2015美賽特等獎(jiǎng)原版論文集35778_W

1、Human Capital Dynamic Network Model of Team ScienceSummaryAs an indispensable part of team science, managing human capital in organizations directly determines the companys productivity. This paper tries to combine network model with team science.Firstly, build the human capital static network: we u

2、se ICMs 370 positions as nodes, the affiliations and cooperative relationships as edges. For different nodes of position, we define some quantified values that can reflect basic attributes of the position based on proper assumptions. By building the Post Archives Matrix(PAM), we can record the inter

3、nal attributes of each position. This matrix can be really helpful to simulate the real conditions. For every edge (, ), the value is 1 if and only the node and node have the working relationship. Then we put forward the relationship compactness calculation method, which combines affiliation and coo

4、perative relationship, and this is applied to quantify team performance.Secondly, build the human capital dynamic network model: we regard employees demission, promotion and recruitment as the main causes of network evolution and internal churn in the company. Based on the real conditions and some r

5、easonable assumptions, we designed three evolution driving algorithms. For demission algorithm, there are two conditions: if the employee who wants to leave is in low level, he can dismiss directly; if he is in middle level, promotion and recruitment algorithm must be called to fill the position. Wh

6、ats more, we consider carefully about the declination of working enthusiasm and the increasing in churn rate for surrounding people when there is one employee churn. For promotion algorithm, we determine the promotion conditions for different level to realize the layer-by-layer promotion of internal

7、 employees. Besides, promotion is always in priority to recruitment. For recruitment algorithm, we regard the 2/3 of the vacant position as recruitment plan and we build the on- position time vector to represent delaying effects.Thirdly, focusing on the issues that the supervisor needs us to conside

8、r, we draw the conclusions: in the next two years, the recruitment and training cost are 26.22 and 140.15; When the churn rate reaches 25% and 35%, working rate is steadily below 80% and bring some negative effects such as the declining of company performance and employees enthusiasm; The no-externa

9、l recruitment policy is beneficial to maintain the company performance and working rate, but we still have to admit that it will cause the declining of enthusiasm of middle-level employees.Finally, we regard friendships, competition and Human Capital as three network layers to describe the connectio

10、n compactness in the whole team. By using the main statistical indicators (such as the average length of path), we draw the conclusion that multilayer network can reflect internal connections more precisely and comprehensively than human capital network.更多數(shù)學(xué)建模資料請(qǐng)關(guān)注微店店鋪“數(shù)學(xué)建模學(xué)習(xí)交流”/

11、RHO6PSpAContents1Introduction1111.4Problem analysis Literature review. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Terminology and definitions . . . . . . . . . . . . . . . . . . . . . . .

12、 . . . . . . .Our work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2Human Capital Evolution Network Model3344466777910101012132.12.2Model overview and concepts definition . . . . . . . . . . . . . . . . . . . . . . . . . .Human capital static network model . .

13、. . . . . . . . . . . . . . . . . . . . . . . . . ...42.2.5The main assumptions of static human capital network model . . . . . . . . . .The definition of node and edge . . . . . . . . . . . . . . . . . . . . . . . . . .Node attributes in the network . . . . . . . . . . . . . . . .

14、. . . . . . . . . . .The input and initialization of staticnetwork model. . . . . . . . . . . . . . . .Output of static network model . . . . . . . . . . . . . . . . . . . . . . . . . .2.3Three evolution driving algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..22.3.3Employ

15、ee dismission algorithm . . . . . . . . . . . . . . . . . . . . . . . . .Employee promotion algorithm . . . . . . . . . . . . . . . . . . . . . . . . . .Employee recruitment algorithm . . . . . . . . . . . . . . . . . . . . . . . . . .2.4Simulation results of the model . . . . . . . . . . . . . . .

16、. . . . . . . . . . . . . . . ..22.4.3Prediction for ICMs budget requirements . . . . . . . . . . . . . . . . . . . . .Effects of the changing churn rate . . . . . . . . . . . . . . . . . . . . . . . . .Effects of no external recruitment of middle-level employees . . . . . . . . . . .3Multil

17、ayer Network Model3.1The multilayer network for ICM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.2The analysis of multilayer network . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1616174Sensitivity Analysis4.1 Uncertain effects produced by stochastic simulation . . . . . .

18、 . . . . . . . . . . . . . .4.2 Subjective effects produced bysome coefficients . . . . . . . . . . . . . . . . . . . . .1718185Conclusion5.1Strengths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.2Weaknesses . . . . . . . . . . . . . . . . . . . . . . . . . . . .

