2015 MCM 赛题点评 C题

2015-4-25 17:02| 发布者: magic2728| 查看: 1158| 评论: 6|原作者: magic2728

摘要: 题目有点长，也就是信息有点多，也就是不需要额外的知识了，是个好事，更加反映了数学建模就是一个量化处理信息的过程，利用我们大脑中的知识化腐朽为神奇的一场美丽的表演。本题网络建模背景，不过建模思想亘古不变 ...

题目有点长，也就是信息有点多，也就是不需要额外的知识了，是个好事，更加反映了数学建模就是一个量化处理信息的过程，利用我们大脑中的知识化腐朽为神奇的一场美丽的表演。

本题网络建模背景，不过建模思想亘古不变得渗透在字里行间，还是：建立函数关系，并用一切数学手段去理解这个函数关系，解决遇到的问题。

Problem C

Managing Human Capital in Organizations

Building an organization filled with good, talented, well-trainedpeople is one of the keys to success.(bk1) But to do this, an organization needs to do morethan 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 newhires to replace those leaving the organization.（pr1） Individuals play unique roles within theirorganizations, both formally and informally.Thus, the departure of individuals from an organization leaves important informationaland functional components missing that need to be replaced. This is true for sports teams, commercial companies, schools anduniversities, governments, and almost any formal group or organization of people.(pr1')

Human resource (HR) specialists help senior leadership manage personnelby improving retention and motivation, coordinatingtraining, and building good teams. (bk2)In particular, leaders seek to create an effectiveorganizational structure, where people are assigned to positions appropriate to their talents and experience, andwhere efficient communication systems are inplace to facilitate development of innovative ideas and quality products (commodities or services). Thesetalent management and team building aspectsof HR management are remaking many modern organizations. Managing the fluid network of human capital within anorganization requires understandingpersonnel loyalties to the company and to subgroups; building trust in the workplace; and managing the formation, dissolutionand retention of formal and informal ties betweenpeople. When people leaving for other jobs or retiring are replaced, the resulting turbulence is collectively termedorganizational “churn”.(bk2') Your team hasbeen asked by your HR manager todevelop a framework and model for understanding churn within the Information Cooperative Manufacturing (ICM) organization of 370 people. ICM is in a highly competitive market place, leading to challengingissues related to effectively managing its humancapital.

The HR manager wants to map the human capital in the organization bybuilding a network model.(spm1) Here are some issues your company faces:

1. ICM aims to identify the risk （imp1）of churn in its earlystages, as it is cheaper to gain the loyalty of an employee early in their career ratherthan have to improve the culture once ithas soured. It is more productive to have a motivatedworkforce from the start rather thanhaving to provide incentives to prevent people from leaving.

2. A worker is more likely to churn if he or she was connected to otherformer employees who have churned. Thuschurn seems to diffuse （imp2）from employee to employee, so identifying those that are likely to churn is valuableinformation to prevent further churning.

3. One HR issue is matching employees to the right position such thattheir knowledge and abilities can be maximized. （imp3）Currently each employee gets an annual evaluation based on performance as judged by the supervisor.These ratings are currently not used by the HRoffice.

4. ICM recognizes that middle managers（imp4） (Junior Managers, Experienced Supervisors, Inexperienced Supervisors) often feel stuck in their jobswith little opportunity to advance, causingthem to leave the company when they find a comparable or better job. These mid-levelpositions are critical ones that unfortunately suffer high turn-over (twice the average rate of the rest of the company) and seem to need fillingall the time.

5. Recruiting good people is difficult, time consuming and expensive.ICM usually has only 85% of its 370 positions filled at any time and, because of administrative delays and office capacity and internal promotions,the HR office is actively hiring about 8-10% of theICM positions (about 2/3 of the current vacancies).（rsc1）

6. In order to move up into the higher management-level positions,people are currently required to haveseveral years of experience in the company atspecificlevels and types of positions. This can pose major obstaclesfor the HR department.（imp5）

7. The churn rate has been increasing steadily, especially for middle managers. The ICM HR manager sees this as the biggest challengethe company faces. The CEO panicked when hearingthat the current churn rate is 18% per year.（rsc2）

8. Because ICM is always worried about being short-handed, marginal andpoor

employees are allowed to stay on inan attempt to lower the churn and, therefore,

very few employees are relieved or fired. This results in lower qualityemployees

who often stay with the company for a full career. This quality issueis causing

concern with the management, but no one seems to have a solution.（imp6）

9. Your organization is proud of its modest CEO-to-worker salary ratio (i.e.,the

CEO salary is approximately 10 times the median of the salaries of all the

employees in the organization as compared to hundreds of times themedian as

found in many companies).

The ICM HR manager has recently put together a comprehensive organizationalgraph

(Figure 1) and detailed statistics describing the basic structure, staffing, recruiting costs,

trainingcosts, and salaries of the companyemployees (Table 1).（rsc3） The company has

never conducted any analyses, modeling or simulation of the HRfunctions of the

company. Therefore, she feels that now is the time to automate and analyze the HR

elements of ICM using network science.（spm1s）

file:///C:/Users/tpzh/AppData/Local/Temp/msohtmlclip1/01/clip_image002.jpg

Figure 1: The rigid structure and supervisory nature of ICM comes from the requirement that each branch or staff office with an* consists of two divisions of 7

people. Otherwise, each entry in this chart without an * consists of 4staff people.

