Dynamics of the intervention strategy of job burnout of coal miners

Abstract

This research focus on the formation mechanism and intervention strategy of coal miners’ job burnout, based on a simulation study using system dynamics method. The simulation result indicates that, work assignment alienation has higher sensitivity to intervention strategies than other elements of coal miners’ job burnout, while health damage is least sensitive to intervention. The top three adoptable strategies shall be reasonable working hours, self-psychological adjustment, and psychological counseling program. As the impact of one intervention strategy weakens with time, it is necessary to constantly change intervention strategies or to adopt a strategy combination to intervene miners’ burnout. This study explains the formation mechanism of coal miners’ job burnout and offers targeted advice for coal enterprises, aiming to effectively improve their safety management mechanism and to reduce casualties.

Keywords

Coal miners job burnout intervention strategy system dynamics simulation

1 Introduction

“Job burnout” refers to a series of negative symptoms, such as the physical and psychological depletion in work, decrease in working abilities, loss of enthusiasm, and indifference towards others. Gao, et al. [1], propose that coal miners, who are having job burnout, tend to feel bored and exhausted, and have physical and mental fatigue from inefficient mitigation of long term working pressure. If the job burnout lasts, the miners keep negative inertia both mentally and physically, and have dispersed attention and reduced safety awareness. Consequently, it not only lowers productivity, but also causes production safety accidents.

Multiple reasons cause job burnout, in a complex and nonlinear way. Zhou, Li and Mei [2] propose that, coal miners’ lacking of job resources causes job burnout, with the mediating effects of psychological capital and fatigue. Factors, including miners’ work environment, work assignment, work relationship, work security, health damage and sense of work achievement, etc., should be brought into the intervention strategies. Besides, these factors could change and interact with each other with time.

Cihan Mermer, Hatice Şengül [3], Chen, et al. [4], Javier Galvez, et al. [5] and propose that system dynamic is an effective tool to address dynamics of complex systems. Liu and Chen [6] examines the interaction and feedback between factors of the security defense system by system dynamic simulation experiments. Xu and Luo [7] studies the dynamic feedback relationship between factors and intervention strategies of civil aviation maintenance personnel’s job burnout. This paper builds a system dynamic simulation model, using Vensim software, to further strengthen the research on job burnout of coal miners.

2 Proposing the intervention strategy set of job burnout

Coal miners’ job burnout is mainly manifested in six aspects: work environment alienation, work assignment alienation, work relationship depletion, work safety depletion, health damage and low sense of work achievement. So that the intervention strategies are proposed in the above six aspects respectively.

2.1 Strategies to alleviate work environment alienation

Due to the dirty and messy underground environment, the crowded and narrow operation space, and the damp and dark underground micro-climate, miners suffer work environment alienation, which could be alleviated by improving the working environment and increasing the level of mechanization, as detailed in Table 1.

Table 1
Intervention Strategies for work environment alienation

Intervention content Intervention strategies Specific interventions

Work environment alienation 1. Improve the working environment; 1. Improve lighting intensity; 2. Improve color contrast underground;

2. Raise the level of mechanization

3. Warm panel layout;

4. Integrated management information system;

5. Fully mechanized mining and fully mechanized excavation operations

Intervention content	Intervention strategies	Specific interventions
Work environment alienation	1. Improve the working environment;	1. Improve lighting intensity; 2. Improve color contrast underground;
	2. Raise the level of mechanization
		3. Warm panel layout;
		4. Integrated management information system;
		5. Fully mechanized mining and fully mechanized excavation operations

2.2 Strategies to alleviate work assignment alienation

Work assignment alienation rises mainly because of miners spending long time on one single but unchangeable task, while their work load is quite heavy. Therefore, we could improve it by reasonably arranging working hours, salary incentive, increasing mechanization level, enriching work content, etc., as detailed in Table 2.

Table 2
Work assignment alienation intervention strategy set

Intervention content Intervention strategies Specific interventions

work assignment alienation 1. Enrich work content; 1. Job rotation and job expansion;

2. Salary incentive; 2. Four shifts and six hour system;

3. Increase mechanization level; 3. Reduce night shift; 4. Fully mechanized mining and fully mechanized excavation; 5. Raise salary

4. Reasonable arrangement of working hours

Intervention content	Intervention strategies	Specific interventions
work assignment alienation	1. Enrich work content;	1. Job rotation and job expansion;
	2. Salary incentive;	2. Four shifts and six hour system;
	3. Increase mechanization level;	3. Reduce night shift; 4. Fully mechanized mining and fully mechanized excavation; 5. Raise salary
	4. Reasonable arrangement of working hours

2.3 Strategies to alleviate the depletion of work relationships

Miners’ work relationship depletion is mainly due to the lack of communication between miners and superior leaders, the indifference between colleagues, and insufficient support from the organization. As shown in Table 3, strategies, such as employee assistance program, psychological counseling program, confiding and self-psychological adjustment, could be effective.

