动物门, 甲壳动物亚门); 棘皮动物(诸如星鱼、海参、海胆等, 棘皮动物门); 还有藻类. 就喂养的类型而言, 有初级生产者(光合作用制造者 — 它们可以是单细胞浮游植物、蓝藻或多细胞藻类); 滤食动物(菌株浮游生物、有机颗粒, 有时候是水里的细菌); 食碎屑动物(吃泥土并消化其中的有机分子和养分); 食草动物(吃初级生产者); 以及捕食动物(食肉动物). 和在陆地上一样, 大多数食肉动物吃食草动物或更小的食肉动物, 但是在海洋里它们也吃很多滤食动物和食碎屑动物. 大多数动物具有10-20%的生长效率, 所以它们所摄入物的80-90% 转化这种或那种形式的排泄物(一些转化为耗散的热量、另一些转化为身体的排泄物, 等). 在生物多样性环境中珊瑚的作用主要是划分空间, 并通过给予大多数物种在其相对比较小的空间里有其自己发展的生存环境使得各物种可以凝聚和共存 — 都市化高层建筑在水里的类似做法. 珊瑚还可以提供有助于清洁海水的一定数量的滤食动物. 海域能支持珊瑚生长的能力有赖于许多因素, 最重要的因素是水质. 例如, Bolinao的珊瑚可以在含有50-100万个细菌/每毫升和0.25 ug叶绿素/每升(一种光合作用的生物量的替代物)的海水中能够生存和繁殖. 而在用围栏圈养鱼的水域里当前看到的情况却是高于1000万个细菌/每毫升和15 ug叶绿素/每升. 由于虱目鱼渔场过量的营养物促进了窒息珊瑚生长的海藻的快速生长, 以及来自虱目鱼渔场的颗粒流降低了珊瑚进行光合作用的能力. 所以, 在珊瑚幼体能够开始生长前, 必须确立可以接受的海水的质量. 对珊瑚的其他威胁包括由于大气中二氧化碳的增加导致的海水酸度的增加造成的珊瑚礁的退化, 以及由于全球变暖导致的海水温度升高造成的珊瑚礁的退化. 可以把这些看作是二级威胁, 在本问题中我们不予专门的处理.

问题的陈述

本问题的挑战在于要提出切实可行的混养系统来替代当前虱目鱼的单一养殖使之能够大大改善水质, 从而使珊瑚幼体能够在该区域生根扩展. 无论从短期和长期的角度看, 你们的混养系统都应该经济上是吸引人的而且对环境是无害的.

1. 对引进渔场前Bolinao原先的珊瑚礁生态系统进行建模: 研制一个完整的珊瑚礁食物网的模型, 该食物网包括唯一的捕食鱼种虱目鱼, (由你们选择的)一种特殊的食草鱼, 一种软体动物, 一种甲壳动物, 一种棘皮动物以及一种海藻. 以一种你们认为是合理的方式详细说明每个物种的数量; 列出你们所用的原始资料或者说明你们是怎么估计出这些种群的数量. 就清楚表述你们的模型而言, 详细说明每个物种怎样和其他物种相互作用. 说明你们的模型是怎样预测足以保证珊瑚物种能够持续健康生长的稳定的水质水平的. 如果你们的模型没有给出足够高的水质水平, 那么就按你们认为最合理的方式来调整每个物种的数量直到确实达到了满意的水质水平为止, 并清楚描述你们调整了那些物种的数量以及为什么你们所做的改变是合理的.