Therefore, the 370 total employees are organized in 46 divisions of 7people and 12

offices of 4 people.

file:///C:/Users/tpzh/AppData/Local/Temp/msohtmlclip1/01/clip_image004.jpg

Table 1: The HR manager has provided you with this critical HR data on numberand level of employees, average salary, the average costsand time of external recruitment for variouslevels of personnel, and annual training costs. The median income of the company is defined as s. The value of s for ICM does rise slowlywith the inflation rate

so all the decision makers in ICM are comfortable with reports anddecisions based on

the changing and relative value of s, instead of exact monetary values.

Tasks:

The ICM HR department work-tasks and research questions from your HRmanager include the following:

1) Build a Human Capital network model of ICM organization’s personnel situation using the data provided. You may have to make bold assumptions to build the model —be sureto describe the model and your assumptions.（spma：tree model，get determinedposition of it，correspondto several states：recruit time, cost, number ofpeople, salary, training cost, churn degree and ability level）

2) Use your model to identify dynamic processes within the Human Capital network. Describe and incorporate dynamic processes involvedin (1) organizational churn (e.g., influence, dissatisfaction) and (2) direct andindirect effects on the organization’s productivity. You may have to make some bold assumptionsto explain theseprocesses. Describe your model and all your assumptions.(spmb: churn spreading(will be steady) rules, productivity evaluation method on the result of that)

3) Use your model to analyze your organization’s budget requirements fortalent

management in terms of s for bothrecruiting and training over the next 2 years.(spmc: calculate as modeled in aand b)

4) Can ICM sustain its 80% fullstatus for positions if the annualchurn rate for all

positions goes to 25%? How about 35%? What are the costs of thesehigher

turnover rates? What are the indirect effects of these high churnrates?(spmd:relation between status rate and churn rate(parameter))

5) The ICM HR supervisor wants to use your model to simulate the impact of30%

churn in both junior managers and experienced supervisors with(rsc4s) 1) no external

recruiting and 2) promoting only qualified employees for the next two years.

Other churn values should remain at 18% in your model. Explain to herthe

impactof that situation on the HR health of theorganization.

6) Your supervisor calls this kind of talent management —team science. She has

provided you with these references to start your work:

E. Salas, N.J. Cooke, and M.A. Rosen. (2008). On Teams, Teamwork, andTeam

Performance: Discoveries and Developments. Human Factors: The Journal of the

Human Factorsand Ergonomics Society June 2008 vol. 50 no. 3 540-547.

D. Stokols, K.L. Hall, B.K. Taylor, R.P. Moser (2008). The Science ofTeam Science:

Overview of the Field and Introduction to theSupplement, Am J Prev Med

2008;35(2S): S77-S89.

Ultimately, she wants to connect your Human Capital network to other organizationalnetwork layers such as information flow,trust, influence, and friendship that the other offices of ICM are consideringbuilding. The HR manager’s vision is that the HRoffice should take the lead in this effort to connect the network models of the organization and wants your team toconsider how that could happen. For thatconsideration she provides the reference

Mikko Kivelä, Alexandre Arenas, Marc Barthelemy, James P. Gleeson,Yamir

Moreno, Mason A. Porter. (2013). Multilayer Networks,J. Complex Networks, 2(3):

203-271 (2014); arXivpreprint arXiv:1309.7233, 2013.

Summarize the potential use of team science and multi-layered networksin fulfilling the vision of your HR manager.(mss1)

7) Write a 20-page report on your organizational model and its functionand the issues that the supervisor wantsyou to consider. The one-page executive summary of the report does not count; therefore, you can submit a totalof 21 pages, maximum.(mss2)

本题背景是网络建模，这个是描述人类头衔结构的基本工具，每个位职（每个人）可以当成一个节点，可以升迁上去的职位（认识的人）之间有边，边的权重可以理解为升迁难度（人之间的熟悉程度，上下级关系），节点的权重可以是表格中的量以及churn 影响率和职位要求，人员数量，以及人的能力值和churn 值，以此为基础将题目中的信息结构化，转化为数学表达量后，依题意进行评价和优化。

文中提到9点要求，这些要求有的是思路和方法的暗示，有的是限制性条件条件，已经在题干中标明，一定要分别处理：限制不能违反，暗示要找最优的方式理解。

1 说明早期的churn 传播是不稳定的，需要把churn 的分布情况对时间求函数，说明发展情况；2 说明稳态的churn 情况也是一个动态平衡，在网络结构里进行模拟；3 暗示人员安排需要优化以及有人员能力评估模型；4 高危职位需要引入另外的参数表达； 5. 满员率参数限定； 6. 人员流动限定条件暗示；7. 修改churn参数的灵敏度分析； 8. 低职位churn 作弊行为处理； 9. 工资等参数限定，以及网络结构，不可改；

以上提到的点是贯穿后面的建模的，根据task 部分，需要如下分模型：

a. 用网络模型对头衔结构的描述，这个已经在开头提到，以职位或者人为节点，升迁和认识为边附上权重，在此结构下描述所有的信息；

b. churn 传播模型，自行设定传播规则，模拟传播动态过程和稳态情况；

c. 花费预算，在a 的框架，b 传播造成的人员流动条件下计算，评价模型的思路，优化模型的解法，根据评价花费的函数，优化可以调整的网络参数，结构；

d. 建立职位率和churn 参数之间的关系，并以此作灵敏度分析；

e. 从统一churn 参数变为双参数，增加d 的难度，分析变化情况；

f. 拓展到新的网络结构。further working 部分，描述即可；

完成全文，大功告成，好运！