Table 3
Work Relationship Depletion Intervention Strategy Set

Intervention content Intervention strategies Specific interventions

Work Relationship Depletion 1. Employee assistance program; 1. The superior-subordinate dialogue mechanism; 2. Team life meeting;

2. Psychological counseling program;

3. confiding; 3. Talk;

4. Self-psychological adjustment 4. Logistics service team;

5. Mutual help group;

6. Participate in recreational activities and develop hobbies

Intervention content	Intervention strategies	Specific interventions
Work Relationship Depletion	1. Employee assistance program;	1. The superior-subordinate dialogue mechanism; 2. Team life meeting;
	2. Psychological counseling program;
	3. confiding;	3. Talk;
	4. Self-psychological adjustment	4. Logistics service team;
		5. Mutual help group;
		6. Participate in recreational activities and develop hobbies

2.4 Strategies to alleviate the depletion of work safety

The production of coal has much hidden trouble in safety, especially when managers neglect safety regulations simply for increasing output, so that miners feel less secured. Therefore, proposals like safety culture management, risk identification ability, psychological counseling program and self-psychological adjustment are given to solve work security depletion, as detailed in Table 4.

Table 4
Strategy Set for Work Security Depletion Intervention

Intervention content Intervention strategies Specific interventions

Work Security Depletion 1. Safety Culture Management; 1. Hidden trouble closure management;

2. Risk identification ability; 2. Persuading and help-education mechanism;

3. Psychological Counseling program; 3. Emergency drills; 4. Safety education;

4. Self-psychological adjustment

5. Risk identification ability development;

6. Safety awareness in coal production;

7. The safety supervision system combing of Education prevention, inspection and control, reward and punishment, persuasion and help-education;

8. Psychological safety instructions;

9. In-depth security talks;

10. Typical incentives

2.5 Strategies to alleviate health damage

Physically, the Long-term underground work makes miners exposed to a large amount of dust and noise, and cause diseases like bronchial, neurasthenia,etc. Psychologically, the dark and wet environment easily leads to boredom, anxiety and other psychology problems. Therefore, this paper proposes to alleviate health damage through physical exercise, psychological counseling, Self-psychological adjustment and other strategies, see Table 5.

Table 5
Health damage intervention strategy set

Intervention content Intervention strategies Specific interventions

Health damage 1. Physical exercise; 1. Regular running training;

2. Psychological Counseling; 3. Self-psychological adjustment 2. Muscle training; 3. Regular physical examination; 4. Establish counseling room, activity room, relaxation room, vent room, tea room;

5. Establish a team of counselors;

6. Health program for miners

Intervention content	Intervention strategies	Specific interventions
Health damage	1. Physical exercise;	1. Regular running training;
	2. Psychological Counseling; 3. Self-psychological adjustment	2. Muscle training; 3. Regular physical examination; 4. Establish counseling room, activity room, relaxation room, vent room, tea room;
		5. Establish a team of counselors;
		6. Health program for miners

2.6 Strategies to relieve low sense of work achievement

With little opportunity of promotion, low social status, disproportionate return on pay and inability to integrate into modern life, miners hardly have the senses of success. Therefore, this paper proposes to use salary increase, self-psychological adjustment, psychological counseling and employee assistance program to alleviate miners’ low sense of work achievement, as shown in Table 6.

Table 6
Low sense of work achievement intervention strategy set

Intervention content Intervention strategies Specific interventions

Low sense of work achievement 1. Salary incentive; 2. Self-psychological adjustment; 3. Psychological counseling program; 4. Employee assistance program 1. Individual growth and career design;

2. Affection management; 3. Diversified incentives;

4. Enriching the life after work

Intervention content	Intervention strategies	Specific interventions
Low sense of work achievement	1. Salary incentive; 2. Self-psychological adjustment; 3. Psychological counseling program; 4. Employee assistance program	1. Individual growth and career design;
		2. Affection management; 3. Diversified incentives;
		4. Enriching the life after work

3 Causality and flow chart of job burnout intervention for miners

3.1 Causality diagram

Through the above intervention strategy analysis, the causality diagram of coal miners’ job burnout is displayed in Fig. 1. The figure describes the reasons of the dynamic change of job burnout, the intervention strategies of each factor and their feedback structures. It shows that each factor and its intervention strategies depend on each other. A change of one or more indicators would make a difference on the whole system level.

Fig. 1

Causality map of Job Burnout of Coal Miners.

The causality diagram contains the following feedback loops:

3.1.1 The work environment alienation intervention subsystem consists of two feedback loops:

Work environment improvement ↑⟶ work environment alienation ↓⟶ job burnout ↓⟶ unsafe behavior ↓⟶ job burnout intervention ↓⟶ improve work environment ↓

Increase mechanization level ↑⟶ work environment alienation ↓⟶ job burnout ↓⟶ unsafe behavior ↓⟶ job burnout intervention ↓⟶ increase mechanization level ↓

3.1.2 The work assignment alienation intervention subsystem consists of four feedback loops:

Enrich work content ↑⟶ work assignment alienation ↓⟶ job burnout ↓⟶ unsafe behavior ↓⟶ job burnout intervention↓⟶ enrich work content

Salary incentive ↑⟶ work assignment alienation ↓⟶ job burnout ↓⟶ unsafe behavior ↓⟶ job burnout intervention ↓⟶ salary incentive ↓

Increase mechanization level ↑⟶ work assignment alienation ↓⟶ job burnout ↓⟶ unsafe behavior ↓⟶ job burnout intervention ↓⟶ increase mechanization level

Reasonable arrangement of working hours ↑⟶ work assignment alienation ↓⟶ job burnout ↓⟶ unsafe behavior ↓⟶ job burnout intervention ↓⟶ reasonable arrangement of working hours.

