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\begin{document}

\title{Digital Twin Simulation Modeling Process with System Dynamics: An
application to Naval ship operation}



\author[1]{jinwoo choi}%
\author[2]{Seongam Moon}%
\author[3]{Soonhong Min}%
\affil[1]{Republic of Korea Navy}%
\affil[2]{Korea National Defense University}%
\affil[3]{Yonsei University}%


\vspace{-1em}



  
  \date{May 26, 2024}


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\selectlanguage{english}
\begin{abstract}
Digital twin (DT) has been around for many years, but there is no widely
accepted standardized tool or method. In this study, system dynamics was
proposed as a tool that can be integrated into multi-scale,
multi-physics, and multi-disciplinary, which are continuously becoming
issues in the DT field. Various heterogeneous data from multiple
protocols or platforms could be integrated into one model. Through the
five-step model building process, it was possible to integrate the
theories and various models studied in the past. In this study,
\emph{the operation and maintenance system of ROK Naval ships} is
implemented as a proposed method. Various physics, scales, and
disciplines such as failures of ships, maintenance ability of repair
shops and schedule pressure of mechanics were reflected. It was possible
to observe non-intuitive correlations and potential problems caused by
the latent effect of the high-fidelity DT model. The proposed method is
also capable of updating through continuous data calibration or
real-time interworking with external statistical analysis tools.%
\end{abstract}%



\sloppy


\section*{Introduction}

{\label{introduction}}

Although widely used statistical and simulation models are excellent
methods for data analysis, they have limitations in analyzing the
complex real world. Statistical analysis can build high-fidelity models
through calibration using big data, but it is difficult to implement a
wide range of models (Richardson, 2015). This is because, as the model
becomes more complex, programming becomes more difficult, and excessive
time is consumed for analytical calculations. Simulation can model and
analyze a wide world based on real data and theories. Although these
models have advantages in verification, validation and optimization
aspects, they have limitations in distribution assumptions or are not
easy to apply during simulation run-time (Liu et al., 2021). Consider
analyzing the logistics supply chain. The models implement a large-scale
logistics system that not only reflects the various processes of SCM,
but also considers precise demand patterns and raw material supply
conditions. In simulation-based analysis, it is possible to build,
verify, and optimize the model of the entire SCM, but it is difficult to
include detailed parts such as failure of logistics equipment such as
conveyor, palletizer, and folk lift. Their failures can become a
bottleneck and affect the entire SCM, but in general, in the simulation
model, these accidents are reflected as random event occurrences based
on statistical theory. e.g., it is assumed that the failure of conveyor
occurs randomly in a Normal (5, 10). On the other hand, using a
statistical model, it is possible to analyze the failures of logistics
equipment in a highly realistic way using big data. However, if the SCM
is extended to a wide range, the complexity becomes too large, making it
very difficult to build a model. Digital twin (DT) can simulate a wide
world with high fidelity. DT is not a term referring to a specific
technology. It is an idea that simulates the fusion of many existing
cutting-edge technologies. It becomes a replica of reality by
implementing the real world as closely as possible and calibrating it
with data. It was originally proposed as a concept to support
decision-making in the design phase of a product (Grieves and Vickers,
2017), but it is being used as an analysis tool of the total life cycle
(Tao et al., 2019). The use of DT has the advantage of being able to
understand anomalous events or unknown phenomena (Tao et al., 2018), but
two major issues have not been established in academia. First, it is
difficult to integrate multi-scale, multi-physics, and interfaces. DT
studies should integrate models across lifecycle stages, taking into
account various levels of detail and all relevant disciplines (Boschert
and Rosen, 2016). There are 4 phases (design, manufacturing, service,
retire) in the total life of a product (Liu et al., 2021). The units of
various influence factors such as people, equipment, and systems are all
different. It is difficult to build an integrated model considering
their interfaces and protocols during the total lifecycle. Second, due
to integration difficulties, a standardized process widely used for DT
modeling has not yet been established. Existing DT studies utilize tools
that are easy to implement for each phase of the total lifecycle. Many
types of tools such as Predix, ANSYS, Bluemix, and MindSphere are being
used. Most of the past DT studies have only integrated these multiple
models into simple input/output (Liu et al., 2021). Therefore, there is
a need to establish a standardized process that can fundamentally solve
the mutual influence of different disciplines, time and space, and
different formats and protocols. As a method to solve the two problems,
this study proposes the construction of a digital twin using system
dynamics (SD). In SD, it is possible to implement a complex world with a
feedback loop composed of root causes (Sterman, 2010). Multiple data
scales of heterogeneous physics existing on various platforms can be
integrated, and multiple time horizons can be controlled, making it easy
to build an integrated model. The latest SD tools have dramatically
increased the reality by overcoming the limitations of traditional
simulation models such as distributional assumptions, and a method to
analyze the system model analytically is also provided. In particular,
it is possible to support WinBurg-based MCMC in the system dynamics
model, and to support interworking with programming languages R and
Python. Application during run-time became possible, and data
calibration became easy, resulting in very high fidelity (Richardson,
2015). In other words, if a DT model is built using SD, data of
different formats and protocols and multi-disciplinary interface support
are possible. Since SD models for each phase of the total life have
already been studied a lot, it is possible to build a DT model by
integrating them. Therefore, in this study, we propose to construct a DT
model using SD. The proposed method is applied to \emph{the operation
and maintenance system of ROK Naval ships}. This system is the service
phase of its total life. It is often known that the implementation of
the service phase is the most difficult. This is because the service
target is decentralized and it is difficult to consider all utilization
in various environments (reliability, convenience, real-time operation
status, maintenance strategy, etc.). Through the model building process
proposed in this study, the process of integrating multi-scales and
multi-disciplinary of multi-physics is confirmed, and anomalous events
or unknown latent effects are identified. The remainder of this paper
consists of six sections. The title of each section (Fig. 1) is the DT
construction process using SD we propose. After selecting the target
system, we explore and analyze the root causes. Various methods such as
statistical modeling (B-spline, Bayesian estimation, phase type
distribution fitting, etc.) and simulation are applied for analysis
(Chapter 2). The dynamic variables related to the analyzed root causes
are implemented as a system dynamics model (Chapter 3). The models built
in Chapter 3 are applied as one module constituting the integrated
model. In Chapter 4, the model is integrated and validated according to
the causal relationship between modules. Simulate and analyze the
integrated DT model to identify potential problems and latent effects
(Chapter 5). Chapter 6 summarizes the results and limitations of the
study and suggests future research directions.