2. 对Bolinao当前的虱目鱼单一养殖建模

a. 首先假设虱目鱼的养殖会抑制其他动物物种的生长, 研究它将产生的影响. 通过移去(即, 令种群数目为零)所有的食草鱼, 所有的软体动物, 所有的甲壳动物以及所有的棘皮动物. 令所有的其他物种数量和你们在上面的完整模型中的数量相同. 因为你们已经移去了虱目鱼的自然食物供应; 你们需要引进一个常数项, 该常数项是渔民对圈养虱目鱼的喂养; 选择这项使得你们的模型保持平衡. 你们的模型现在预测的是什么样的稳定水质水平? 该水质水平足以保证你们珊瑚物种能够持续健康生长? 与观察结果比较, 并描述怎样把你们的结果与观察结果进行比较.

b. 虱目鱼的养殖并非完全抑制所有其他的动物物种的生长, 而且水质也可能并不像你们在2a 中建议的那么坏, 所以通过重新引进所有被移去的物种并且只调整它们的数量直到水质和当前在Bolinao观察到的水质一致来模拟当前Bolinao的生态情况. 把你们得到的这些物种的数量与它们当前在Bolinao观察到的这些物种的数量进行比较, 并讨论对你们的模型做什么样的改变会使得你

们对各种群数量预测与观察结果更加接近.

3. 对经由混养来抢救Bolinao的生态环境进行建模: 你们要寻求无须人类活动的帮助的前提下力争用混养渔业来替代当前的单一养殖使得海水足够清洁从而能够重建你们在问题1中建模的原来的珊瑚生态系统. 想法就是引进一组互相依赖的物种使得无论养殖虱目鱼的渔民投放的是什么样的饲料, 他/她的“牲畜”都会把它们全部吃掉, 而不会有(或只有极少的)剩余营养物和颗粒物(饲料和粪便)掉进下面的新长出来的珊瑚生长地. 此外, 为了向人类提供食物并增加其价值你们还要设法从这种混养系统中获得具有商业价值的可以食用的生物物质.

a. 研发一种商业性的混养系统来抢救Bolinao的生态环境. 从你们在2 b部分的“当前”的圈养模型开始, 并且引入既能清洁海水又能生产有价值、可收获的生物物质的额外的物种来做这件事. 例如, 你们可以用贻贝，牡蛎，蛤蜊或者其他的有经济价值的滤食动物排成围拦来去掉虱目鱼的某些排泄物. 有经济价值的藻类植物可以在靠近水面的围拦边上生长(在那里他们可以获得足够的光线), 而且某些藻类还可以作为喂养虱目鱼食物的小食草鱼的饲料. 清楚地表述你们的模型以及达到稳定状态的各物种的数量.

b. 报告你们的模型的输出信息. 你们优化的是什么, 所加的约束是什么, 为什么? 你们的模型给出的是什么样的水质? 你们的模型给出的收获有多少, 其经济价值怎样? 为进一步改善水质你们要付出多少费用? 换言之, 从你们的最优的结果而言, 为提高水质一个单位你们要付出的费用相当于多少与收获物等价的美元?

4. 科学: 讨论人类消耗所需的各物种的捕捞量. 我们怎样利用你们的模型来预测或者理解人类消耗所需的捕捞量? 捕捞一磅食肉动物的鱼类和捕捞一磅海藻同样重要, 所以我们应该寻求极大化总的捕捞重量, 或者我们应该区分(按照每种鱼种的价格来度量的)价值所以我们应该寻求极大化所捕捞的物种的价值? 或者我们应该极大化所捕捞的物种的总价值减去饲养虱目鱼的费用? 我们是否应该把可以食用的生物量的价值定义为各捕捞物种的价值之和再减去饲养虱目鱼的费用?

5. 极大化总捕捞量的价值: 现在我们希望在人类消耗模型中在保持一种可接受(最好的)水质水平的同时使来自所有活的物种的捕捞量达到高(最大)的市场价值(因为可食用和可销售的副产品都是极大化价值的合法的方式). 改变你们的模型使得捕捞的各个物种等于常量. 什么是你们可以捕捞的(如同上面定义的)生物量的总价值以及相应的水质? 试一下不同的捕捞策略和不同的虱目鱼喂养水平(永远选择能够使你们的模型保持平衡的价值), 并且画出水质作为捕捞价值的函数的图像. 什么样的策论是最优的以及什么是最优的捕捞量?

