Mathematical Model to Predict Leader Self-Awareness and Effective Conflict Management in Manufacturing Companies

Triple A Research Journal of Multidisciplinary (JMD) | Vol.2 Issue1 | August 2018
Triple A Research Journal of Multidisciplinary (ISSN: 2636-5480)
Vol. 2(1): 001 - 010, August 2018
Available online: http://www.triplearesjournal.org/jmd
Copyright ©2018 Triple A Research Journal
Full length Research Paper
Mathematical Model to Predict Leader Self-Awareness
and Effective Conflict Management in Manufacturing
Companies
1*Eluozo SN and 2Ukpong Uwem Johnson
1Department of Civil Engineering, College of Engineering, Gregory University, Uturu, Abia State, Nigeria
2Department of Management Sciences, Akwa Ibom State University
Corresponding author:
Eluozo S.N.
Department of Civil Engineering,
College of Engineering, Gregory University
Uturu, Abia State, Nigeria.
E-mail address:
ndusolo2018@gmail.com
ABSTRACT
Self-awareness and effective conflict management were subjected
into evaluation, this was to monitor the extend at which such
managerial concept experienced impact from positive and negative
condition, various dimension that were observed to express
relationship were involved to evaluate different rate of effects on
leader self – awareness in manufacturing companies, other influential
parameters were conflict management. These variables were
observed to relate through increase collaboration as a result
generate improved communication between customers and staffs for
better efficiency and productivity in manufacturing companies. The
study expresses various output through simulated parameters at
different period and conditions, the derived simulation values were
subjected to model validations, and both parameters developed
favorable fits, the study expressed its significance by monitoring
leader self-awareness in manufacturing companies, these were
evaluated through assessment of effective conflict management to
generates improved communication between customers and staffs in
manufacturing companies.
Keywords: Mathematical model, leader self-awareness, and
manufacturing companies.
INTRODUCTION
Organizations has over time realized that success takes
more than intellectual excellence and that we need another
sort of skills just to survive and certainly to thrive in the
increasingly dynamic work environment the competencies
of emotional intelligence such as self-awareness, empathy,
social skills are consciously taken into consideration, and
more-so, literatures on effective and efficient performance
and management of organization has assumed multiple
dimensions Johnson et al. (2018) therefore with recourse
to the current organizational dynamics that range from
intellectual excellence and other measures such as self
awareness, empathy and social skills, the need to
empirically examine the influence of self-awareness in
effective conflict management is highly needed. Therefore,
the study is aimed at with mathematical model examine the
influence of self-awareness on increased collaboration and
improved communication
Literature review
The underpinning theory for this study is the social learning
theory. Social learning theory is a prime to organizational
learning. The general statement of social learning theory is
that cognitive and symbolic activities as well as self-
regulatory nature of human interaction are important to
learning, based on these facts we are using the social
learning theory to explain the need for leader’s