\section*{Root cause exploration and
analysis}

{\label{root-cause-exploration-and-analysis}}

The target system of this study is the operation and maintenance system
of ROK Naval ships. Finding out what elements are included in the system
is important in determining root causes. Brain storming or mind-map can
be used. This process requires expert opinion. This is because it is
necessary to determine the root causes by identifying the relationships
among various influencing factors included in the system (Section 2.1).
Root causes are analyzed using statistical models such as Bayesian
inference, phase-type distribution, linear/multi regression, SD
simulation models, existing theories about human work speed, and survey
results (Section 2.2).

\textbf{2.1. Root cause exploration}

In addition to mind maps, you can use other methods such as
brainstorming. These methods generally classify associative words
hierarchically, but the classification is not important here. The key is
to think of associative (or related) elements and make connections. The
root causes search result through the mind map of the Operation and
Maintenance System for ROK Naval ships is shown in Fig. 2. Starting from
the target system, the causal relationships of the associative elements
are indicated by arrows. Among them, those that affect many factors
(Failure Probability), those that affect the policy of the system
(Maintenance policy), those that require a separate analysis independent
of the system (Maintenance technology), and the academic theory
(Schedule pressure) are root causes. It is necessary to reflect the
expert's domain knowledge rather than the analyst's subjective judgment.

