2020A题原文

Problem: The Best Summer Job

Although it's only November, you need to start planning for your 2021 summer job. You have a variety of choices this year and want to determine your "best" choice. You pose this problem for your team of math friends:

We have many opportunities for a summer job. Some allow us to work from home virtually/electronically, some are a walk or bike ride away, and others require us to drive or take a train. Each job offers differing numbers of hours each week and the hourly rates also vary. Some involve physical activity, or at least not sitting at a desk (e.g. cashier at a store, lifeguarding, or wait staff at a restaurant), while others are mostly sedentary and perhaps use analytical and organizational skills (e.g. data analysis, office administration, or research).

Let's develop a model that will evaluate the choices we have for our summer jobs and help us all find the "best" job. While we certainly want to earn and save some money, we also want to have time for recreation activities (e.g. exercise, outings, and social time with friends). Let's make our model one that will be helpful for all high school students to think about and analyze their summer job options.

1. What factors should high school students who are looking for a summer job consider? List and describe the various factors your team identifies. Note that factors may be quantitative or qualitative, constant or variable, and deterministic or probabilistic. Be sure to include units as appropriate.

2. Use your factors to develop a model or algorithm (or set of models/algorithms) for a high school student to use to evaluate their summer job options based on their own situation and preferences as inputs to your model.

3. Test your model with at least ten fictional persons that you create with reasonable data. Explain your development of these fictional persons and the data you chose. Analyze the results of the application of your model on these persons.

4. Describe and show how you would present your model for a person to understand and use. For example, you might use a webpage or an app or a school newspaper article. NOTE: You do not need to publish an actual webpage or develop an actual app, but describe and provide the layout of your proposed presentation.

Your PDF solution of no more than 25 total pages should include:

• One-page Summary Sheet.
• Table of Contents.
• Your complete solution.
• References list.

Note: The HiMCM Contest now has a 25 page limit. All aspects of your submission count toward the 25 page limit (Summary Sheet, Table of Contents, Reference List and any Appendices).

问题提出与分析

问题提出

2020A题“最好的暑期工作”问题是一个很生活化的问题：中学生考虑在暑期找一份短期工作，来攒点钱或者丰富生活阅历等。同时在选择工作时也要考虑方方面面的因素，比如薪酬待遇、工作强度，综合考虑各方因素最终“挑”出一份“最好”的工作。

虽说这个问题很生活化，但对于大部分参加HiMCM比赛的中国学生而言，其实离自己的生活也很远。在留学或升学的巨大压力下，大部分学生暑期选择的是各种学习班以及比较能提升个人背景的竞赛活动，而非去选择做一份暑期工作。毕竟家长和孩子也不差这份“薪资”，相比于“体验生活”，或许还有更“靓丽”的比赛值得参与。至于对于美国本土的孩子，他们是否认为一份暑期工作“值得”，我并不清楚。

当然，这不妨碍学生们来代入情境，进而尝试解决这个问题。谁说一定要有亲身体验才能进行建模呢？2020年B题是关于濒危物种保护的话题，离日常生活就更远了。

“假如我要选择一份暑期工作，我会怎么做呢？”

问题分析

在上述假定情况下，“工作”一定是要做的了，而不必再纠结“要不要做”了。既然要做，那作一番背景研究是有必要的了，去了解

• 找暑期工作的原因
• 找工作要考虑的因素
• 可选择的工作范围
• 寻找工作的平台
• ......