Solo and Johnson 002
consciousness as regards emotional intelligence and
effective conflict management. Several theories have come
up with multiple theories on emotional intelligence,
however most theories appear to include and focus on the
same four main components of emotional intelligence:
perception of once and others emotion, understanding and
utilization of that knowledge (Ciarrochi et al., (2000).
Goleman & Boyatzis, (2002) have proposed an inductively
based theory of emotional intelligence which has been
tested with emotional intelligence competence which has
been tested with intelligence competent inventory (ECI).
Both theories are similar in that they each propose
awareness and regulation of emotion at the individual
social level.
Increased collaboration
Collaboration works by integrating ideas set out by multiple
people. The object is to find a creative solution acceptable
to everyone. Collaboration, though useful, calls for a
significant time commitment not appropriate to all conflicts.
For example, a business owner should work collaboratively
with the manager to establish policies, but collaborative
decision-making regarding office supplies wastes time
better spent on other activities. Jehn and Mannix, (2001).
Contends that “conflict is a multi-dimensional construct”
Rahim (2002) further stressed that management of conflict
involves diagnosis and intervention. Proper diagnosis
should measure the amount of conflict, style of handling
interpersonal conflicts, sources of conflicts, organizational
learning and effectiveness. Conflict management involves
implementing strategies to limit the negative aspects of
conflict and to increase the positive aspects of conflict at a
level equal to or higher than where the conflict is taking
place (David, 2013). It is not concerned with eliminating all
conflict, conflict management as a concept, has been
conventionally linked with conflict containment and
settlement. In social life, conflicts do occur, but family
members, friends and relatives manage them. Same form
of conflict management should apply to organizations and
to the top management. Conflict is prevalent to all social
life; it is an inevitable part of living because it is related to
situations of scares resources, division of functions, power
relations and role-differentiation Gilbert (2005). Conflict
management avoids conflicts to a great extent and thus
also reduces the stress and tension of leader. No one likes
to carry his tensions back home and if you fight with your
staffs and other people, you are bound to feel
uncomfortable and restless even at home.
Increased collaboration: Increased collaboration
involves participants working together on the same tasks,
rather than in parallel on separates portions of task.
However, Dillenbourg et al. (1996) note that some
spontaneous division of labor may occur during
collaboration. Thus, the distinction between the two is not
necessarily clear-cut. According to Dillenbourg et al.
(1996), in cooperation is only required for assembling
partial results. Increased Collaboration is the best effective
conflict management strategy according to Rabin (2002).
This is because it delivers a win-win outcome. It is called a
win-win approach. It does not require either side to give up
a valued position. Rather, both sides honestly seek new
and common higher grounds. This kind of problem-solving
requires an atmosphere of trust and mutual respect, the
surfacing of hidden agendas, and a genuine willingness on
both sides for effective conflict management. Thomas &
Kilmann (1974) collaborators are high in accommodation.
They view integrative behavior as it requires the parties to
think of the best interests of both sides rather than just their
own. Nevertheless, Cahn and Abigail (2002) prefer not to
describe a process, instead of focusing on the principles
that the parties need to apply for a collaborative solution to
occur. They define these as separating people from the
problem, focusing on interests, brainstorming options and
finding objective criteria on which to base decisions Cahn
and Abigail (2007). They posit that parties need to
demonstrate collaborative behaviors to achieve win-win
outcomes.
Leader Self-Awareness
According to Goleman (1998) self-awareness refers to
one’s capacity to know his internal states intuitive voice,
preference and resources. A leader with self-awareness
will have emotional awareness which is a state of
recognizing his emotions and their effects. The leader with
self-awareness knows his strength and weaknesses, and
such has self-confidence which is a person’s sense of self-
respect and capability. Self-awareness is the ability of an
individual to sense the internal emotional emotions and
feelings. Self-aware individuals are able to read their
feelings and link them with what they think and act. It is
also known as “emotional literacy: McGarvey, (1997). Self-
awareness is used to regulate the rational and emotional
mental processes in balanced ways to provide an
emotional support for the rational mind to make logically
correct and socially acceptable decisions and judgments
(Tischler et al., 2002).
Improved communication
Improved communication has a big role to play in effective
conflict management. It has been observed that poor
communication most often results in misunderstandings
and eventually conflicts. Communication has to be clear
and precise for the avoidance of conflict. Improved
communications, and the need for comprehensive
supportive care, are recognized to lead to effective conflict
management. The dissimilarity in the ideas and opinion of
individuals results in a conflict. There is need for individual
adjustment within the organization in other to avoid
conflicts. Most conflict in the organization occurs as a
result of lack of effective communication among the work
force. And lack of information is also a major course of
conflict in the organization. The types of communication
also play a major role in the organization. Clear, concise,