\textbf{2.2. Root cause analysis}

This section introduces only the outline of the root causes in Fig. 2.
For details of the analysis, refer to the following studies. Failure
probability (Moon and Choi, 2021; Choi and Moon, 2022), Maintenance
policy (Choi et al., 2020; 2021; Park et al., 2021), Maintenance
technology (Choi and Moon, 2021), Schedule pressure (Oliva and Sterman,
2001). Failure probability is a root cause that affects many other
factors. ROK Naval ships are maintained at regular intervals based on
MTBF (Mean time between failure) according to the recommendations of the
equipment manufacturers. Nevertheless, failures continue to occur.
Recently, many efforts have been made to find the failure pattern over
the total life using actual failure data (Zammori et al., 2020; Wang and
Yin., 2019; Dikis and Lazakis, 2019). The failure pattern over the total
lifetime is called the failure function. Ship failures are divided into
two categories. One is that even if the performance of the equipment is
partially degraded, it is possible to perform the mission. The other is
a failure that immediately fails and requires repair by returning to the
home port. In this study, the first is called normal failure and the
second is called critical failure. The two failure functions were
estimated by hierarchical Bayesian inference (Moon and Choi, 2021),
combining trend and probability (Choi and Moon, 2022), respectively. The
failure function is not in the form of a constant straight line. In some
cases, failures during the total life cycle occur frequently and vice
versa. Therefore, the MTBF-based policy of maintenance at regular
intervals is inefficient. Choi et al. (2020; 2021) derived an
appropriate maintenance interval based on the failure function. Park et
al., 2021 analyzed maintenance intervals based on the naval fleet's ship
arrangement. A system dynamics model was implemented and analyzed for
the phenomenon of queues occurring due to mission delay and maintenance
work delay. The maintenance policy to which the failure function was
applied was advantageous in terms of operability of ships and repair
shops. Since maintenance is performed by humans, the efficiency may vary
depending on the technology of the repair shop. Choi and Moon (2021)
made Bayesian estimation of the change in equipment condition before and
after maintenance. Results ROK Navy's repair shop was able to complete
an average of about 74\% of repairs. In other words, if there are 100
faulty locations, it means that 74 locations are completely repaired
after planned maintenance and 26 locations are insufficiently
maintained. On the other hand, Oliva and Sterman (2001) argued that the
speed of work varies by 75\textasciitilde{}125\% depending on the
workload. In this study, based on this, the variability of the
maintenance amount performed by mechanics was given.

\section*{Root cause model design}

{\label{root-cause-model-design}}

System dynamics can simultaneously reflect multi-physics, multi-scale,
multi-interaction and multi-disciplinary in the model. The units of
elements reflected in the model vary. Multi-physics includes ships,
spare parts, mechanics, age of ships, and multi-scale includes manpower,
number of ships, spare parts, mechanics, etc. If a more specific model
is built, the types are more diverse. In this chapter, the root causes
analyzed in Chapter 2 are implemented as a system dynamics model. Each
root cause model is used as a module of the integrated model. Modules
are linked according to causality.

\textbf{3.1. Failure function modules}

The advantage of using the lookup function of System dynamics is that it
can express an unusual distribution. By implementing the average and
variance of the daily failure probability during the total life of the
failure functions as a system dynamics model, the occurrence of failures
during the total life can be simulated. Fig.3(a) and (b) are the average
of daily normal / critical failure function, respectively. Modules were
constructed as shown in Fig. 4 using the mean and variance of the
estimated failure functions. The two failure functions and variance are
implemented, and the input/output relationship is briefly shown. The
physics at this stage is a number of malfunctioning spare parts or
equipment. Both failure functions have the same scale. Critical failure
should be classified into physics different from normal failure because
it is repaired by arriving at the port immediately after failure.
Critical failure and normal failure are separated through integration
with other modules (section 4).