6. 号召采取行动: 给Pacific Marine Fisheries Council (太平洋水产委员会)的主任写一份你们发现的有关珊瑚生长中生物多样性和水质的关系的结论的信息报告. 报告要包括修复像Bolinao那样的生态环境的策略以及要多长时间才能修复. 用有说服力的理由来提出第5部分中你们的最优捕捞/喂养策略, 并提出能执行你们的计划的捕捞/喂养配额策略. 通过提出你们计划下的捕捞价值和当前Bolinao情况下的捕捞价值之比来说明你们的策略的优势. 从生态学的角度来讨论你们的混养系统的利弊得失.

开始你们的研究时可以利用的参考资源

https://www.wendangku.net/doc/c81983600.html,/wiki/Integrated_Multi-trophic_Aquaculture

https://www.wendangku.net/doc/c81983600.html,/wiki/Coral-reef

https://www.wendangku.net/doc/c81983600.html,/infobooks/Coral/home.html

补充信息(略)

(译注: 本题的作者是位于加州的斯克里普斯海洋研究所(Scripps Institute of Oceanography, CA) 的 Melissa Garren.)

(叶其孝译, 吴庆宝校，原题来源于https://www.wendangku.net/doc/c81983600.html,)

我国学生参加2009年美国大学生数学建模竞赛(MCM)

和交叉学科建模竞赛(ICM)情况简介

2009年美国大学生数学建模(通讯)竞赛于美国时间2009年2月5日到9日举行，共有中国、中国(香港) 、美国、澳大利亚、加拿大、芬兰、德国、匈牙利、印度尼西亚、爱尔兰、墨西哥、新加坡、南非、英国14个国家和地区的大学生参加了这项竞赛。2049个队参加并递交了论文, 其中参赛MCM的1675个队, 参赛ICM的374个队. 中国有1624个队参赛，约占79%。总共9个队获MCM-2009的特等奖，2个队获ICM-2009的特等奖。中国参队中，清华大学有一个队获MCM-2009的特等奖, 位于徐州的中国矿业大学有一个队获ICM-2009的特等奖并荣获INFORMS奖(美国运筹学与管理科学学会奖)。竞赛结果的统计见下表。

表一2009中国学生获奖情况统计

参赛队数特等奖(O)队数一等奖(M)队数二等奖(H)队数三等奖(P)队数总数中国总数中国总数中国总数中国总数中国

MCM 1675

1282a占

76.53%

9 1占

11.1%

294179占

60.88 %

298256占

85.91%

1074 846占

78.77%

ICM 374

342b占

91.44% 2 1占

50.0%

36 26占

72.2 %

144135占

93.7%

192 180占

93.75%

表注：a. 其中包括香港特区9个队；b. 其中包括香港特区3个队。

说明： 以下表中O = Outstanding，特等奖之意，其论文发表在The Journal of Undergraduate Mathematics and Its Applications（UMAP）上；M = Meritorious，一等奖之意；H = Honorable Mention，二等奖之意；P = Successful Participation，三等奖（成功参赛奖）之意；A = MCM A 题；B = MCM B题；C = ICM。

表二、2009年MCM/ICM中国学生参赛队详细列表

1.学校（中文）

2.学校（英文）A得分B得分C得分

装甲兵工程学院Academy of Armored

Force Engineering

PPH M

安徽大学Anhui University P H HHH

安庆师范学院Anqing Teachers College P

安徽工业大学Anhui University of

Technology

P

鞍山师范学院Anshan Normal University PP HP

北京航空航天大学BeiHang University MMMMMMMMMM HH PPP

北京电子科技学院

Beijing Electronic

Science and Technology

P

北华大学Beihua University PPHH 北京林业大学Beijing Forestry University HPP HHP PP

北京理工大学Beijing Institute of

Technology

PPPPMMMPPMPPPPP PPHHM PPPP

北京交通大学Beijing Jiaotong University PPPPPPPPPPPPPPPPPPP PPH HHHPPPPPP

北京语言大学Beijing Language and

Culture University

MHMPPHPH PP

HHPPP

北京师范大学Beijing Normal Universify PPPPPPPPPPP PPPPPPPPHHH

HMM

北京邮电大学Beijing Univ. of Posts &

Telecomm.