003 Triple A Res. J. Multidisci.
accurate and time communication of information from
leaders will help to ease both the number and severity of
conflicts and lead to improved communication in the
organization. Conflict may be between managers and their
staff, between team members, departments, or managers.
Conflict may be expressed openly, but it may also be
hidden, in the form of irritation, resentment, loss of morale
and lack of commitment. Hidden conflict is easy to miss
and therefore can be particularly damaging. If nothing is
done to address the underlying issues, conflict may
escalate - from gossip, backbiting and criticism to shouting
matches, threats and possible violence. Such
consequences can often be prevented by taking early
action to address the issues. The following is focuses on
steps for handling interpersonal conflict within the
workforce, as opposed to conflict with customers, which
requires a different form of resolution. It is imperative
however to stressed that increased communication within
the organization helps in enhancing the strength of the
organization and to a greater extend increase the
production of the organization.
It is the job of an employee to meet the expectations of
his manager, but if those expectations are misunderstood,
conflict can arise. Managers need to spend time clearly
communicating their goals to employees and then
confirming those goals in writing. A manager should also
encourage her employees to ask questions about their
goals and hold regular meetings to discuss the goals and
how best to reach them.
Breakdown in Communication: If a department requires
information from another department to do its job, and the
second department does not respond to the request for
information, a conflict can arise. Some interdepartmental
disagreements might trigger a nonresponsive attitude that
can quickly become an internal conflict. Another way of
creating this sort of conflict is by giving a circular response
such as an issue being perpetually "under review." When
people or departments are late in responding to information
requests, or they are withholding information on purpose, it
is best to address the situation immediately with a personal
meeting with both sides to resolve the situation.
Misunderstanding the Information According to Robert
(2008), internal conflict can sometimes arise as the result
of a simple misunderstanding. One person may
misunderstand information, and that can trigger a series of
conflicts. To deal with this kind of situation, it is best to
have the person admit her misunderstanding and work with
the affected parties to remedy the situation. For example, if
the production manager misunderstands the product
manufacturing goals, then the sales manager may not
have enough products to sell. Taking responsibility for a
mistake can quickly defuse a potential organizational
conflict.
Leader Self-awareness and effective conflict
management involves having a realistic assessment of
one’s abilities. People who have this strength are aware of
their strength and weaknesses, open to candid feedback
from others, and are willing to learn from past experiences.
This courage comes from certainty, through self-
awareness about the individual capabilities, values and
goals Davidson (2009). The theory tends to buttress the
fact that self awareness has a lot to do with the effective
ways of conflict management amongst individuals in the
organization. Individual self-awareness also effectively
contributes to improved employee’s ability in achieving
organizational goals. Being self-aware also enables the
employees to constantly remain conscious both as an
individual and within groups in the organization. Dirette
(2010) stressed that self-awareness is broken down into
four levels of Arousal and attention, Sensory and motor,
Cognitive and lastly Psychosocial. To them at the arousal
and attention, to ideas developed or any arousal is either
very slow or poor due to our inability to pay attention or
respond with close concentration because of distracting
surrounding us. The sensory and motor stage is where we
can explain our sense of feeling such as movement,
fatigue, satisfaction and more advance skills of processing
our perceptions due to our developed competence to pay
attention, comprehend and memorize.
Leader-Member Exchange relationship is a leadership
construct which evolved from the Vertical dyad linkage
theory of Dansereau et al. (1975) that focused on the two-
fold (dyadic) relationship between leaders and
subordinates (Green, 2008). The theory explained that a
leader develops a different quality of relationship with each
of his subordinates and not a uniform relationship.
Truckenbrodt, (2000), explains that Leader-Member
Exchange relationship is a leadership construct which
focuses on a two-way (dyadic) relationship between the
leader (manager) and each of his subordinates (member).
The theory posits that a manager or leader forms a
different quality of relationship with each of his
subordinates or the Rank-and-File officers, which tends to
influence the Rank-and-File officers access to resources
and performance (Graen and Uhl-Bien, 1991). This
relationship extends beyond the terms of employment and
job description. Such Leader-Member Exchange
relationship may be high quality or low quality. The
subordinates who enjoy a high-quality Leader-Member
Exchange relationship are referred to as in-group
members while the subordinates in a low-quality Leader-
Member Exchange relationship are known as out-group
members.
THEORETICAL BACKGROUND
𝑑 𝑐 𝑑
𝑑𝑥
+ 𝑉(𝑦)𝑐 𝑑 = (𝑦)𝑐 𝑑
𝑛
(1.0)
Dividing equation (1.0) all through by 𝑐 𝑑
𝑛
we have
𝑐 𝑑
−𝑛 𝑑 𝑐 𝑑
𝑑𝑥
+ 𝑣(𝑥)𝑐 𝑑
1−𝑛
= (𝑦) (1.1)
Let
P=𝑐 𝑑
1−𝑛
(1.2)

