
(bk1)Zoological parks (zoos) exist to serve four primary purposes: (1) wildlife conservation, (2) scientific research, (3) education, and (4) recreation. They are designed with all these purposes in mind. When they are responsibly designed and well run, zoos can excel at fulfilling all four of their primary purposes. (pr1)However, when zoos are poorly designed, they fall short of effectively fulfilling one or more of these purposes.
(bk2)The design of all zoos begins with examining the land available. (imp1)Once the land has been deemed acceptable, the designer must consider the layout with regards to the safety and experience of animals, employees, and visitors.
(spm1, rsc1)Your team has been asked by the Council Obsessed with Maximizing Animal Prosperity (COMAP) to design a zoo on a 1-square-kilometer plot of land of your choosing. (imp2)COMAP is willing and able to purchase the land you need, so the exact dimensions and location of the plot can be completely flexible. (bk3)Moreover, they have assured you that access to water, sewer, and electricity can be provided to any location within reason. This allows your team to assume that the land that you choose is acceptable for use as a zoo so you can focus your efforts on creating your design.
(spm1')COMAP's goal is to get the best quality product. Therefore, while there are significant resources available, they are not unlimited. (imp3)For your team this means that while you have a lot of flexibility in your design process and the location of your zoo, your product could be passed over if it is too logistically difficult to facilitate or is too overelaborate.
Requirements.
- Understand the Problem.
• (rsc2)How can a zoo achieve the four primary purposes?
o How can a zoo contribute to wildlife conservation?
o How can a zoo contribute to scientific research?
o How can a zoo contribute to education?
o How can a zoo contribute to recreation?
• (imp4)What do you need to consider for the animals?
o What animals will you keep and what are their needs?
o What kind of enclosures do you need for the animals?
o What animals can cohabitate?
o What kinds of buffers are needed between what animals?
o What kinds of safety concerns do you need to consider for the animals?
• (imp5)What do you need to consider for the employees?
o What kinds of set ups do they need to be safe doing their jobs?
o What kinds of amenities do they need?
• (imp6)What do you need to consider for the visitors?
o What is necessary for safety?
o What kinds of amenities do they need?
o What kinds of things are necessary to make the zoo a place they want to visit?
-
(spm1'')Create Your Zoo Design Model. Design a zoo that will meet the needs of the animals, employees, and visitors. Be sure to address all COMAP's considerations provided in the introduction to this document and the considerations you identified above. (imp7)You will need to make some assumptions to complete your design. Perhaps you will need to make assumptions about the number of employees and/or visitors, the goals of the zoo, or the availability of resources, among other things. (mss1)You must provide a clearly labeled scale drawing of the map of your zoo design.
-
Apply Your Model. (mss2)Provide a 2-page visitor's guide that could be handed out at the entrance to the zoo. (spm2)In the visitor's guide, you should tell them how to maximize their recreational and educational experience at your zoo.
-
(mss3)Expand Your Model and Reflect on Your Analysis. There are many groups around the world who make sure that animals in captivity are safe, healthy, and happy. Provide a maximum 2-page memo that COMAP can send to these groups when they inquire about the zoo you designed for them. In your memo, consider whether your zoo design could be used for a different collection of animals.
-
(mss4)Share Your Model and its Results. Write a 1-page letter to convince COMAP to choose your zoo design. You should be sure to explain how your design sets the zoo up to be able to achieve the four main purposes of zoos.