\textbf{3.2. Add maintenance policy module}

Ships are operated under the policy of performing planned maintenance
(1.5 months) after a certain operational operation (4.5 months). In
Section 3.1, the unit of model was number of failures. The unit for
planning maintenance is the number of ships. Although their scale is
different, they are easily integrated in system dynamics. The part
marked in red in Fig. 5 is the maintenance policy module. Maintenance
criterion determines the number of operating days of a ship. It may be
set to a different date depending on the policy (In the case of
Condition based maintenance (CBM), the maintenance time is determined
based on the ship status. In CBM, this variable determines the number of
flexible operating days). After 137 days or 138 days, the ship in the
Battle field moves to the Repair shop. After 45 days of movement, the
ship moves to the Battle field through Return to field. Fig.6(a) shows
the relationship of ship movement. Although the two modules have
different units, they interact and work at the same time. Fig.6(b) shows
the change of failures according to the operation and maintenance of the
ship. Failures accumulated from 137 to 138 days are repaired for 45
days. The total life of the ship is 31 years. Since operation and
maintenance are repeated twice a year, there are exactly 62 peaks in
Fig. 6(b). Through the merging of two modules with different units, it
can be seen that the system dynamics supports multi-scale.

\textbf{3.3. Add maintenance technology and schedule pressure module}

It is difficult to complete the maintenance of a ship 100\% perfectly.
In other words, it is difficult to return to the same condition as new
after maintenance. The repair shop's technical skills and natural aging
are the reasons for this. Maintenance technology refers to this
phenomenon. Choi and Moon (2021) estimated the technical level of Naval
ship's repair shop by Bayesian inference. On average, it was repaired at
a level of 74\%. If maintenance is performed with 100 failures, 26
failures cannot be completely repaired and remain on the ship. On the
other hand, Oliva and sterman (2001) studied that the speed of a
person's work varies by 75\textasciitilde{}125\% depending on the
workload. Mechanics can perform maintenance faster when there is a lot
of work and more slowly when there is less work. The standard working
day for the Navy is 8 hours. When they are busy, they can perform 10
hours' worth of maintenance (8*1.25). The disciplines were applied using
system dynamics. The model in Fig. 7 includes disciplinary (schedule
pressure) and maintenance technology (Effective of maintenance).
Although the scales of all modules are different, building them into one
model is not different from the process of building a system dynamics
model in general.

\section*{Model integration and
validation}

{\label{model-integration-and-validation}}

The module building process in Section 3 includes the integration
process. This is a process for establishing the interface relationship
between modules. Based on this, the integrated model should set the same
number of ships, mechanics, maintenance policy, etc. The method is the
same as the add process in section 3, but the model becomes visually
complex as shown in Fig. 8. The simulation result of the integrated
model should be able to simulate the real result as it is. Therefore,
validation through robustness or sensitivity tests in DT is more
important. The implementation of the functions included in the modules
of Section 3 utilized the lookup function of the system dynamics tool
(Vensim). The purpose of this study is to show that multi-physics and
multi-scale problems can be solved by using system dynamics. In the DT
building process, these lookup functions can be designed to be
continuously updated during the simulation process. This is because the
latest tools support data calibration using MCMC (Markov chain monte
carlo) and link with programming languages (python, R, etc.) or other
analysis methods (analysis tools). For details, see Richardson (2015),
S\selectlanguage{ngerman}ücüllü, C., \& Yücel (2014). The integrated model is shown in Fig. 8.
Compared to the model in Section 3.3, it is visually more complex, but
the model operation process is the same. The items additionally
reflected in the model are as follows. The number of ships increased
from 1 to 6. A virtual waiting space was applied because a queue may
occur in the movement of the ship between the battle field and the
repair shop. It was modified to handle normal failure and critical
failure separately. And the night additional work of the mechanics was
set to be possible up to 4 hours a day. The ages of the 6 ships are all
different, and the ages of the actual naval fleet ships are applied. In
the work of increasing the number of ships to 6, it is necessary to make
sure that the priorities of entering the repair shop do not conflict,
but it is not difficult. It should be noted that multi-physics support
is possible. Although tangible and intangible physics such as ships,
number of people, and manpower have their own scales, they interact with
each other through causal relationships. Validation of some variables
included in the DT model is shown in Fig. 9. All reflected variables
must be checked one by one. All variables of the model reflected reality
well.