3.1.3 The work relationship exhaustion intervention subsystem consists of four feedback loops:

Employee assistance program ↑⟶ work relationship depletion ↓⟶ job burnout ↓⟶ unsafe behavior ↓⟶ job burnout intervention ↓⟶ employee assistance program

Psychological counseling program ↑⟶ work relationship depletion ↓⟶ job burnout ↓⟶ unsafe behavior ↓⟶ job burnout intervention ↓⟶ psychological counseling program

Talk ↑⟶ work relationship depletion ↓⟶ job burnout ↓⟶ unsafe behavior ↓⟶ job burnout intervention ↓⟶ confiding ↓

Self-psychological adjustment ↑⟶ work relationship depletion ↓⟶ job burnout ↓⟶ unsafe behavior ↓⟶ job burnout intervention ↓⟶ Self-psychological adjustment ↓

3.1.4 The Work safety depletion intervention subsystem consists of four feedback loops:

Safety culture management ↑⟶ work safety depletion ↓⟶ job burnout ↓⟶ unsafe behavior ↓⟶ job burnout intervention ↓⟶ safety culture management

Risk identification ability ↑⟶ work safety depletion ↓⟶ job burnout ↓⟶ unsafe behavior ↓⟶ job burnout intervention ↓⟶ risk identification ability ↓

Psychological counseling program ↑⟶ work safety depletion ↓⟶ job burnout ↓⟶ unsafe behavior ↓⟶ job burnout intervention ↓⟶ psychological counseling program

Self-psychological regulation ↑⟶ work safety sense depletion ↓⟶ job burnout ↓⟶ unsafe behavior ↓⟶ job burnout intervention ↓⟶ self-psychological regulation ↓

3.1.5 The health damage intervention subsystem consists of three feedback loops:

Physical exercise ↑⟶ health damage ↓⟶ job burnout ↓⟶ unsafe behavior ↓⟶ job burnout intervention ↓⟶ physical exercise ↓

Psychological counseling program ↑⟶ health damage ↓⟶ job burnout ↓⟶ unsafe behavior ↓⟶ job burnout intervention ↓⟶ psychological counseling program

Self-psychological adjustment ↑⟶ health damage ↓⟶ job burnout ↓⟶ unsafe behaviors ↓⟶ job burnout intervention ↓⟶ Self-psychological adjustment ↓

3.1.6 The low sense of work achievement intervention subsystem consists of four feedback loops:

Salary Incentive ↑⟶ Low sense of work achievement ↓⟶ Job burnout ↓⟶ Unsafe behavior ↓⟶ Job burnout intervention ↓⟶ Salary incentive ↓

Self-psychological adjustment ↑⟶ Low sense of work achievement ↓⟶ Job burnout ↓⟶ Unsafe behavior ↓⟶ Job burnout intervention ↓⟶ Self-psychological adjustment ↓

Psychological counseling program ↑⟶ low sense of work achievement ↓⟶ job burnout ↓⟶ unsafe behavior ↓⟶ job burnout intervention ↓⟶ psychological counseling program

Employee assistance program ↑⟶ Low sense of work achievement ↓⟶ Job burnout ↓⟶ Unsafe behavior ↓⟶ Job burnout intervention ↓⟶ Employee support program

3.2 Construction flow chart of intervention strategies for job burnout of miners

Using Vensim, we establish a construction flow chart of the job burnout intervention strategy for coal miners, as shown in Fig. 2. There are 9 state variables, such as job burnout intervention, work environment alienation. It has 17 rate variables, such as job burnout intervention increment and work environment alienation increment. There are 30 auxiliary variables as well, such as increasing mechanization level, improving work environment and enriching work content.

Fig. 2

Flow Chart of Job Burnout Intervention Strategies for Coal Miners.

As shown in Fig. 2, there are 9 subsystems in the intervention strategy system of coal miners’ job burnout, which are respectively job burnout intervention subsystem, job burnout subsystem, unsafe behavior subsystem, work environment alienation system, work assignment alienation system, work relationship depletion subsystem, work safety depletion subsystem, health damage subsystem and low sense of work achievement subsystem.

4 Variable setting and system dynamics equation

Take Y mine area as the research subject, where miners have typical job burnout and suffer psychological and physiological fatigue, low enthusiasm for work, low sense of achievement, etc,. In addition, the Y mine area has established a psychological counseling mechanism and a health management mechanism.

As discussed above, there are 9 state variables, 17 rate variables and 30 instrumental variables, as shown in Table 7.