HMMMHHHPPPH MMMPPP

MHHHHHH

HPPPHHHH

PPP

北京化工大学Beijing University of

Chemical Technology

PH P

H

北京物资学院beijing wuzi university PPPH

滨州学院Binzhou University P HPP

首都经济贸易大学

Capital University of

Economics and Business

H P

HHHP

华中师范大学Central China Normal

University

MP

中南大学Central South University HPPPPMMPP HPPP HH

中央财经大学

Central University of

Finance and Economics

MH PPPH

HHPPPPHH

HHPPP

长安大学Chang'an University PPH

成都信息工程学院

Chengdu University of

Information Technology

PP

成都理工大学Chengdu University of

Technology

M H

中国农业大学China Agricultural

University

P PPH

P

中国药科大学China Pharmaceutical

University

H

中国地质大学China University of

Geosciences

PPPPPPHH P PPP

中国矿业大学China University of Mining

and Technology

PPPPP PPP

OHHPPPP

中国石油大学

China University of

Petroleum

PPPHPPPPM HHHMPPPPPP

P

P

College of Computer and

Information, Fujian

PH College of Information

Science and Engineering

PPH

中国青年政治学院China Youth University for

Political Sciences

P P

重庆交通大学Chongqing Jiaotong

University

PP

重庆大学Chongqing University PPH PPPPHM PPPPP 楚雄师范学院Chuxiong Normal University P

中国民航大学Civil Aviation University Of

China

PPPPPPPP M

大连民族学院

College of Science;

Dalian Nationalities

PPPPPPPP PPP

PPPP College of Computer

Science and Engineering

PPPPM H

P

河北理工轻工学院

College of Light

Industry,Hebei Polytechnic

PP M

大连海事大学Dalian Maritime University PPHPPMPPPPMMPP HMPPPPPPP PPP 海军大连舰艇学院Dalian naval academy PP PPPH

大连东软信息学院Dalian Neusoft Institute of

Information

PP PM

大连大学Dalian University PP HHM HHHPPPP

大连理工大学Dalian University of

Technology

PPMPPMHMPPPPMPH

MPPPHPPPPP

HHHHMPPPPP

HHHHPPPH

HHHHHPPP

大庆石油学院Daqing Petroleum Institute HHHPP

Department of Mathematics,

School of Information

P Department of Physics H

Doctor

M 东华大学Donghua University PPPPP HHPPP P

华东师范大学

East China Normal

University

PPPPPHMPPHPP PPPPH

Electronic Engineering

Institute

PM

华东理工大学East China University of

Science and Technology

PH PPP

HHPHH

复旦大学Fudan University MPP H MHP 福建师范大学Fujian Normal University MMPP P

赣南师范学院GanNan Normal University PH HP

广东商学院Guangdong University Of

Business Studies

M

广东工业大学Guangdong University of

Technology

HP

广西师范学院Guangxi Teachers Edcation

Univercity

PPP P

贵州大学Guizhou University P

杭州电子科技大学Hangzhou Dianzi University PPPPPM HHPPP

哈尔滨工程大学harbin engineering university HHHMMPPP HHPPPPPPPPP

PP

HHHHPP

哈尔滨工业大学Harbin Institute of

Technology

PPPPPPPPPPPPMMMPP

PPPPPPPPPPPPPPPPPPH

PHPPMHPMPPPP

HHMMPPPPPP

PPP

MHHHPPMH

HHHHHPPP

PPPP

哈尔滨医科大学Harbin Medical

University

H

哈尔滨商业大学Harbin University of

Commerce

PP PP

哈尔滨理工大学Harbin University of Science

and Technology

PMPHP H

H

河北工程大学Hebei University of

Engineering

P

合肥工业大学Hefei University of

Technology

PPPPH P

HHP

黑龙江大学Heilongjiang University HP P

河南科技学院Henan Institute of Science

and Technology

P P

P

河海大学Hohai University HHMMM

淮阴师范学院Huaiyin Teachers College P

华中科技大学Huazhong University of

Science and Technology

PPPPM HHMMPP

H

湖南科技大学

Hunan University of

Science and Technology

P Hunan Institute of

Humanities,Science and

PPPPPH

湖南大学Hunan University PPHHPPP PPPP HPPP 内蒙古大学Inner Mongolia University PPH PP H

中科院声学所INSTITUTE OF

ACOUSTICS

P

东北大学

Institution of Math ;

