Abstract—In this paper, a human capital network model is established based on an organization’s actual situation with a focus on its dynamic process, which can help people better understand churn and manage human resource in organizations. First, we give a definition to describe the importance of staff offices within the organization and then utilize their importance rank to categorize all the offices into four groups. Based upon the priority of these groups, all employees are distributed into their appropriate positions. After the personnel assignment, a human capital network is constructed for further analysis. In the second part, having taken employee turnover, recruitment and promotion into account, we build a dynamic model to explain these processes within the human capital network based on Markov Chain Theory. For employee turnover, we study the factors (intrinsic motivation and external influence) which decide an employee’s churn probability and develop a method to predict this probability, inspired by the PageRank algorithm. We also simulate the dynamic process to calculate the number of recruitment, according to the number of position vacancies. In addition, promotion probability is introduced to quantify the promotion process. Finally, we extend our model to a multi-layered network.
Keywords-network analysis; human capital; mathematical modelling; computer simulation;
I. INTRODUCTION One of the most important factors for an organization or
a commercial company to survive and succeed is its personnel, or human resource. A competitive organization always pays great attention to keeping itself filled with capable, well-trained people. And to achieve this, it not only needs to hire really good applicants during the recruitment process but also needs to distribute human resource properly, retain senior employees and make reasonable strategies for filling job vacancies. In this regard, many big companies in the current world market concentrate on reducing personnel turnover to maintain itself well-organized.
Much of attention from both academia and company managers has been focused on understanding the causes for employee turnover. Donald P. Moynihan examined the influence of social networks and value congruence on turnover intention among public and nonprofit employees [1]. Abassism discussed many causes of turnover, including hiring practices, managerial style, lack of personal and team
recognition, etc. [2]. Researchers have also investigated into employee churn prediction. For example, V. Vijaya Saradhi et al. carried out a case study for building and comparing predictive employee churn models [3].
To better understand employee churn, we build a dynamic model based on a human capital network to analyze, simulate and predict an organization’s personnel situation.
II. METHODOLOGY In the first part, we distribute all employees into their
appropriate positions. After the personnel assignment, we build a human capital network to indicate relations and interactions among employees for further analysis.
In the second part, having taken employee turnover, recruitment and promotion into account, we establish a dynamic model within the human capital network based on Markov Chain Theory. We also give a clear definition of productivity and discuss the direct and indirect effects of organizational churn on it.
Next, we apply our model to some specific cases to verify its functionality. We use nonlinear programming to get the minimum budget for the next two years. Moreover, we utilize MATLAB to simulate the dynamic processes caused by employee turnover and then analyze the change of churn rate and personnel distribution with time as well as their influence on the health of the organization’s human resource.
Furthermore, a three-layered network is built and improvements are made to the former equation of churn probability based on the complex interpersonal relationship existing in the multi-layered network.
III. BUILD THE HUMAN CAPITAL NETWORK MODEL
A. Determining a Position’s Importance To build the human capital network model of a given
organization’s personnel situation, firstly, we need to place the total employees of different levels into appropriate positions.
The organization’s HR manager has provided us with a graph describing the structure and supervisory nature of the organization. This treelike graph encompasses thirty-five staff offices from the CEO at the top of the tree to Branch at the bottom. Obviously, offices are not equally important within the organization because of their different positions.
We assume there are two factors that reflect a position’s importance: 1) the distance between the position and the highest position; 2) the number of subordinate employees under its supervision.
Thus, we propose the concept of ‘Position Importance’ for a specific staff office within the organization.
Definition 1. (Position Importance) Position Importance denotes the importance of a position in the organization. The equation for quantitative calculation can be written as:
/ .k k kI n d (1) where, nk represents the number of its subordinate
employees (including people right in this position) and dk represents the distance between the position and CEO.
We have recognized that all positions are located in five layers of the structure and we decide the distance between two adjacent layers is 1. In this way, we can determine the relative importance of all the positions.
Generally, the importance rank list matches well with our common sense; nevertheless, some unreasonable results appear. In our calculation, HR’s rank is quite low because it is a small office and it doesn’t have any subordinate branches. In fact, HR plays an indispensable role in an organization who helps senior leadership manage personnel and supervise the human resource health of the entire organization. Another unsatisfying result is that the ranks of the CFO and CIO are not as high as expected. Though they don’t supervise a lot of employees directly like the Production Manager, they exert special influence on the organization’s function. In this regard, their actual importance should be greater.