Table 7
System Dynamics Variables of Job Burnout Intervention Strategies

State variables Rate variable Instrumental variables

Job burnout intervention L₁ Job burnout intervention increment R_1I Increase the mechanization level A₁

Work environment alienation L₂ Work environment alienation increment R_2I Improve the working environment A₂

Work assignment alienation L₃ Work environment alienation decrement R_2D Enrich work content A₃

Work relationship depletion L₄ Work assignment alienation incrementR_3I Salary incentive A₄

Work safety depletion L₅ Work assignment alienation decrement R_3D Reasonable arrangement of working hours A₅

Health damage L₆ Work relationship depletion increment R_4I Employee assistance program A₆

Low sense of work achievement L₇ Work relationship depletion decrement R_4D Psychological counseling program A₇

Job burnout L₈ Work safety depletion increment L_5I Confiding A₈

Unsafe behavior L₉ Work safety depletion decrement R_5D Self-psychological adjustment A₉

Health damage increment R_6I Safety Culture Management A₁₀

Health damage decrement R_6D Risk identification ability A₁₁

Low sense of work achievement increment R_7I Physical exercise A₁₂

Low sense of work achievement decrement R_7D Hostile underground environment A₂₁

Job burnout increment R_8I Narrow operation space A₂₂

Job burnout decrement R_8D Bad operation conditions A₂₃

Unsafe behavior increment R_9I Heavy work load A₃₁

Unsafe behavior decrement R_9D Monotonous work content A₃₂

Long work hours A₃₃

Non-harmonious relations with colleagues A₄₁

Lack of support from leaders A₄₂

Lack of support from organization A₄₃

Serious safety Conflict A₅₁

Many hidden safety dangers A₅₂

Lacking safety supervision A₅₃

Psychological damage A₆₁

Physical damage A₆₂

Disproportionate return on pay A₇₁

Little opportunity of promotion A₇₂

Low social status A₇₃

Less modernized life A₇₄

State variables	Rate variable	Instrumental variables
Job burnout intervention L₁	Job burnout intervention increment R_1I	Increase the mechanization level A₁
Work environment alienation L₂	Work environment alienation increment R_2I	Improve the working environment A₂
Work assignment alienation L₃	Work environment alienation decrement R_2D	Enrich work content A₃
Work relationship depletion L₄	Work assignment alienation incrementR_3I	Salary incentive A₄
Work safety depletion L₅	Work assignment alienation decrement R_3D	Reasonable arrangement of working hours A₅
Health damage L₆	Work relationship depletion increment R_4I	Employee assistance program A₆
Low sense of work achievement L₇	Work relationship depletion decrement R_4D	Psychological counseling program A₇
Job burnout L₈	Work safety depletion increment L_5I	Confiding A₈
Unsafe behavior L₉	Work safety depletion decrement R_5D	Self-psychological adjustment A₉
	Health damage increment R_6I	Safety Culture Management A₁₀
	Health damage decrement R_6D	Risk identification ability A₁₁
	Low sense of work achievement increment R_7I	Physical exercise A₁₂
	Low sense of work achievement decrement R_7D	Hostile underground environment A₂₁
	Job burnout increment R_8I	Narrow operation space A₂₂
	Job burnout decrement R_8D	Bad operation conditions A₂₃
	Unsafe behavior increment R_9I	Heavy work load A₃₁
	Unsafe behavior decrement R_9D	Monotonous work content A₃₂
		Long work hours A₃₃
		Non-harmonious relations with colleagues A₄₁
		Lack of support from leaders A₄₂
		Lack of support from organization A₄₃
		Serious safety Conflict A₅₁
		Many hidden safety dangers A₅₂
		Lacking safety supervision A₅₃
		Psychological damage A₆₁
		Physical damage A₆₂
		Disproportionate return on pay A₇₁
		Little opportunity of promotion A₇₂
		Low social status A₇₃
		Less modernized life A₇₄

According to the principle of system dynamics modeling, based on the flow diagram of the intervention strategy of coal miners’ job burnout, the system dynamics equation set is established as follows: $L_{1} = INTEG (R_{1 I}, R_{10})$ (1) $L_{i} = INTEG (R_{iI} - R_{iD}, R_{i 0}) i = (2, 3 \dots 9)$ (2) $R_{2 I} = \sum_{i = 1}^{3} b_{2 i} \times A_{2 i}$ (3) $R_{3 I} = \sum_{i = 1}^{3} b_{3 i} \times A_{3 i}$ (4) $R_{4 I} = \sum_{i = 1}^{3} b_{4 i} \times A_{4 i}$ (5) $R_{5 I} = \sum_{i = 1}^{3} b_{5 i} \times A_{5 i}$ (6) $R_{6 I} = \sum_{i = 1}^{3} b_{6 i} \times A_{6 i}$ (7) $R_{7 I} = \sum_{i = 1}^{3} b_{7 i} \times A_{7 i}$ (8) $R_{1 I} = L_{8} \times b_{11}$ (9) $R_{8 I} = \sum_{i = 2}^{7} b_{8 i} \times L_{i}$ (10) $R_{9 I} = b_{91} \times L_{8}$ (11) $R_{8 D} = C_{81} \times L_{1}$ (12) $R_{9 D} = C_{91} \times L_{1}$ (13) $A_{i} = C_{i} L_{1} i = (1, 2 \dots 12)$ (14)

$(\begin{matrix} R_{2 D} \\ ⋮ \\ R_{7 D} \end{matrix}) = C_{ij} (\begin{matrix} A_{1} \\ ⋮ \\ A_{12} \end{matrix}) i = (1, 2 \dots 7), j = (1, 2 \dots 12)$ (15)