\section*{Simulation, analysis and global
optimization}

{\label{simulation-analysis-and-global-optimization}}

Analyzing the simulation results of the DT model is the same as
analyzing reality. Real variables are composed of complex causal
relationships. In the DT model, many loops are created by the connection
of modules. In the case of Fig. 8, there are about 230,000 loops. Humans
cannot intuitively know these complex relationships. So, in reality,
sometimes unexpected results can come out. This is due to the influence
of variables that were not considered. Assume that the Naval operation
period is relatively longer than the maintenance time. The longer the
equipment run time, the more failures. As maintenance costs increase,
total life cycle cost increases. This sequence may seem like a natural
result. However, the simulation results show that the total life cycle
cost is reduced. See section 5.1 for more details. In the DT model, it
is possible to simulate latent effects or potential problems that occur
due to the simultaneous influence of multiple modules and variables. By
checking the simulation results, the relationship between cause and
effect can be established. Examples are the relationship between the
operating period of the ship and the total life cost, or the
relationship between the number of mechanics and the failure probability
of the ship. In this study, linear regression is simply used, but a
high-precision method such as multi-regression may be applied if
necessary (section 5.2). It is meaningful to perform optimization by
integrating all the variables, but computation time constraints may
occur. In this study, a rough optimization is performed using the
equation calculation established by linear regression (section 5.2).
Section 5.2 examines maintenance policies with the DT model. As shown in
Table1, a total of 4 models are composed. In the current Naval policy,
ships start maintenance 1.5 months after 4.5 months naval operation.
However, to simulate advanced policies such as condition-based
maintenance, it is assumed that normal failure means the condition of
the ship. Normal failure limits the performance and worsens the
condition of the ship. On the other hand, the repair period is not fixed
at 1.5 months, but consider the situation in which the maintenance
period can be terminated as soon as the repair is completed.

Table 1 4 Models\selectlanguage{english}
\begin{longtable}[]{@{}lll@{}}
\toprule
Model & Criteria for maintenance & Repair period\tabularnewline
\midrule
\endhead
Model 1 (PFM\_FRP) & ? PFM : Period fixed maintenance & ? FRP : Fixed
repair period\tabularnewline
Model 2 (PFM\_NRP) & ? PFM : Period fixed maintenance & ? NRP :
Non-fixed repair period\tabularnewline
Model 3 (FFM\_FRP) & ? FFM : Failure rate fixed maintenance & ? FRP :
Fixed repair period\tabularnewline
Model 4 (FFM\_NRP) & ? FFM : Failure rate fixed maintenance & ? NRP :
Non-fixed repair period\tabularnewline
\bottomrule
\end{longtable}

Model 1 is the current Navy policy. Model 4 is similar to Condition
based maintenance (CBM). Perform maintenance according to the condition
of the ship and start naval operation as soon as maintenance is
completed. Models 2 and 3 are alternatives that can be used in the
process of developing CBM from the current policy. Because the military
is a conservative group, they tend to avoid innovative improvements.
Models 2 and 3 can be used in this case.

\textbf{5.1. Non-intuitive correlation}

The DT model is composed of a complex causal relationship, and a latent
effect occurs during the interface process between modules. A potential
problem is sometimes found due to the latent effect. The correlation of
simulation results included a potential problem. This is because the
results showed that if the improved maintenance policy promoted by ROK
Navy was continuously applied, the cost and the probability of mission
failure would increase. Due to military security concerns, details
cannot be disclosed. This was due to the limitations of human analytical
ability. This section explains that non-intuitive results can be
confirmed by using the DT model through an example.