Based on the above analysis, we make slight changes to the rank list and categorize all the positions into four groups according to their relative importance:
Group 1: CEO, VP Group 2: CFO*, CIO*, HR, Production Manager*,
Sales Marketing, Research, Facilities, Program Manager*
Group 3: Director1, Director2, Director3, Director4, Director5, Director6, Network*, Information*, Plant Blue*, Plant Green*, Regional*, World Wide*, Internet*
B. Personnel Assignment Using our categorization result obtained in Section III,
we put all employees in their appropriate positions within the structure. The subsequent personnel assignment process is explained as follows:
Step 1. Distribute the top four levels of employees in terms of positions’ relative importance. (Higher levels of employees match with more important positions.)
Step 2. Fill all the vacant positions with employees from higher levels of position to lower levels of position.
The assignment result is given in Fig. 1.
CEO4A
CIO1A 2B 9E 2G
CFO1A 2B 9E 2G
Research2B 2E
HR1B 1E 2G
Program Manager2B 10E 2G
Sale Marketing
Facilities2B 2E
VP4A
Production Manager6B 6E 2G
Plant Blue2C 10E 2G
Plant Green2C 10E 2G
Regional2C 10E 2G
Word Wide2C 10E 2G
Networks2C 10E 2G
Informaition2C 10E 2G
Director12C 1F 1G
Director22C 1F 1G
Director31C 1D 1F 1G
Director42C 1F 1G
Director52C 1F 1G
Director62C 1F 1G
BranchA2D 12F
BranchB2D 12F
BranchC2D 12F
BranchD2D 12F
BranchE2D 12F
BranchF2D 12F
BranchG2D 12F
BranchH2D 12F
BranchI2D 12F
BranchJ2D 12F
BranchK2D 12F
BranchL2D 12F
Internet2C 10E 2G
CEO4A
CIO1A 2B 9E 2G
CFO1A 2B 9E 2G
Research2B 2E
HR1B 1E 2G
Program Manager2B 10E 2G
Sale Marketing
Facilities2B 2E
VP4A
Production Manager6B 6E 2G
Plant Blue2C 10E 2G
Plant Green2C 10E 2G
Regional2C 10E 2G
Word Wide2C 10E 2G
Networks2C 10E 2G
Informaition2C 10E 2G
Director12C 1F 1G
Director22C 1F 1G
Director31C 1D 1F 1G
Director42C 1F 1G
Director52C 1F 1G
Director62C 1F 1G
BranchA2D 12F
BranchB2D 12F
BranchC2D 12F
BranchD2D 12F
BranchE2D 12F
BranchF2D 12F
BranchG2D 12F
BranchH2D 12F
BranchI2D 12F
BranchJ2D 12F
BranchK2D 12F
BranchL2D 12F
Internet2C 10E 2G
Figure 1. The result of personnel assignment
After personnel assignment, we can build the human capital network to describe leader-member relations and colleague relations within the organization, schematically shown in Fig. 2. g
Figure 2. A schematic graph of the human capital network
IV. UNDERSTANDING CHURN: A DYNAMIC PERSPECTIVE
A. Three Factors: Churn, Recruitment and Promotion Apparently, our established human capital network is not
a static one. Current employees may leave or retire and new employees get in all the time. In addition, people with required working experience have the opportunity to be promoted into higher manager-level positions. These factors together result in a dynamic network, whose structure is changing from time to time.
Organizational churn is a major cause for employee structure to fluctuate. We consider the possibility of an employee to leave his or her present job is decided according to two aspects: intrinsic motivation and external influence.
175175
An employee’s intrinsic motivation to leave stems from various reasons, including low job satisfaction, job mismatch and personal issues, etc. Meanwhile, the peer effect plays a quite significant role in determining a person’s possibility to leave. Former employees who have churned will stimulate turnover among workers connected to them in the company.
Definition 2. (Churn Probability) Churn Probability βi denotes an employee’s probability to leave his (or her) present job position.
01 1( ).