The meaning of each parameter above is displayed in Table 7. In addition, R_i0 (i = 1,2,3,4,5,6,7,8,9) is the initial value of L_i (i = 1,2,3,4,5,6,7,8,9). b_2i (i = 1,2,3) is the influence coefficient of A_2i (i = 1,2,3) on R_2I. b_3i (i = 1,2,3) is the influence coefficient of A_3i (i = 1,2,3) on R_3I. b_4i (i = 1,2,3) is the influence coefficient of A_4i (i = 1,2,3) on R_4I. b_5i (i = 1,2,3) is the influence coefficient of A_5i (i = 1,2,3) on R_5I. b_6i (i = 1,2,3) is the influence coefficient of A_6i (i = 1,2,3) on R_6I. b_7i (i = 1,2,3,4) is the influence coefficient of A_7i (i = 1,2,3,4) on R_7I. b₁₁ and b₉₁ are the influence coefficients of L₈ on R_1I and R_9I, respectively. b_8i (i = 2,3,4,5,6,7) is the influence coefficients of L_i (i = 2,3,4,5,6,7). C₈₁ and C₉₁ are the influence coefficients of L₁ on R_8D and R_9D, respectively. C_i (i = 1,2,3,4,......,12) is the influence coefficient of L₁ on A_i (i = 1,2,3,4,......,12). C_ij is the influence coefficients matrix of A_i (i = 1,2,3,4,......,12) on R_iD (i = 2,3,4,5,6,7), which equals to zero if there is no effect.

5 Parameter assignment

In the simulation, Y mine area is used as the simulation object, and the influence coefficient is mainly calculated by expert scoring and analytic hierarchy process (AHP). The state variables, rate variables and auxiliary variables are calculated by questionnaire data and analytic hierarchy process (AHP), with averaging process, in line with the present mining area data. The data is normalized in order to eliminate the effect of units inconsistency.

5.1 Determination of the initial level of state variables

The initial value of state variables are determined by questionnaire data and expert scoring method. The objectives and indicators were assessed by 10 experts, first-line miners, administrators and technicians in the mine area, and all the impact levels were set within the interval (0,1), as shown in Table 8.

Table 8
Initial level of state variables

Variable Initial value Variable Initial value

Job Burnout Intervention L₁ 0.362 Health damage L₆ 0.389

Work environment alienation L₂ 0.221 Low work achievement L₇ 0.231

Job alienation l₃ 0.458 Job burnout L₈ 0.456

Work Relationship depletion L₄ 0.512 Unsafe behaviors L₉ 0.337

Work safety alienation L₅ 0.561

Variable	Initial value	Variable	Initial value
Job Burnout Intervention L₁	0.362	Health damage L₆	0.389
Work environment alienation L₂	0.221	Low work achievement L₇	0.231
Job alienation l₃	0.458	Job burnout L₈	0.456
Work Relationship depletion L₄	0.512	Unsafe behaviors L₉	0.337
Work safety alienation L₅	0.561

5.2 Weight setting of the work-intervention subsystem

Through expert interview and network analytic hierarchy process, the weights of internal factors of job burnout intervention subsystem are obtained. The following objectives and indicators are scored by 10 experts, first-line miners, administrators and technicians in the mine area, as shown in Table 9.

Table 9
Weight setting of job burnout intervention subsystem

System Variable Weight System Variable Weight

Job burnout intervention subsystem Increase the mechanization level A₁ 0.112 Job burnout intervention subsystem Psychological counseling program A₇ 0.078

Improve work environment A₂ 0.009 Talk A₈ 0.045

Enrich Work Content A₃ 0.102 Self-psychological Adjustment A₉ 0.114

Salary incentives A₄ 0.120 Safety culture management A₁₀ 0.120

Reasonable arrangement of working hours A₅ 0.102 Risk identification ability A₁₁ 0.046

Employee assistance program A₆ 0.056 Physical exercise A₁₂ 0.096

System	Variable	Weight	System	Variable	Weight
Job burnout intervention subsystem	Increase the mechanization level A₁	0.112	Job burnout intervention subsystem	Psychological counseling program A₇	0.078
	Improve work environment A₂	0.009		Talk A₈	0.045
	Enrich Work Content A₃	0.102		Self-psychological Adjustment A₉	0.114
	Salary incentives A₄	0.120		Safety culture management A₁₀	0.120
	Reasonable arrangement of working hours A₅	0.102		Risk identification ability A₁₁	0.046
	Employee assistance program A₆	0.056		Physical exercise A₁₂	0.096

5.3 Determination of influence coefficient of rate variable

Various factors, which are complex and changeable, could affect rate variables. At present, there is not a unified calculation on the influence of these rate variables, whose change is mostly due to the change of internal factors within the system. Considering both the present mine area data and expert talk, we proceed data and get the influence coefficients as follows.

b_2i (i = 1,2,3) is the influence coefficient of A_2i (i = 1,2,3) on R_2I, equaling to 0.245,0.329 and 0.4521, respectively. b_3i (i = 1,2,3) is the influence coefficient of A_3i (i = 1,2,3) on R_3I, equaling to 0.129, 0.412 and 0.369, respectively. b_4i (i = 1,2,3) is the influence coefficient of A_4i (i = 1,2,3) on R_4I, equaling to 0.698, 0.256 and 0.471, respectively. b_5i (i = 1,2,3) is the influence coefficient of A_5i (i = 1,2,3) on R_5I, equaling to 0.36, 0.156 and 0.214, respectively. b_6i (i = 1,2,3) is the influence coefficient of A_6i (i = 1,2,3) on R_6I, equaling to 0.231, 0.263 and 0.278, respectively. b_7i (i = 1,2,3,4) is the influence coefficient of A_7i (i = 1,2,3,4) on R_7I, equaling to 0.369, 0.146 and 0.321, respectively. b₁₁ and b₉₁ are the influence coefficients of L₈ on R_1I and R_9I, equaling to 0.459 and 0.412, respectively. b_8i (i = 2,3,4,5,6,7) is the influence coefficients of L_i (i = 2,3,4,5,6,7), equaling to 0.214, 0.362, 0.123, 0.412, 0.512, 0.621 and 0.345, respectively. C₈₁ and C₉₁ are the influence coefficients of L₁ on R_8D and R_9D, equaling to 0.125 and 0.246, respectively. C_i (i = 1,2,3,4,......,12) is the influence coefficient of L₁ on A_i (i = 1,2,3,4,......,12). C_ij is the influence coefficients matrix of A_i (i = 1,2,3,4,......,12) on R_iD (i = 2,3,4,5,6,7), which equals to zero if there is no effect.