Northeastern University

MHPHHH

江苏大学Jiang Su University PM

江西科技师范学院Jiangxi Science & Tech.

Normal University

P

揭阳职业技术学院Jieyang Vocational

&Technical College

H

吉林大学Jilin University PPPPPPPPPPPMP HHH

HPPPPMH 兰州大学Lanzhou University PPPH PM

聊城大学LiaoCheng University PP P PHP

后勤工程学院Logistical Engineering

University

P HPP

鲁东大学Ludong University PP H

南昌航空大学

Nanchang Hangkong

university

HPPP math H Mathematical Modeling

Innovative Practice Base

M

南昌大学Nanchang university PPPPPP PP

南京林业大学Nanjing Forestry University H

南京师范大学Nanjing Normal University PPPPPP

南京大学Nanjing University PMPHPPHPMP MPPPPPP P

南京邮电大学

Nanjing University of

Post&Telecommunications

HPPPM

PHP NanJing University Of

Information Science

H P

南京理工大学

Nanjing University of

Science and Technology

PPPHHH PM

PPP

南开大学Nankai PPP HMP 南通大学Nantong University PP PP

国防科学技术大学National University of

Defense Technology

MPPPPHPPHPM HHHMPP

MMHHHPP

华北电力大学North China Electric Power

University

HHPPPPPP PPPP HPP

北方工业大学North China University of

Technology

M

东北农业大学Northeast Agricultural

University

P HPP

中北大学North University of China PPPP

西北农林科技大学Northwest A&F University HP HHH 西北大学Northwest University MPPPP H

西北工业大学Northwestern Polytechnical

University

PPPPPH MPPP

MMP

北京大学Peking Univ. MPPMMPPMMPHMMP

PP

HMMPP

PHHHHHHM

HHHP

解放军理工大学PLA University of Science

and Technology

MP MM

MHP

青岛农业大学Qingdao Agricultural

University

H

青岛理工大学QINGDAO TECH.

UNIVERSITY

PPP

青岛大学Qingdao University, China P

泉州师范学院Quanzhou Normal

University

M

人民大学Renmin University MMPPPP M

Research Center of Control

& Simulation;

H

School of Information

Engineering, Hangzhou

M P School of Management and

Engineering, Nanjing

M

School of Control Science

and Engineering, North

PPP PP School of Economic

Mathematics,Southwestern

P

School of Information

Technology

PP School of Information ,Xi'an

Communication

PP

School of Mathematics &

Statistics

PH

School of Mechanical Eng.