𝑑𝑝
𝑑𝑦
= (1 − 𝑛)𝑐 𝑑
𝑑𝑦
𝑐 𝑑
𝑑𝑦
=
1
1−𝑛
𝑑𝑝
𝑑𝑦
(1.3)
Substituting equation (1.2) and (1.3) into equation (1.1) we
have that
1
1−𝑛
𝑑𝑝
𝑑𝑥
+ 𝑉(𝑦)𝑝 = (𝑦) (1.4)
Multiplied equation (1.4) all through by (1-n)
𝑑𝑝
𝑑𝑦
+ 𝑉(𝑦)(1 − 𝑛)𝑝 = (𝑦)(1 − 𝑛) (1.5)
Equation (1.5) is linear in p. we applied the integrating
factor method as follows:
𝐼. 𝐹 = 𝑒∫ 𝑝(𝑦)
𝑑𝑦 (1.6)
Where
𝑝(𝑦) = 𝑉(𝑦)(1 − 𝑛) (1.7)
Substituting equation (1.7) into (1.6) we have
𝐼. 𝐹 = 𝑒∫ 𝑢(𝑦)(1−𝑛)
𝑑𝑦
= 𝑒 𝑉(𝑦)(1−𝑛) ∫ 𝑑𝑦
= 𝑒 𝑉(𝑦)(1−𝑛)𝑦
𝐼. 𝐹 = 𝑒 𝑉(𝑦)(1−𝑛)𝑦
(1.8)
Multiplied all through equation (1.5) by equation (1.8) we
have
𝑒 𝑉(𝑦)(1−𝑛)𝑦 𝑑𝑝
𝑑𝑦
+ 𝑉(𝑦)(1 − 𝑛)𝑒 𝑉(𝑦)(1−𝑛)𝑌
𝑝 =  (𝑦)(1 −
𝑛)𝑒 𝑉(𝑦)(1−𝑛)𝑦
𝑑
𝑑𝑥
(𝑒 𝑉(𝑦)(1−𝑛)𝑦
𝑝) = (𝑦)(1 − 𝑛)𝑒 𝑉(𝑌)(1−𝑛)𝑦
𝑑(𝑒 𝑉(𝑦)(1−𝑛)𝑦
𝑝) = (𝑦)(1 − 𝑛)𝑦𝑑𝑦
Integrating both sides we have
∫ 𝑑[𝑒 𝑉(𝑦)(1−𝑛)𝑦
𝑝] = (𝑦)(1 − 𝑛) ∫ 𝑒 𝑉(𝑦)(1−𝑛)𝑦
𝑑𝑦
𝑒 𝑉(𝑌)(1−𝑛)𝑌
𝑝 = (𝑦)(1 − 𝑛) ∫ 𝑒 𝑉(𝑦)(1−𝑛)𝑦
𝑑𝑦 (1.9)
But to integrate (𝑦)(1 − 𝑛) ∫ 𝑒 𝑉𝑢(𝑦)(1−𝑛)𝑥
𝑑𝑥 we let
𝐷 = 𝑉𝑢(𝑥)(1 − 𝑛)𝑥 (1.10)
𝑑𝐷
𝑑𝑥
= 𝑉𝑢(𝑦)(1 − 𝑛)
So that
𝑑𝑥 =
𝑑𝐷
𝑉𝑢(𝑦)(1−𝑛)
(1.11)
Substituting (1.10) and (1.11) into (1.9) we have
𝑒 𝑉𝑢(𝑦)(1−𝑛)𝑦
𝑝 = (𝑦)(1 − 𝑛) ∫ 𝑒 𝐷 𝑑𝐷
𝑒 𝑢(𝑥)(1−𝑛)𝑥
𝑝 =
(𝑦)(1−𝑛)
𝑒 𝑉𝑢(𝑦)(1−𝑛)𝑦
+ 𝐴 (1.12)
Divide equation (1.12) all through by 𝑒 𝑉𝑢(𝑦)(1−𝑛)𝑦
we have
𝑝 =
(𝑦)
𝑉𝑢(𝑦)
+ 𝐴𝑒−𝑉𝑢(𝑦)(1−𝑛)𝑦
(1.13)
Substituting equation (1.2) into equation (1.13) we have
𝑐 𝑑
1−𝑛
=
(𝑦)
𝑉𝑢(𝑦)
+ 𝐴𝑒−𝑉𝑢(𝑦)(1−𝑛)𝑦
METHODOLOGY OF THE STUDY
Mathematical model techniques were applied for the study,
deterministic model techniques were applied, the
variables were subjected into mathematical tools, these
developed a system that generated governing equation,
these were derived to produced model for the study, these
predictive solution were also subjected to simulations were
parameters were varied at different conditions base on the
system, the derived simulation parameters will be
compared with measured values from the fields for model
validation.
RESULTS AND DISCUSSIONS
Tables 1 -6, Figure 1 -6 expresses the growth rise in self
awareness from effective conflict management, the figure
experienced linear exponential growth; this observation
implies that the system evaluated the effect from conflict
management as an influential dimension that determined
the effectiveness of self Awareness in manufacturing
companies. Moreso, the figures also express the pressure
or positivity from increase collaboration and improved
communication as a source for self awareness growth for
efficiency of manufacturing companies in Port Harcourt, the
dimensions were observed to establish higher percentage
of influence for efficient self awareness in such
manufacturing organization, such level of managerial
conceptual framework were evaluated through the
dimensions to express their various rate of efficiency in the
growth rate of leader self awareness. The expansions or
growth rate of self-awareness were observed at different
periods, the figures though in linear exponential rate
developed variations of values at different locations, the
lowest parameter at different locations were as a result of
linear declined of these dimensions in the system, even
though they appear to be in linear phase. These
expressions imply that these variables in the system will
always determined the output of leader self awareness in
manufacturing companies, the predictive parameters from
derived model were subject to simulation, and both
parameters developed faviourable fits for model validation.