2i j j k kj kj k
qn n
(2)
where, nj is the number of colleagues in the same office; nk is the number of superior staff connected; β0 represents the intrinsic motivation; q is a constant; αj, αk represent a position’s probability to be filled by an employee; βj, βk represent the churn probability of the employee’s colleague and superior staff respectively.
Here, we give some explanations for the above equation. In accordance with our former analysis, this
equation is made up of two parts: intrinsic motivation, β0; external influence, which is described by the rest terms in this equation.
Both colleagues in the same staff office as the employee and this person’s superior staff will exert external influence on his (or her) churn probability.
αjβj represents colleague j’s influence. Only when there is a person occupying j position can this influence exist. Thus, we introduce αj to describe a position’s probability to be filled by an employee. 1/ nk will get us the average influence from all the employees in this staff office.
αkβk represents a superior employee k’s influence. The meaning of each notation is the same as that in the above explanation.
Moreover, the influence from a colleague and the influence from a superior employee are different. The effect of a senior person’s turnover will of course be bigger. In this regard, we introduce and simplify this difference as a constant coefficient 0.5.
For our problem, due to the lack of detailed information about employees, we cannot exactly identify the intrinsic motivation. But we can use the organization’s current churn rate, 18%, as the value of β0. Moreover, the HR manager has pointed out that mid-level positions suffer from high turnover (twice the average rate for the rest of the company) so the churn rate for different levels of employees will vary.
On the other hand, external influence from former churned peer can be investigated based on our network model, as is described directly in (2). And Fig. 3 is an intuitive figure to demonstrate the mechanism of external influence. The blue node represents an employee, while the big circle represents a staff office. The line represents links between people.
In the end, the number of churned employees at a specific level, thus can be calculated as:
1
.N
c in (3)
Employee
Staff Office
Figure 3. Part of the human capital network
With some employees leaving, vacancies appear, exerting a negative impact on the company’s development. Therefore, recruitment or promotion should be conducted to fill up these holes and to ensure the company functions well. Next, we will mainly discuss these two processes within an organization.
For a specific level (i level) of employees, the number of recruitment can be written as:
(1 ).r icn NT
(4)
where, c is a constant coefficient (for a vacancy, there are two approaches to fill it: outside recruitment and inside promotion. The constant c represents the probability to fill a vacancy by recruiting new employee); T is the median time to recruit an employee at this level (Since recruiting process needs a period of time, we only consider a span of unit time); N is the total number of employees at this level; αi is a position’s probability to be filled by an employee at this level.
Senior manager
Junior manager
Experienced supervisor
Inexperienced supervisor
Experienced employee
Inexperienced employee
Figure 4. Five kinds of promotion in the organization
We take five kinds of promotion into account, shown in Fig. 4. We suppose that inexperienced employees will become experienced after a period of time, so promotion from this level of employees to its upper level exists. Administrative clerk will not get promoted. And we believe
176176
that the probability of occurrence for each kind of promotion is equal. Furthermore, for an employee, with his work hours increasing, the probability for him or her to get promoted will increase correspondingly. Thus we can write a time-dependent equation to depict this increase as:
0(1 ) .ttp p (5)
where, λ is the growth rate; t represents time (unit: month); p0 is the original probability of promotion, which is different for different levels of employees.
Then, we can determine the number of people promoted per month from one level to its upper level:
(1 ) .p tn c N p (6) where, N is the total number of employees at this level; pt
is the probability of promotion; the constant coefficient is c because apart from external recruitment, the rest vacancies can only be filled by promoted people from lower level
B. Identify the Dynamic Processes within the Network After illustrating three elementary factors: turnover,
recruitment and promotion, we further analyze the dynamic processes within our human capital network and run computer simulations.
We set our study objective as a certain level of employees and the unit of time as one month. To describe changes of the human resource network, we need to first choose the parameters as representation.
Definition 3. (HR state vector) The vector is written as: 1 2 3( ) .T
t N
)) .T
N (7) where, αt is the probability for a position of this level to
be filled by an employee at t moment; βj is the churn probability of every employee at this level.
We observe the HR state vector at the start of every month and suppose a month’s state is only related to its former month’s condition, similar to the methodology in Markov Chain Theory. We write the following equation to describe the changing process:
1 , ,= ( ) / .t t r p in p out cn n n n N (8) where, np,in is the number of employees promoted from a
lower level; np,out is the number of employees promoted to a higher level.