Table 2 Correlation examples\selectlanguage{english}
\begin{longtable}[]{@{}lll@{}}
\toprule
Variable & Variable & Coefficient\tabularnewline
\midrule
\endhead
Operation period & Mean number of critical failures &
0.58\tabularnewline
Operation period & The cost of spare parts during the total life cycle &
-0.86\tabularnewline
\bottomrule
\end{longtable}

In Table 2, a large operation period means that there are many naval
operations. That is, the degree of exposure to failure is large. The
coefficient of both variables is 0.58. At this time, since many failures
occur, the cost of spare parts will be larger during the total
lifecycle. This is interpreted intuitively. However, the coefficient of
operation period and cost of spare parts during the total lifecycle is
-0.86. This can be found in the Navy's maintenance policy. In the
current policy of 1.5 months maintenance after 4.5 months of operation,
if the operation period is increased, the total number of preventive
maintenances performed during the total lifecycle decreases. In other
words, it is also interpreted to mean that the cost of spare parts used
for preventive maintenance is higher than the cost of spare parts caused
by critical failure during the total lifecycle. Even if the unit price
of spare parts used for critical failure is much higher than the cost
used for preventive maintenance. This may seem simple to interpret, but
to naval policy makers, it is not. This is because the increase in total
lifecycle cost caused by the increase in critical failure was taken for
granted. When the correlation of all variables is checked, the more
complex the relationship, the more difficult it is to interpret.
However, the analysis results can be used as important. Among them, the
interpretation that maintaining the current policy could lead to
catastrophic results was also found. If the DT model is used, potential
problems caused by the latent effect can be discovered only by
correlation analysis.

\textbf{5.2. Linear regression and optimization}

If the results of DT simulations can be analyzed and optimized, the
system can be improved. Each simulation result of the four models was
linearly regressed. Compared to non-linear, it is easier to understand
the relationship between variables. Depending on the purpose,
multi-regression or other statistical methods may be applied. Fig. 10
shows the results of linear regression of operational availability (Ao)
and probability of critical failure (Probability\_CF). Their
relationship is related to the reliability of the mission. This is
because the success rate of the mission is determined depending on which
policy is adopted after setting the target Ao. If Probability\_CF is
small at the target Ao line, it can be said that the policy has a high
mission success rate. As shown in Fig. 10, in the case of PFM\_NRP and
FFM\_NRP, Probability\_CF is 0 at target Ao. In the regression with a
higher dimension, FFM\_NRP had a lower Probability\_CF at Ao. The
relationship between PFM\_FRP and FFM\_FRP is noteworthy. FFM\_FRP is
the basis of CBM. Since the maintenance time is flexibly determined,
normal failures accumulated in the ship can be effectively repaired.
However, if FFM\_FRP is applied, Probability\_CF is higher than the
current maintenance policy (PFM\_FRP) in target Ao. In other words, it
has the advantage of being able to effectively repair failures, but the
probability of mission failure during naval operation is higher. If the
navy pushes forward to apply CBM, it can be seen that not only FFM but
also NRP should be promoted at the same time. In the case of this
research model, 1.2 billion simulations were required for each model in
order to confirm all the necessary scenarios in ROK Navy. In the
performance of the computer used in the study (Intel Core i7 2.6Ghz,
16GB DDR4 RAM), about 5 seconds was consumed for one simulation. Linear
regression can be used as a method to solve time-consuming problems in
large-scale simulations such as DT. This is possible by constructing an
optimization objective equation and performing arithmetic calculations
using a linear regression equation between the independent variable and
the dependent variables constituting the objective equation. The Navy
needs a policy with high operational availability, low mission failure
rate (probability of critical failure), and low total lifecycle cost.
Expression (1) is equivalent to expressing their
relationship.\(\frac{\text{Operational\ availability}}{Probability\ of\ critical\ failure\times\ Life\ cycle\ cost}\)(1) It took about 16 minutes to check the
optimization results of the models with the objective of Equation (1).
The method using the linear regression equation has the advantage of
being able to quickly check the rough results, although the accuracy
will be lower than that of simulating all scenarios or calculating
through non-linear relational equations.