Analysis:
对比往年试题,这道题目的背景和实际要处理问题的复杂性要大得多,如果刨去这些提示,基本已经很接近大学生比赛的题目了。另外就是除了模型外,给定根据模型结论需要完成的真实任务居然有4个之多,应该创了历史记录了。不过这些都是纸老虎,我们仍然用最原始的三类信息标注法破解题意,并按数学规划问题来优化求解记了。
审题
(相关标记含义见《美赛审题方法简介》)
bk1: 动物园的4个基本目标,到后面重提才确定,这就是基本必须要考察的目标要素;
pr1: 当没有设计好时,4个目标不能全部达成;
bk2: 设计动物园前需要选址;
imp1: layout是暗示的可控变量,目标要考虑3类对象:animals, employees, vistors,属性是safety和experience;
spm1: design表明这又是一个规划类的优化问题;
rsc1: 最大1km ^ 2的大小是给定的参数;
imp2: 占地大小和位置分布是可控变量;
bk3: 只管设计核心内容,其他保障不用考虑;
spm1': goal和best继续表明为规划类的优化问题;
imp3: 说明设计还是要考虑其他保障作为的限定条件的,只是不用作为主要考虑,更不需要作为目标;
rsc2: 重提bk1的四大目标,那把这4个因素作为目标框架必须完整考虑了;
imp4: animals:可控变量有动物类型选择、围栏选择、共存情况(即分布方法)、缓冲带类型;目标变量有安全性;
imp5: employees:可控变量有工作环境设置、便利设施;目标变量:安全性;
imp6: vistors:目标变量:安全性、吸引力;可控变量:便利设施;
spm1'':design重提,3类对象重提,前面所有imp和rsc提醒注意;
imp7: 对于未知的细节可以假设和设计,比如employ和visitor数量、目标设定和资源条件情况等;
mss1: 设计结果图;
mss2: 游客向导;
spm2: 达成最优娱乐和教育目标的游览方式,是在spm1基础上联动的关于游客的优化模型;也可以看作spm1的子模型,共同完成所有目标;
mss3: 便签,说明spm1模型求解结果的结论使用,且在给定不同动物种类时;
mss4: 信,用spm1, 2模型的结果说明;
思路
看起来这题信息量很多,但我们仍然可以依照优化问题的模型框架依次把审题中的信息对照落实:
y(决策目标):有3个维度:
-
内容角度4个:野生动物保护、科学研究、教育、娱乐;
-
对象类型3个:动物、雇员、游客;
-
属性考虑2个:安全性、体验感;
即严格来讲有4 * 3 * 2个目标需要考虑,但实际上很多组合不成立,后续的暗示也重点关照了部分组合,实际重点考虑的是:
-
野生动物保护:生存长短、健康状况、活跃程度等(动物);喂养水平等(雇员影响)、不被过度打扰等(游客影响);这些都能构成安全+体验的综合影响;
-
科学研究:和提示的对象类型无关,题目中也没有其他地方提到,可以归到野生动物保护上去,保护好了自然就提供了研究价值,且研究也不能破坏保护;
-
教育:有所收获、学到知识、感悟自然等(游客)、动物状况等(动物影响)、服务提供等(雇员影响);安全性和体验感都要考虑,分别要达标和最优;
-
娱乐:玩得开心、内容丰富不重复、路线不累(游客)、动物状况等(动物影响)、服务内容(雇员影响);安全性和体验感都要考虑,分别要达标和最优;
其中imp4, 5, 6提到的都是安全性,因此要重点考虑,但其他合理的目标也需要重点选择一些考虑,不考虑的要当假设排除掉写清楚;
结合标题提到的负责和有趣,可以拆解以上目标为2点:
y1:野生动物保护目标,通过动物达成,安全和体验都很重要;
y2:游客的教育和娱乐目标,重点在娱乐,安全性则是限制条件,体验是核心;
x(决策变量):
x1:布局:占地大小和位置分布、区域划分、用什么动物、怎么分布它们、用什么围栏和缓冲带,工作人员的环境、便利设施的设置(类型、位置、分布等);
x2:游客向导:即在x1的布局下给定的路线图,能达成游客的娱乐和教育目标;
r(范围):
x1:不超过1km ^ 2、不能过度使用资源保障,其他的根据查到的资料自行假设;
x2:不重复游览、不进入危险区域满足安全目标、不能过度使用资源保障等等;
f(目标函数):
f1:在给定的布局x1下,计算y中关于野生动物保护部分的目标结果,无法计算的部分一直作假设简化到能计算为止;
f2:在给定f1的最优结果下x1下,计算y中游客的教育和娱乐目标在不同x2的路线下的达成情况,不好计算的部分同理进行简化和假设;
(这里把f拆解为f1, 2两个阶段分别做,是为了简化问题,复杂做可以融合在一起优化,但midmcm的难度来看没有必要,题目中也没有暗示或要求这么做,反而是分开提的。)
p(参数):
p1:最大面积;雇员数量、游客数量、动物种类数和数量,生存长短和活动面积的关系系数、健康状况和种类分布的影响系数、活跃程度和生存密度的关系系数;喂养水平和投入的关系系数;打扰和游客数量的关系系数等等;
p2:x1的最优解即为其参数;
f1和f2即对应本题的spm1和spm2,其中mss1即f1最优解x1的图形化表达,mss2即f2的最优解x2的图示;mss3则要描述spm1模型的内容,并把动物选择变为参数来提供结果;mss4重点写spm1, 2的优点,包括设计的各个要素和结果两个角度。
评注
这题的信息量、复杂度为近年最高。不过同学们也别担心,大家都是公平竞争,我猜选这题的人数可能也相对会少些,最后还是按比例划定成绩的。最终选哪题可以仔细对比3个题目后,队伍内经过充分讨论后再做决定,并坚决执行。
大家一定要反复读题和看以上审题和思路,帮助你捋清楚题目在问什么,需要重点考虑哪些点,以形成最终的思路和答题结构再行动,切忌慌乱。虽然信息量大,但思路框架还是不变的,只要不被吓倒,各个击破,这反而成为你们的优势。
加油,青春无悔!