The method to calculate βi has already been proposed in our former section. Here, we make a further amendment to this equation after taking the influences of recruitment and promotion on an employee’s churn probability into consideration.
, ,1 0
1' [ ( ) ( )].c p out r p ini i t
t
n n n nN N
(9)
Equation (2) is based on a static model; equation (9) is based on the dynamic processes of recruitment and promotion; thus it is related to time. For those employees who have just been promoted from a lower level and to a higher level, other employees’ influence can be ignored. Therefore, their churn probability is only determined by intrinsic motivation; for the rest of the employees in a staff office, their churn probability is still βi, calculated in (2).
This amended equation indicates that when new employees are added into the company, the churn probability
of older employees will drop a bit, which is in accordance with reality.
In the following part, we perform some simulation and calculation using MATLAB software.
We first try to determine the value of c. In fact, we find that the number of employees will stabilize eventually no matter what the value of c is. Moreover, the stabilized number of employees becomes bigger when c goes up, as is demonstrated in Fig. 5. To make the organization function well, we set the value of c as 0.24.
Figure 5. Stabilized number of employees with different values of c
We then apply our model to predict employee churn rate and the number of employees (churned, recruited) in the future with simulation results shown in Fig. 6.
Figure 6. Change in the number of total employees
C. Effects on Productivity To analyze the direct and indirect effects of
organizational churn on productivity, we need to first give a definition of productivity for an organization.
Definition 4. (Productivity): Productivity denotes a company’s ability to make profits or create value. The calculation equation can be written as: = .i i i
iP v (10)
where, γi denotes an employee’s motivation to work; vi represents the value of an employee.
In the meantime, we use the churn probability to describe an employee’s motivation to work. 1 .i i (11)
In (10), vi embodies organizational churn’s direct effect. While γi is actually the indirect effect. Explanation is given as follows:
177177
Churn causes direct changes in the number and distribution of human capital within the network, therefore, the total value of employees will change accordingly. In the long term, as we assumed in Section III, peer churn will influence other employees’ churn probability, which can be also interpreted as motivation. This influence is indirect. Applying (10) and (11), we can calculate the value of productivity for each month. The change curve is shown in Fig. 7.
Figure 7. Productivity change
In Fig. 7, the change of productivity is consistent with the change in the number of total employees (Fig. 6), the increase at the beginning is due to increase in number of total employees. When the number of employees decreases, productivity will sharply drop.
D. Optimize the Budget: A Talent Management The organization’s budget will contain mainly two parts
of expenditure: cost of recruitment and annual training cost. Based upon our dynamic network model, we can write
the expression of budget: = ( ).i i t r r
iB N C n C (12)
where, i represent a specific level of employees; N is the total number of employees at this level; α is the probability for a position of this level to be filled by an employee; Ct is the annual training cost for this level of employees; Cr is the median cost of recruitment.
The best operation strategy for an organization is to optimize this budget while at the same time keeping the organization function well. We can use a simple model of linear programming to work out the best strategy. The optimization process is illustrated as follows:
min ( )s.t . 370 0.85.i
i
B f cN (13)
We draw a curve to demonstrate how the budget changes with c varying, shown in Fig.8. The budget monotonically increases when the value of c becomes larger. According to the discussion in the former section, when the value of c reaches 0.24, the budget will be the minimum. The corresponding budget and number of recruitment at this point are 400 , 314.5 respectively.
With this optimization result, the company can formulate their initial strategy of managing human resources, including recruitment new employees and elevating senior workers.
Figure 8. Budget change with the value of c
E. A Case Study: Impact on the HR Health In this section, we will use our model to simulate the
impact of 30% churn in both junior managers and experienced supervisors (other churn values should remain at 18%) for the next two years. We assume no external recruiting exists and only qualified employees can be promoted.
For a specific level of position, its personnel change caused by promotion includes two parts: ( )
, (1 ) .ip in in i in p N (14)
( ),out 1 1(1 ) .i
p out i in p N (15) Where, i is the rank of level; n(i)
p,in is the number of employees promoted from a lower level; n(i)
p,out is the number of employees promoted to a higher level.
As is stated in Section III, the probability of promotion varies among different levels. We give Table I to illustrate this difference.