$cij = (\begin{matrix} 0.123 & 0.154 & 0.412 & 0 & 0.156 & 0.451 & 0.222 & 0.987 & 0.110 & 0.351 & 0.587 & 0.245 \\ 0.345 & 0.432 & 0 & 0.236 & 0 & 0.147 & 0.124 & 0 & 0 & 0 & 0 & 0.312 \\ 0.543 & 0.235 & 0 & 0.248 & 0 & 0.141 & 0.213 & 0.421 & 0.123 & 0.213 & 0.381 & 0.355 \\ 0.327 & 0.421 & 0.219 & 0.534 & 0.238 & 0 & 0.331 & 0 & 0.321 & 0.456 & 0.331 & 0 \\ 0 & 0.256 & 0.216 & 0 & 0.231 & 0 & 0.332 & 0.467 & 0.451 & 0.371 & 0.268 & 0 \\ 0 & 0.412 & 0 & 0 & 0.012 & 0 & 0.312 & 0 & 0 & 0 & 0 & 0.567 \end{matrix})$

5.4 Constant term

The constant term itself would not be changed by other factors, but fluctuates with time. Meanwhile, the amplitude of the fluctuations depends on different reasons, such as external environment, etc. Table function is used as the transformation tool of constant terms, in order to characterize their variation characteristics.

The simulation is 12 months, with a 1 month step-length. The values of the table function of constants are calculated, based on the present mine area data and opinions of experts. The results are as follows:

$\begin{matrix} Hostile Underground {Environment A}_{21} = WITH \\ LOOKUP (Time, ([(1, 0 . 3) - (12, 0 . 5)], \\ (1, 0.394), (2, 0.405), (3, 0.413), (4, 0.424), (5, 0.438), \\ (6, 0.457), (7, 0.457), (8, 0.457), (9, 0.457), \\ (10, 0 . 457), (11, 0 . 457), (12, 0 . 457)) \end{matrix}$ (16) $\begin{matrix} Narrow Operation Space A_{22} = WITH LOOKUP \\ (Time, ([(1, 0 . 1) - (12, 0 . 2)], (1, 0 . 213), (2, 0 . 212), \\ (3, 0 . 213), (4, 0 . 214), (5, 0 . 214), (6, 0 . 211), (7, 0 . 214), \\ (8, 0.24), (9, 0.214), (10, 0 . 214), (11, 0 . 214), (12, 0 . 213)) \end{matrix}$ (17) $\begin{matrix} Poor Operation Conditions A_{23} = WITH LOOKUP \\ (Time, ([(1, 0 . 3) - (12, 0 . 4)], (1, 0 . 312), (2, 0 . 312), \\ (3, 313), (4, 0 . 312), (5, 0 . 313), (6, 0 . 314), (7, 0 . 313), \\ (8, 0 . 313), (9, 0 . 313), (10, 0 . 313), (11, 0 . 313), (12, 0 . 313)) \end{matrix}$ (18) $\begin{matrix} Heavy Work Load A_{31} = WITH LOOKUP (Time, \\ ([(1, 0 . 5) - (12, 0 . 7)], (1, 0 . 612), (2, 0 . 612), (3, 0 . 613), \\ (4, 0 . 612), (5, 0 . 613), (6, 0 . 614), (7, 0 . 613), (8, 0 . 613), \\ (9, 0.613), (10, 0 . 613), (11, 0 . 613), (12, 0 . 613)) \end{matrix}$ (19) $\begin{matrix} Monotonous Work Content A_{32} = WITH LOOKUP \\ (Time, ([(1, 0 . 1) - (12, 0 . 2)], (1, 0 . 423), (2, 0 . 423), \\ (3, 0 . 423), (4, 0 . 423), (5, 0 . 423), (6, 0 . 441), (7, 0 . 441), \\ (8, 0.412), (9, 0 . 412), (10, 0 . 412), (11, 0 . 412), (12, 0 . 412)) \end{matrix}$ (20) $\begin{matrix} {Long Working Hours A}_{33} = WITHLOOKUP (Time, \\ ([(1, 0 . 5) - (12, 0 . 6)], (1, 0 . 423), (2, 0 . 423), (3, 0 . 423), \\ (4, 0 . 423), (5, 0 . 423), (6, 0 . 441), (7, 0 . 441), (8, 0 . 412), \\ (9, 0.412), (10, 0 . 412), (11, 0 . 412), (12, 0 . 412)) \end{matrix}$ (21) $\begin{matrix} Non - harmonious Relations with Colleagues A_{41} = \\ WITH LOOKUP (Time, ([(1, 0 . 2) - (12, 0 . 3)], \\ (1, 0 . 223), (2, 0 . 223), (3, 0 . 223), (4, 0 . 223), (5, 0 . 223), \\ (6, 0 . 241), (7, 0 . 241), (8, 0 . 212), (9, 0 . 212), (10, 0.212), \\ (11, 0 . 212), (12, 0 . 212)) \end{matrix}$ (22) $\begin{matrix} Lack of Support from Leaders A_{42} = WITH LOOKUP \\ (Time, ([(1, 0 . 3) - (12, 0 . 4)], (1, 0 . 316), (2, 0 . 316), \\ (3, 0 . 316), (4, 0 . 316), (5, 0 . 311), (6, 0 . 311), (7, 0 . 311), \\ (8, 0 . 311), (9, 0 . 311), (10, 0 . 311), (11, 0 . 311), (12, 0 . 311)) \end{matrix}$ (23) $\begin{matrix} Lack of Support from Organization A_{43} = WITH \\ LOOKUP (Time, ([(1, 0 . 3) - (12, 0 . 4)], (1, 0 . 378), \\ (2, 0 . 378), (3, 0 . 379), (4, 0 . 379), (5, 0 . 379), (6, 0 . 379), \\ (7, 0 . 379), (8, 0 . 379), (9, 0 . 379), (10, 0 . 379), (11, 0 . 379), \\ (12, 0.379)) \end{matrix}$ (24) $\begin{matrix} Serious Safety Conflict A_{51} = WITH LOOKUP (Time, \\ ([(1, 0 . 5) - (12, 0 . 6)], (1, 0 . 574), (2, 0 . 574), (3, 0 . 574), \\ (4, 0 . 574), (5, 0 . 574), (6, 0 . 574), (7, 0 . 575), (8, 0.574), \\ (9, 0 . 575), (10, 0 . 575), (11, 0 . 579), (12, 0 . 579)) \end{matrix}$ (25) $\begin{matrix} Many Hidden Dangers A_{52} = WITH LOOKUP (Time, \\ ([(1, 0 . 6) - (12, 0 . 7)], (1, 0 . 674), (2, 0 . 674), (3, 0 . 674), \\ (4, 0 . 678), (5, 0 . 678), (6, 0 . 678), (7, 0 . 678), (8, 0 . 678), \\ (9, 0 . 679), (10, 0 . 679), (11, 0 . 679), (12, 0 . 679)) \end{matrix}$ (26) $\begin{matrix} Lack of Safety Supervision A_{53} = WITH LOOKUP \\ (Time, ([(1, 0 . 5) - (12, 0 . 6)], (1, 0 . 574), (2, 0 . 574), \\ (3, 0 . 574), (4, 0 . 578), (5, 0 . 578), (6, 0 . 578), (7, 0 . 578), \\ (8, 0 . 578), (9, 0 . 579), (10, 0 . 579), (11, 0 . 579), (12, 0 . 579)) \end{matrix}$ (27) $\begin{matrix} Psychological Damage A_{61} = WITH LOOKUP (Time, \\ ([(1, 0 . 3) - (12, 0 . 4)], (1, 0 . 341), (2, 0 . 311), (3, 0 . 311), \\ (4, 0 . 312), (5, 0 . 312), (6, 0 . 313), (7, 0 . 313), (8, 0 . 313), \\ (9, 0 . 313), (10, 0 . 313), (11, 0 . 313), (12, 0 . 313)) \end{matrix}$ (28) $\begin{matrix} Physical Damage A_{62} = WITH LOOKUP (Time, \\ ([(1, 0 . 3) - (12, 0 . 4)], (1, 0 . 341), (2, 0 . 341), (3, 0 . 341), \\ (4, 0 . 341), (5, 0 . 341), (6, 0 . 342), (7, 0 . 342), (8, 0 . 341), \\ (9, 0 . 342), (10, 0 . 343), (11, 0 . 343), (12, 0 . 343)) \end{matrix}$ (29) $\begin{matrix} Disproportionate Return on Pay A_{71} = WITH LOOKUP \\ (Time, ([(1, 0 . 4) - (12, 0 . 5)], (1, 0 . 412), (2, 0 . 411), \\ (3, 0 . 411), (4, 0 . 414), (5, 0 . 416), (6, 0 . 401), (7, 0 . 403), \\ (8, 0.401), (9, 0 . 401), (10, 0 . 409), (11, 0 . 412), (12, 0 . 422)) \end{matrix}$ (30) $\begin{matrix} Little Opportunity of Promotion A_{72} = WITH LOOKUP \\ (Time, ([(1, 0 . 3) - (12, 0 . 4)], (1, 0 . 341), (2, 0 . 311), \\ (3, 0 . 311), (4, 0 . 312), (5, 0 . 312), (6, 0 . 313), (7, 0 . 313), \\ (8, 0.313), (9, 0 . 313), (10, 0 . 313), (11, 0 . 313), (12, 0 . 313)) \end{matrix}$ (31) $\begin{matrix} Large Safety Conflict A_{51} = WITH LOOKUP (Time, \\ ([(1, 0 . 5) - (12, 0 . 6)], (1, 0 . 571), (2, 0 . 571), (3, 0 . 571), \\ (4, 0 . 572), (5, 0 . 572), (6, 0 . 574), (7, 0 . 575), (8, 0.574), \\ (9, 0 . 576), (10, 0 . 576), (11, 0 . 576), (12, 0 . 576)) \end{matrix}$ (32) $\begin{matrix} Low Social Status A_{73} = WITH LOOKUP (Time, \\ ([(1, 0 . 4) - (12, 0 . 5)], (1, 0 . 411), (2, 0 . 411), (3, 0 . 411), \\ (4, 0 . 412), (5, 0 . 412), (6, 0 . 414), (7, 0 . 575), (8, 0.414), \\ (9, 0 . 416), (10, 0 . 416), (11, 0 . 416), (12, 0 . 416)) \end{matrix}$ (33) $\begin{matrix} Less Modernized Life A_{74} = WITH LOOKUP (Time, \\ ([(1, 0 . 3) - (12, 0 . 4)], (1, 0 . 323), (2, 0 . 324), (3, 0 . 324), \\ (4, 0 . 324), (5, 0 . 324), (6, 0326), (7, 0 . 326), (8, 0 . 326), \\ (9, 0 . 326), (10, 0 . 326), (11, 0 . 321), (12, 0 . 326)) \end{matrix}$ (34)