and Automation,

P School of Software

Engineering

H M

西安通信学院School of Science, Xi'an

Communication Institute

MPP

山东大学Shandong University PMPPPHMPPPPMMPPP

PP MPMHPPPPP

MPMPPPPPPPPHHMPP

HPPPPPMPP

HHHPPPPPP MHPPPPP

山东科技大学ShanDong University of

Science and Technology

MPPHPPPMP PP

上海外国语大学附属外国语学校Shanghai Foreign Language

School

HHHHH HMPP

上海嘉定第一中学Shanghai Jiading No,1

Senior High School

P HP

上海交通大学Shanghai Jiao Tong

University

PPMHPPHPMPP HHP P

上海师范大学Shanghai Normal University P HP 上海大学Shanghai University PPPPPPPM HHPPP P

上海电力学院Shanghai university of

electric power

P

上海金融学院Shanghai Finance

University

P PPPPP

上海财经大学Shanghai University of

Finance & Economics

PPPPPMPPPHHHHHPP HHMPPPPP P

上海市育才中学Shanghai Yucai High

School

P

绍兴文理学院Shaoxing University HP HP

沈阳航空工业学院

Shenyang Institute of

Aeronautical Engineering

PPPPPPPPP HPPPP

PHPPPPP

沈阳师范大学Shenyang Normal University PPPP

沈阳药科大学Shenyang Pharmaceutical

University

P P

沈阳工业大学Shenyang University of

Technology

P HP

深圳职业技术学院Shenzhen polytechnic PPPPPPPPH HP HP

石家庄铁道学院

SHIJIAZHUANG

RAILWAY INSTITUTE

HPM

四川农业大学Sichuan Agricultural

University

HPP

HP

四川大学Sichuan University PPHPMMMM HHHP H

华南农业大学South China Agricultural

University

HH PPPP

HP

华南师范大学South China Normal

University

MPPP PP

HH

华南理工大学South China University of

Technology

HHHHHHP P HHP

东南大学Southeast University MMHPPMPPM MHHHPPPH MMHP

南方医科大学Southern Medical University PH

西南大学Southwest University PPPPH HHHMPP MHP

西南民族大学Southwest University for

Nationalities

PP

西南科技大学Southwest University of

Science and Technology

PH

西南财经大学Southwestern University of

Finance and Economics

PPMPPPPPMPPHPPPPP

PH

P

中山大学Sun Yat-Sen University PPPPP MH

太原理工大学Taiyuan University of

Technology

H

苏州大学Suzhou University P HHHPP 天津大学Tianjin University PPPP

天津商业大学Tianjin University of

Commerce

PP

天津科技大学

Tianjin University of

Science & Technology

P PP

同济大学Tongji University PPPP PPP

福建农林大学

Traffic College, Fujian

Agriculture and Forestry

P PP

P

清华大学Tsinghua University MHHOPMPM H HPP

电子科技大学Univ. of Elec. Sci. and Tech.

of China

MMPPMMPPPMHPPH M HPPP

对外经济贸易大学

University of

International Business

and Economics

HHHHPPPPP

MP

广西大学University of Guangxi HPPPP HP

北京科技大学

University of Science and Technology Beijing HHPPPPPPP MPHHHHHH HP

中国科技大学 University of Science and Technology of China M 温州大学 Wenzhou University P 皖西学院 West Anhui University HP 武汉大学 Wuhan University PPPPPPHPHPP

MPPPPP

PP

武汉科技大学 Wuhan University of Science and Technology MPPPPPHHH HHHPPP

厦门大学 Xiamen University

P

P

H

西安交通大学 Xi'an Jiaotong University MMMPPPHH HMPPP HHPP 西安电子科技大学 Xidian University, School of Science PMMPP PH MHMHP 西安交通大学-利物

浦大学 Xi'an Jiaotong-Liverpool

University MMHPPPPP MMP

徐州建筑职业技术

学院 Xuzhou Institute of Architectural Technology M H 徐州工程学院 Xuzhou Institute of Technology PH P 烟台大学 Yantai University PPP 扬州大学 Yangzhou University

P

云南大学 Yunnan University PPPPPP MPPPP 枣庄学院 Zaozhuang University H

浙江工商大学 Zhejiang Gongshang

University

MPPPPPH HH HPPP 浙江师范大学 Zhejiang Normal University

PPPPPPP

HP

HH

浙江理工大学

Zhejiang Sci-Tech

University PH PP P 浙江大学

Zhejiang University MPPPPHHHH

MMHPPP

MMMHPPHP PPHHHH

浙江财经学院 Zhejiang University of Finance and Economics P PP 浙江工业大学 Zhejiang University of

Technology

PPPH HHPPP

浙江万里学院

Zhejiang Wanli University H HH

Zhengzhou Institute of Electronic Technology HPPPP

P

Zhengzhou Information Engineering Institute PPPPPH HM M Zhengzhou Institute of

Science PP P

Zhengzhou Institute of Surveying and Mapping

PP P