TABLE I. PROMOTION PROBABILITIES FOR DIFFERENT LEVELS
Under the current condition, we study the change of
annual churn rate for the next two years.
Figure 9. Change of annual churn rate
Fig. 9 shows that the stabilized churn rate has increased compared to the original churn rate, which is obviously detrimental to HR health.
178178
We further investigated into the human resource distribution change for the next two years. The result is given in Fig. 10.
Figure 10. Human resource distribution at different time
The pie charts above indicate that the percentage of ordinary employees (experienced employee, inexperienced employee and administrative clerk) is decreasing, while the percentage of managers is increasing. This distribution change will affect the production efficiency of the organization, thus damaging the HR health.
V. MODEL EXTENSION Real situation often can’t be accurately captured by a flat
graph model. This will lead to multi-layer networks [5]. In many natural systems, a set of entities interact with each other in complicated patterns that can encompass multiple types of relationships, vary with time, and include other types of complications. Such systems can be called multi-layer systems or multi-layer network [6].
In this part, we connect our human capital network to other organizational layer. We take friendship network and social network within the company into consideration and combine them with our former single-layered network to establish a three-layered network.
The relation between multiple layers of network lies in the common nodes they share. Through these common nodes, information can flow and be exchanged in different layers of the network. Common nodes are the bridge for transferring information.
CE
B
C
B
E
A
C
AB
D
Social network
Human capital network
Friendship network
A
B
C
E
Friendship network
Human capital network
Social network Figure 11. The three-layered network
Compared with single-layered network, multi-layered network has a significant advantage: it describes the relations and interactions among people comprehensively from
various aspects, which is closer to the actual condition. Here, our three-layered is schematically shown in Fig. 11. We can clearly see there exist some common nodes. For example, A appears both in the friendship network and the human capital network; and B appears in all the three layers of networks.
Furthermore, interpersonal relationship among people in our three-layered network is analyzed. Take A, B, and C for example, A is connected with B in the human capital network and they are connected through C in the friendship network. Thus, A and B are not only colleagues in the same staff office, but also are C’s good friends. It is easy to imagine the friendship network will contribute more to the relation between A and B.
Multi-layered network will assist us in quantifying the influence flow among employees. For analyzing the churn probability in our three-layered network, we redefine the churn probability for an employee in the following equation:
'' ''0i j j
jj
bn
(16)
kj
k ij
wd
(17)
where, nj is the number of people connected, both directly
and indirectly; Χj denotes Person j ’s influential contribution to the churn probability; b is a constant; k is the number of networks where the employee and Person j are connected; wk represents the network’s importance; dij is the shortest path of connection in a specific network.
VI. CONCLUSION We have constructed a human capital network within an
organization. Based on this network, a dynamic model is built to describe an employee’s churn probability and to simulate the staff turnover process. The results of employee turnover, productivity change and budget estimation are reasonable and convincible, indicating our model is effective and well-rounded. This work can help companies and organizations better understand personnel churn internally and optimize their management strategies and business plans.
REFERENCES [1] Donald P. Moynihan and Sanjay K. Pandey. (2008). The Ties that
Bind: Social Networks, Person-Organization Value Fit, and Turnover Intention. J Public Adm Res Theory 18 (2): 205-227
[2] Abassism, D and Hollmank, W. (2000). "Turnover: the real bottom line". Public Personnel management, 2 (3): 333-342.
[3] V. Vijaya Saradhi, Girish Keshav Palshikar. (2011). Employee churn prediction. Expert Systems with Applications, Volume 38, Issue 3, Pages 1999-2006.
[4] Urban, J. M., Weaver, J. L., Bowers, C. A., and Rhodenizer, L. (1996). Effects of workload and structure on team processes and performance: Implications for complex team decision making. Human Factors, 38, 300–310.
[5] M. Magnani, B. Micenková, and L. Rossi. (2013). Combinatorial analysis of multiple networks, arXiv:1303.4986 [cs.SI].
[6] 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).
![Customers Churn Prediction using Artificial Neural ... · devising of churn policy [16] is depicted in Fig. 2. Fig. 2. The Six Steps for Customer Churn Prediction. Churn prediction](https://static.documents.pub/doc/80x56/5e71a26fb4acff71e10cc1fe/customers-churn-prediction-using-artificial-neural-devising-of-churn-policy.jpg)