Table 1: Predictive and Measured Values of Leader Self Awareness at Different Period
Period Leader Self Awareness Measured field Values
2 1.26E-02 1.10E-02
4 2.69E-02 2.30E-02
6 3.78E-02 3.50E-02
8 5.05E-02 4.71E-02
10 6.31E-02 5.91E-02
12 8.07E-02 7.11E-02
14 9.40E-02 8.32E-02
16 1.07E-01 9.53E-02
18 1.21E-01 1.07E-01
20 1.34E-01 1.19E-01
22 1.48E-01 1.31E-01
24 1.61E-01 1.44E-01
26 1.74E-01 1.56E-01
28 1.88E-01 1.68E-01
30 2.02E-01 1.80E-01
1 1.02E-02 0.0089607
2 2.04E-02 0.0188456
3 3.06E-02 0.0286589
4 4.04E-02 0.0384048
5 5.10E-02 0.0480875
6 6.12E-02 0.0577112
7 7.14E-02 0.0672801
8 8.16E-02 0.0767984
9 9.18E-02 0.0862703
10 1.02E-01 0.0957
11 1.22E-01 0.1050917
12 1.22E-01 0.1144496
13 1.36E-01 0.1237779
14 1.43E-01 0.1330808
15 1.53E-01 0.1423625
16 1.63E-01 0.1516272
17 1.73E-01 0.1608791
18 1.84E-01 0.1701224
19 1.94E-01 0.1793613
20 2.04E-01 0.1886
21 2.14E-01 0.1978427
22 2.24E-01 0.2070936
23 2.35E-01 0.2163569
24 2.45E-01 0.2256368
25 2.55E-01 0.2349375
26 2.66E-01 0.2442632
27 2.75E-01 0.2536181
28 2.86E-01 0.2630064
29 2.95E-01 0.2724323
30 3.06E-01 0.2819