如果要列考虑的因素，还真不少，为了帮助我们理清思路，我们可以及时将自己的思路记录下来，同时当获得新思路或新信息时，及时更新思路，避免忘掉或作重复工作。多人协作可以建立共享文档进行记录，也可以通过共享的知识导图来记录想法。我用过WPS共享思维导图的功能，感觉还可以，一些在线的脑图工具也都可用，不过一定要记得及时保存或备份，以防出现bug导致辛辛苦苦获得的成果丢失。 下面是WPS的分享功能

去网络上搜集一些新闻、博客或者是论文也是很有必要的。不过对于这个很生活化的论文而言，学术论文关于这个话题并不多，但肯定会有类似问题的理论和方法。 以“Summer Jobs for High School Student”为关键词进行google搜索，就有很多回答供参考：

我的浏览器里显示的第一条搜索是关于公司职位空缺的推送

点进去可以看到岗位的要求和内容。 我们细细理一下，可以理出一些和工作有关的要素，比如：

• 对儿童或教育感兴趣(Genuine love and interest in working with children and/or education)——兴趣
• 灵活性，以满足不断变化的需求和要求，同时有效地平衡多个任务(Flexibility to meet changing needs and demands while balancing multiple tasks efficiently) ——灵活性
• 组织能力且关注细节——Strong organization skills and attention to detail —— 组织能力
• 需要工作许可证就业的员工(未满18岁高中未毕业的员工)每天工作时间不得超过8小时，每周工作时间不得超过40小时(Staff requiring a work permit for employment (staff under 18 years of age who have not yet graduated from high school) may not work over 8 hours per day or 40 hours per week)——工作时间
• ...... 逐一看下来会获得很多信息，可以一一整理下来，随着阅读得越来越多，会发现很多相似的内容或反复出现的内容，所花的整理时间也会越来越短。

也会有现成的博客或新闻供参考：

看到类似的新闻，我们可能会感到“如获至宝”，进而感慨“都做得这么好了，还需要我做什么？”确实，类似的文章中似乎已经回答了“好”的工作有哪些。但同时我们也可以发现，如上文的推荐，还很主观化，每个人有自己的需求和想法，怎么能说这几个工作一定适合我呢？能否有一个“量化的方法”来让我更信服呢？
这，也是我们为什么要数学建模的原因了。如果我们拿网上的一篇博文当作我们的成果，且不论已经涉及抄袭了，就算没有抄袭，这也是不符合数学建模比赛和论文的要求的。数学建模论文里没有数学模型可是不合格的呀（不像“鱼香肉丝里没有鱼”，哈哈）。

资料的收集帮我们进一步丰富了对问题背景和解决问题方法的理解，接下来我们就要大体拿出一个问题求解的方案了。分析题目中所列的几个问题，基本上能构成我们解决问题的链条（其实可以视为命题人善意搭建的“脚手架”，引导同学们如何解决问题）：

1. What factors should high school students who are looking for a summer job consider? List and describe the various factors your team identifies. Note that factors may be quantitative or qualitative, constant or variable, and deterministic or probabilistic. Be sure to include units as appropriate.
   
   
2. Use your factors to develop a model or algorithm (or set of models/algorithms) for a high school student to use to evaluate their summer job options based on their own situation and preferences as inputs to your model.
   
   
3. Test your model with at least ten fictional persons that you create with reasonable data. Explain your development of these fictional persons and the data you chose. Analyze the results of the application of your model on these persons.
   
   
4. Describe and show how you would present your model for a person to understand and use. For example, you might use a webpage or an app or a school newspaper article. NOTE: You do not need to publish an actual webpage or develop an actual app, but describe and provide the layout of your proposed presentation.
   
   

我们按照自己对问题的理解，然后结合题目的提示，对问题进行重新叙述（也成为“问题重述”，需要放在论文中，切忌直接翻译问题）。例如

我们需要解决如下问题：

1. 列出影响高中生选取暑期工作的因素及其对应的单位；
2. 建立数学模型或算法可以帮助高中生根据个人需求选取最合适的工作；
3. 构建10个虚拟人物数据，利用所建立的数学模型为这些人推荐最适合的工作；
4. 设计如何通过网页或APP形式（不需要实际构建出网页和APP）展示和应用上述模型。

当然上述问题重述是需要用英文撰写的。基于我们对问题的理解，可以进一步将我们大致的解决方案作下介绍，不用太详细，介绍轮廓即可。流程图也是一个呈现思路的好方式：

对于问题背景有了大概了解之后，就该构建核心的数学模型了，我们下一讲继续分析。