图与网络算法优秀论文１２1

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标题中的“图与网络算法优秀论文121”暗示了这篇研究聚焦于使用图论和网络分析方法来解决特定问题，而描述中的“Human Capital Dynamic Network Model of Team Science”则进一步明确了研究的具体领域：团队科学中的人力资本动态网络模型。这篇论文的主要目标是探索如何在组织中有效地管理人力资本，以提升团队的生产力。 文章构建了一个静态的人力资本网络。在这个网络中，ICM的370个职位被用作节点，节点间的联系——包括隶属关系和合作关系——作为边。通过设定不同的节点（职位）的量化值来反映其基本属性，如工作职责、技能需求等。通过建立职位档案矩阵（Post Archives Matrix, PAM），可以记录每个职位的内部特性，这有助于模拟真实情况。每条边的权重表示两个节点之间是否存在工作关系，权重为1表示存在合作关系。 作者提出了动态网络模型，以涵盖员工离职、晋升和招聘等导致公司内部变化的因素。当网络发生变化时，考虑了员工工作热情的下降和周围员工离职率的上升。离职算法分为低层级员工可直接离职，以及中层员工离职需要通过晋升和招聘填补空缺两种情况。晋升算法设定了不同层级的晋升条件，确保内部员工的逐级晋升，并且优先考虑内部晋升。招聘算法则将空缺职位的2/3视为需要外部招聘，以保持团队的多样性和新鲜血液。 此外，论文可能还探讨了如何利用关系紧密度计算方法来量化团队绩效，结合隶属关系和合作关系，这为评估团队整体表现提供了新的视角。这些网络模型和算法的应用对于理解团队动态、优化人力资源配置、预测团队稳定性以及提升组织效率具有重要意义。 这篇论文通过构建和分析人力资本的静态和动态网络模型，深入研究了团队科学中的关键问题，即如何管理和优化人力资源以提升团队生产力。它引入了量化指标、动态演化规则以及性能评估方法，为组织决策者提供了有力的理论工具。
Human Capital Dynamic Network Model of Team Science
Summary
As an indispensable part of team science, managing human capital in organizations directly determines
the company’s productivity. This paper tries to combine network model with team science.
Firstly, build the human capital static network: we use ICM’s 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 internal 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 cooperative 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 reasonable 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. What’s 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 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 consider, we draw the conclusions: in the
next two years, the recruitment and training cost are 26.22σ and 140.15σ; 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-external 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
connection 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.
Contents
1 Introduction 1
1.1 Problem analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.3 Terminology and definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.4 Our work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2 Human Capital Evolution Network Model 3
2.1 Model overview and concepts definition . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 Human capital static network model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2.1 The main assumptions of static human capital network model . . . . . . . . . . 4
2.2.2 The definition of node and edge . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2.3 Node attributes in the network . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.4 The input and initialization of static network model. . . . . . . . . . . . . . . . 6
2.2.5 Output of static network model . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 Three evolution driving algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3.1 Employee dismission algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3.2 Employee promotion algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3.3 Employee recruitment algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.4 Simulation results of the model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.4.1 Prediction for ICM’s budget requirements . . . . . . . . . . . . . . . . . . . . . 10
2.4.2 Effects of the changing churn rate . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.4.3 Effects of no external recruitment of middle-level employees . . . . . . . . . . . 13
3 Multilayer Network Model 16
3.1 The multilayer network for ICM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.2 The analysis of multilayer network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4 Sensitivity Analysis 17
4.1 Uncertain effects produced by stochastic simulation . . . . . . . . . . . . . . . . . . . . 18
4.2 Subjective effects produced by some coefficients . . . . . . . . . . . . . . . . . . . . . 18
5 Conclusion 18
5.1 Strengths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
5.2 Weaknesses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Team # 35778 Page 1 of 20
1 Introduction
Human capital is an intangible asset, it is relatively abstract and it’s meaning develops with the devel-
opment of our society. Pierre Bourdieu offers a nuanced conceptual alternative to human capital that
includes cultural capital, social capital, economic capital, and symbolic capital
[1]
. Human capital, when
viewed 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 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 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 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.
1.1 Problem analysis
We focus on a more practical problem on the Information Cooperative Manufacturing (ICM) 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 employees often stay with the company for a full career. However, mid-level positions suffer
much higher turnover, and it’s 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 salary
to worker is approximately 10 times. Besides, in terms of time, the earlier an employee gains the loyalty,
the more productive is the organization. What’s more, the annual evaluation based on performance is
judged by the supervisor rather than the HR office.
Our tasks:
• Build a human capital network model of ICM organization’s personnel situation that can identify
dynamic processes to get certain influence such as the cost, the direct and indirect effects on
organization’s productively with a certain churn rate as well as simulate or predict what will happen
with a changed churn rate.
• Build a multilayer ncetwork that can connect our Human Capital network to other organizational
network layers such as information flow, trust, influence, and friendship.
1.2 Literature review
"Human capital" has been and continues to be criticized in numerous ways. Many researchers have en-
gaged in defining and developing this concept
[2] [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 attempt to break down human capital into one or more components for analysis
[4]
-usually called
Team # 35778 Page 2 of 20
"intangibles". Accordingly much more attention is paid to factors that led to success v ersus f ailure where
human management is concerned. The role of leadership, talent, even celebrity 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 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 networks
[5]
. In computer networks, networked computing devices
pass data to each 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 science
[6]
. For instance, a social network is a social structure made up of a set
of social 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 practical
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 network has little
been discussed.
What’s 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,and it is important to take such"multilayer"features
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.
1.3 Terminology and definitions
• 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:
σ
CR
(%) =
2N
R
(N
S
+ N
E
)
× 100%
where, N
R
is the number of employees resigned during the month, N
S
is the number of employees
at the start of the month and N
E
is the total number of employees at the end of the month.
1.4 Our work
This paper tries to combine network model with team science to deal with management issues.In section
2, we build human capital network. Firstly, in part 2 we use ICM’s 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 network 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 model’s initial parameters and algorithms. Finally
,in part 4 ,based on our simulation results, we solve the issues 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 network can reflect internal connections more precisely and
comprehensively than human capital network. In section 4, we do the sensitivity analysis for simulation
Team # 35778 Page 3 of 20
methods and some parameters. In section 5, we draw the conclusion of our model and get our strength
and weakness.
2 Human Capital Evolution Network Model
2.1 Model overview and concepts definition
From 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 should 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 capital 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 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 emphatically 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 follows:
• 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 call 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,
working 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 relationship 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 the description of the problem and the reference given
[7]
,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.
• Corporate performance: Our company’s 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, the 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.

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