6 Analysis of simulation results

The simulation is operated by Vensim, with the step size being set to 1 month and the simulation time being 12 months. The time trends of miners’ job burnout and unsafe behavior are showed in Fig. 3.

Fig. 3

Trends of Job Burnout and Unsafe Behavior of Coal Miners.

In Fig. 3, we find that, both job burnout and unsafe behavior peak at their initial states, which are 9.2 and 7.23 respectively. After 12 months of intervention, there is a significant decrease of both job burnout and unsafe behavior, to 0.75 and 0.25 respectively. The reduction proves the effectiveness of the interventions against job burnout.

The decreasing slopes of both curves imply that, the longer the intervention is implemented, the weaker is its effect. The first five months witness the most significant drop of both levels of job burnout and unsafe behaviors. Then the effect of intervention gradually wanes from May to August. The curves become comparatively flat after August, meaning that the intervention on job burnout and unsafe behavior is rarely effective then. As the job burnout of miners seems to develop anti-intervention antibodies as intervention time grows, the administrators need to change intervention strategy constantly, or to adopt a combination of multiple strategies. In fact, the coal mines in reality are exactly implementing such an intervention system.

Figure 4 shows the trends of work assignment alienation subsystem, work environment alienation subsystem, work relationship depletion subsystem, work safety depletion subsystem, health damage subsystem and low sense of work achievement subsystem. The levels of subsystems all decrease over time, while work assignment alienation subsystem has a maximum reduction, indicating that the job burnout intervention is most effective on alleviating miners’ work assignment alienation. The health damage subsystem has the most flat curve, implying that it is least affected and is least sensitive to interventions.

Fig. 4

Trends of job burnout Subsystem.

The result is in good with reality. Miners’ work assignment alienation is mainly caused by fatigue from long working hours and heavy work load, which could be eased in short term, as long as miners have enough rest and sleep. However, health damage is mainly due to physical and psychological diseases, which is hard to cure only if the intervention lasts in long term.

In practice, subsystems with higher sensitivity, such as work assignment alienation, work relationship depletion, and work safety depletion, should take priority when arranging intervention strategies, because they could be reduced quickly. In daily management, however, administrators should take the less sensitive subsystems seriously, such as the work environment alienation subsystem, low sense of work achievement subsystem and health damage subsystem, because they could hardly be alleviated once occur.

By adjusting the weight of one intervention strategy, while other conditions are kept unchanged, the influence of the specific intervention strategy on job burnout is studied. In this paper, with setting the increment or decrement of each intervention strategy to 0.1, with keeping the weights of other intervention strategies unchanged, the average reduction of job burnout is calculated and compared. The trends of job burnout is shown in Fig. 5.

Fig. 5

The impact of intervention strategies on job burnout.

Figure 5 shows that, though the increment of each strategy is the same, the average decrease rate of job burnout resulted in varies. The average rate reduction of job burnout from different strategies are as follows: increasing the level of mechanization (0.524), improving the working environment (0.459), enriching the work content (0.342), salary incentive (0.612), reasonable arrangement of working hours (0.745), employee assistance program (0.612), psychological counseling program (0.689), confiding (0.597), self-psychological adjustment (0.698), safety culture management (0.543), risk identification ability (0.578), physical exercise (0.469).

It finds that, the least three effective strategies are enriching the work content (0.342), improving the working environment (0.459), and physical exercise (0.469). The top three influential strategies are reasonable arrangement of working hours (0.745), self-psychological adjustment (0.698), and psychological counseling program (0.689), which should be on the priority list of administrators to intervene miners’ job burnout.

7 Conclusion

In this paper, the system dynamics method is used to simulate the intervention strategy of miners’ job burnout. The result shows that work assignment alienation has the highest sensitivity to intervention strategy, while health damage is least sensitive to intervention. Besides, the effect of one intervention strategy decreases over time, because miners seem to get anti-intervention antibodies as intervention time grows. Managers should give priority to three strategies, which are arranging reasonable working hours, self-psychological adjustment and psychological counseling program, in order to get remarkable results.

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