19、. . . . . . . . . . .181919. . .Team # 35778Page 1 of 201IntroductionHuman capital is an intangible asset, it is relatively abstract and its meaning develops with the devel- opment of our society. Pierre Bourdieu offers a nuanced conceptual alternative to human capital that includes cultural capital

20、, social capital, economic capital, and symbolic capital1 . Human capital, whenviewed from a time perspective, consumes time in one of key activities:Knowledge (activities involving one employee);Collaboration (activities involving more than 1 employee);Processes (activities specifically focused on

21、the knowledge and collaborative activities generated by organizational structure-such as silo impacts, internal politics, etc.);Absence(annual leave, sick leave, holidays,etc.).As the complexity of the workplace continues to grow, organizations increasingly depend on teams. Building an organization

22、filled with good, talented, well-trained people is one of the keys to success. More and more people gradually begin to realize its charming power. So it is extremely important for the HR office to assign employee to positions appropriate to their talents and experience. These positions are just the

23、efficient communication systems to facilitate development of innovative ideas and quality products (commodities or services).But how to manage the human capital has always been a great challenge.1.1Problem analysisWe focus on a more practical problem on the Information Cooperative Manufacturing (ICM

24、) organiza- tion of 370 people, which is in a highly competitive market place.Now, the actual situation of the organization: only 85% of its 370 positions are filled at any time. Con- sidering different position layers in which people are required to have certain years of experience, the low quality

25、 employees often stay with the company for a full career. However, mid-level positions suffer much higher turnover, and its often the case that churn seems to diffuse from former employees to oth- ers, so they are critical ones when consider the position changes. As for the CEO, the ratio of their s

26、alary to worker is approximately 10 times. Besides, in terms of time, the earlier an employee gains the loyalty, the more productive is the organization. Whats more, the annual evaluation based on performance is judged by the supervisor rather than the HR office.Our tasks:Build a human capital netwo

27、rk model of ICM organizations personnel situation that can identify dynamic processes to get certain influence such as the cost, the direct and indirect effects on organizations productively with a certain churn rate as well as simulate or predict what will happen with a changed churn rate.Build a m

28、ultilayer ncetwork that can connect our Human Capital network to other organizational network layers such as information flow, trust, influence, and friendship.1.2Literature reviewHuman capital has been and continues to be criticized in numerous ways. Many researchers have en- gaged in defining and

29、developing this concept2 3 . In the early days, it is an aggregate economic view of the human being acting within economies, which is an attempt to capture the social, biological, cultur- al and psychological complexity as they interact in explicit and/or economic transactions. Today, most theories

30、attempt to break down human capital into one or more components for analysis4 -usually calledTeam # 35778Page 2 of 20intangibles. Accordingly much more attention is paid to factors that led to success versus failure where human management is concerned. The role of leadership, talent, even celebrity

31、is explored. How to make the best use of human capital in the organization, more specifically, to retain good people, keep them properly trained and placed in proper positions, and eventually target new hires to replace those leaving the organization has always been a challenge work.Network has been

32、 widely used in various aspects, especially in natural science. For example, biolog- ical networks provide a mathematical analysis of connections found in ecological, evolutionary, and physiological studies, such as neural networks5 . In computer networks, networked computing devicespass data to eac

33、h other along data connections (network links). As more and more people realized the power of the network, other complex networks, such as social network and business network forms the nascent field of network science6 . For instance, a social network is a social structure made up of a set of social

34、 actors (such as individuals or organizations) and a set of the dyadic ties between these actors. Since using network in social areas is newly developed, the theory is relatively scarce and many theories are more focused on how to establish the structure of the network rather than the function-the p

35、ractical use. So it is a novel perspective to build a human capital network to study how the churn and recruit employee will affect the efficiency of the organization. And as teams have increasingly become a way of life in many organizations, using the new concept of team science to build a human ne

36、twork has little been discussed.Whats more, our life is filled with all kinds of networks, if we do more research on these networks, we may find connection between them, especially a set of entities interact with each other in complicated pat- terns that can encompass multiple types of relationships

37、,and it is important to take suchmultilayerfeatures into account to try to improve our understanding of complex systems. So connect our Human Capital network to other organizational network layers such as information flow, trust, influence, and friendship is just our creative and challenging work.1.