Table3: Predictive and Measured Values of Leader Self Awareness at Different Period
3 2.72E-02 0.0258308
6 5.75E-02 0.0523664
9 8.61E-02 0.0786716
12 1.15E-01 0.1048112
15 1.43E-01 0.13085
18 1.72E-01 0.1568528
21 2.01E-01 0.1828844
24 2.29E-01 0.2090096
27 2.51E-01 0.2352932
30 2.87E-01 0.2618
33 3.15E-01 0.2885948
36 3.44E-01 0.3157424
39 3.72E-01 0.3433076
42 4.02E-01 0.3713552
45 4.31E-01 0.39995
Period Leader Self Awareness Measured Field Values
7 7.63E-02 0.07055
9 9.81E-02 0.09295
11 1.19E-01 0.11495
13 1.42E-01 0.13655
15 1.63E-01 0.15775
17 1.85E-01 0.17855
19 2.07E-01 0.19895
21 2.28E-01 0.21895
23 2.51E-01 0.23855
25 2.73E-01 0.25775
27 2.94E-01 0.27655
30 3.11E-01 0.304
Period Leader Self Awareness Measured Values
10 0.102 0.10006
15 0.153 0.15006
20 0.204 0.20006
25 0.255 0.25006
30 0.306 0.30006
35 0.357 0.35006
40 0.408 0.40006
45 0.459 0.45006
50 0.511 0.50006
55 0.561 0.55006
60 0.612 0.60006
65 0.663 0.65006
70 0.714 0.70006
75 0.765 0.75006
80 0.816 0.80006
85 0.867 0.85006
90 0.918 0.90006

Period Leader Self Awareness Measured Values
10 0.109 0.1019
15 0.1635 0.1491625
20 0.218 0.1972
25 0.275 0.2459375
30 0.327 0.2953
35 0.355 0.3452125
40 0.436 0.3956
45 0.4905 0.4463875
50 0.545 0.4975
55 0.5995 0.5488625
60 0.654 0.6004
65 0.7085 0.6520375
70 0.763 0.7037
75 0.8175 0.7553125
80 0.868 0.8068
85 0.9265 0.8580875
90 0.981 0.9091
Figure 1: Predictive and Measured Values of Leader Self Awareness at Different Period
0.00E+00
5.00E-02
1.00E-01
1.50E-01
2.00E-01
2.50E-01
0 5 10 15 20 25 30 35
PredictiveandMeasuredFieldValuesofLeader
SdelfAwarness
Period
Leader Self Awarness
Measurded Values

0.00E+00
5.00E-02
1.00E-01
1.50E-01
2.00E-01
2.50E-01
3.00E-01
3.50E-01
0 5 10 15 20 25 30 35
PredictiveandMeasuredFieldValuesofLeaderSelf
Awarness
Period
Measurded Values
0.00E+00
5.00E-02
1.00E-01
1.50E-01
2.00E-01
2.50E-01
3.00E-01
3.50E-01
4.00E-01
4.50E-01
5.00E-01
0 10 20 30 40 50
PredictiveandMeasuredValuesofLeaderSelf
Awarness
Period
Measurded Values

0.00E+00
5.00E-02
1.00E-01
1.50E-01
2.00E-01
2.50E-01
3.00E-01
3.50E-01
0 5 10 15 20 25 30 35
PredictiveandMeasuredValuesofLeaderSelf
Awarness
Period
Measurded Values
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 20 40 60 80 100
PredictiveValuesofLeaderSelfAwarness
Period
Measurded Values

CONCLUSION
The study has monitor the growth rate of leader self
awareness in manufacturing companies, exponential rise
were experienced, these are base on the effectiveness
conflict management in such co-operate organization,
other were increase collaborations and improved
communication, these parameters detailed the rate of
growth in such manufacturing companies, variation of
derived values were evaluated in terms of relationships on
leader self awareness, these was to establish the efficiency
on the output experienced from the study, the leader self
awareness will always developed the proportion of various
qualities expressed as dimension, this developed concepts
on express effectiveness on conflict management in
telecommunications, the derived model monitor leader self
awareness base on these factors, these include increase
collaboration and improved communication, the derive
solution developed predictive model that were subjected to
model validation with measured field data, and both
parameters developed favorable fits.
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Mathematical Model to Predict Leader Self-Awareness and Effective Conflict Management in Manufacturing Companies

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Mathematical Model to Predict Leader Self-Awareness and Effective Conflict Management in Manufacturing Companies