38、3 Terminology anddefinitions Churn: the resulting turbulence when people leaving for other jobs or retiring are replaced. Churn rate(turnover rate):a measure of the number of individuals or items moving out of a col- lective group over a specific period of time,and it can be defined as follows:CR (%

39、) = 2NR100%(NS + NE)where, NR is the number of employees resigned during the month, NS is the number of employees at the start of the month and NEis the total number of employees at the end of themonth.1.4Our workThis paper tries to combine network model with team science to deal with management iss

40、ues.In section 2, we build human capital network. Firstly, in part 2 we use ICMs 370 positions as nodes, the affiliations and cooperative relationships as edges to build a human capital static network model. Then in part 3 we design three evolution driving algorithms respectively which make the netw

41、ork change with certain initial conditions as well as the development of algorithm in time dimension. Thirdly, focused on the issues that the supervisor need us to deal with, we revise our models initial parameters and algorithms. Finally,in part 4 ,based on our simulation results, we solve the issu

42、es supervisor requires and analyze effects under different conditions. In section 3, after studying the theory of multilayer network, we regard friendships, competition and affiliation as three network layers to describe the connection compactness in the whole team. We also find that multilayer netw

43、ork can reflect internal connections more precisely and comprehensively than human capital network. In section 4, we do the sensitivity analysis for simulationTeam # 35778Page 3 of 20methods and some parameters. In section 5, we draw the conclusion of our model and get our strength and weakness.2Hum

44、an Capital Evolution Network Model2.1Model overview and concepts definitionFrom the perspective of the human resources department, we build the human capital network model to reflect the human capital as well as its changes of each level of employees. According to the require- ments, our network sho

45、uld have the following functions:The network can clearly show the distribution of different levels of employees in each divisions or offices as well as the internal leading and being led relationships, which is the basic structure of the promotion mechanism in the organization.Since it is a human ca

46、pital network, we must pay more attention to the main factors that can affect the human capital, which includes: the ability an employee has had when he gets the position, the productive enthusiasm of the employee, the time an employee stays in certain position and the training he obtained.Our human

47、 capital network is an evolutive network model. It has three fundamental dynamic phenomena: employees internal promotion, employees demission and external recruitment.The churn of the employee is especially worrying in ICM organization that the current churn rate is 18% per year. So we should emphat

48、ically consider the how the churn rate will directly and indirectly affect the total benefit and working rate (the effects on employees relationship and enthusiasm will also be considered). To better illustrate our human capital evolution network, the important elements and concepts are defined as f

49、ollows:Node: The nodes in the network model refer to 370 positions set up in the company. This is quite different from the nodes in a normal social network, which represents the actual person. In order to show the characteristic of these nodes more clearly, we build a matrix with 370 rows, and we ca

50、ll it Post Archives Matrix (denoted as PAM for the following illustration). In the matrix, each line represents a quantitative attribute of certain position. In order to satisfied the function, the quantitative attributes contains the level of position, the on-the-job condition of the position, work

51、ing time and which division or office it belongs to.Edge: Edge is the ditch that two points interact with each other. Focused on the present network that regard position as points, the two most direct connections are the affiliation in the division or the office and the leading and being led relatio

52、nship between divisions. In order to reflect influence of individual jobs on team work, we establish the matrix with the size of 370 370 to reflect the affiliation of different positions, which will be analyzed in the following part of this paper about the discussion of the teamwork.Factor: Based on

53、 the description of the problem and the reference given7,the input factors of the evolution network model are the on-job-rate at the initial time and the churn rate, the output factors are the on-job-rate in the future , corporate performance, team work, the costs of recruitment and training , etc.C

54、orporate performance: Our companys corporate performance is the summation of productiv- ity in each position. In order to calculate changing performance, we consider that the maximum productivity is the summation of basic productivity in certain position and the individual experi- ence. Moreover, th

55、e actual productivity is on the base of the maximum productivity and effected by the individual working enthusiasm as well as team work, which will be illustrated in detail in our model.Team # 35778Page 4 of 20 Minimum time unit: In our model, the minimum time unit is month, which is determined by t

56、he data given. So in each month, we will consider the number of people who submit the resignation, join the company and the people should be recruited by the company respectively as well as their enthusiasm in certain month to calculate the corporate performance in that month.2.2Human capital static

57、 network modelIn order to obtain a network model with evolution function to assess the condition to human capital in the company, we first build a complete Human capital static network model. The reason we call it static is that our network needs multiple dimensions to reflect the condition in all aspects in a certain time for the compan