\section*{Conclusion}

{\label{conclusion}}

Digital twin research has been started for many years, but there is no
standardized tool or method recognized by the academic community. In
this study, system dynamics was proposed as a tool that can solve
integration problems such as multi-scale, multi-physics, and
multi-disciplinary, which are continuously becoming issues in the
digital twin field. By utilizing this, it was revealed that various
heterogeneous data from various protocols or platforms can be integrated
into one model. In addition, the five-step DT construction process was
explained using actual data. Through the simulation results, it was
confirmed that the potential problem caused by the latent effect can be
found, and the method of optimizing it using the results is described in
a rough way, which can contribute to the usability aspect. In this
study, in order to explain the model building process using system
dynamics, the update of variables is omitted (most statistical
model-based modules are implemented with the lookup function). In actual
DT simulation, real data is accumulated and run-time update of root
causes is possible. Details on this can be found in S\selectlanguage{ngerman}ücüllü \& Yücel
(2014) and Richardson (2015). In this study, only the service phase was
implemented among the 4 phases of the total lifecycle, but design,
manufacturing, and retire phases can all be added by using the module
addition method described in this text. Since the system dynamics model
for each phase of the total life has been studied a lot, the DT model
can be completed by integrating them.

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Boschert, S., \& Rosen, R. (2016). \emph{Digital twin---the simulation
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Choi, J. W., Moon, S. A., \& Jo, W. Y. (2021) A Study on the
Probability-Based Planned Maintenance Effectiveness of Naval Combat
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Choi, J. W., \& Moon, S. A. (2022). Rare Event Simulation by Combining
Trend and Probability: An Application to Naval Ship Critical
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Choi, J. W., Moon, H. J., \& Jo, W. Y. (2020) Preventive maintenance
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\textbf{Authors}

\textbf{Jinwoo Choi} (Ph.D. in Military studies, Korea National Defense
University) is lieutenant commander in Korea Naval officer. His
interests include defense digital twin and defense AI development and
applications. He has published in the Applied AI Letters, Industrial
Engineering and Management Systems, Journal of the Korean Institute of
Industrial Engineering, Korean Journal of Logistics, among others. He is
the co-author of Inventory Management with System Dynamics and Smart
Logistics (about the application of defense AI). Recently, he is
interested in IPS (Integrated Product Support) development through
defense digital twin and Bayesian prior distribution elicitation.\selectlanguage{english}
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\includegraphics[width=0.70\columnwidth]{figures/image37/image37}

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\textbf{Seongam Moon} (Ph.D. in Business administration, Yonsei
University) is Professor of Military Supply Chain \& Operations
Management. He serves as Vice President of the Korean Society of
Logistics and Vice President of the Korean Society of Production
Management. Until recently, he served as a policy advisor for the
Ministry of National Defense, a policy advisor for the Ministry of Land,
Infrastructure and Transport, and a management innovation evaluation
team for the Ministry of Strategy and Finance. He has published over 100
papers, including International Journal of Simulation Modeling,
International Journal of Advanced Logistics, among others. His interests
include Military supply chain, Behavioral operations management, System
thinking, Supply chain management, Repair system.\selectlanguage{english}
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\textbf{Soonhong Min} (Ph.D. in Marketing \& Logistics, the University
of Tennessee) is Professor of Supply Chain \& Operations Management and
Associate Director of Center for Global ESG and Business Ethics at
Yonsei University's School of Business in Korea. He has published in the
Journal of Business Logistics, International Journal of Physical
Distribution and Logistics Management, International Journal of
Logistics Management, Journal of Purchasing and Supply Management, the
Journal of Retailing, Journal of the Academy of Marketing Science,
Industrial Marketing Management, Journal of Business and Industrial
Marketing, among others. He also co-authored the book Supply Chain
Management. He is President of Korea Logistics Society, a leading
academic and professional community in the fields of logistics and SCM
in Korea and serves as an Editorial Review Board member of Journal of
Promotion Management.

\textbf{Funding}

This work was supported by research grant of Yonsei University Business
Research Institute in 2022. Author Prof. Min. and Prof. Moon. have
received research support from Yonsei University.

\textbf{Conflicts of interest/Competing interests}

Not applicable

\textbf{Availability of data and material \& Code availability}

Data provided by third parties, Real data from the Republic of Korea
Navy is used in this study, so data sharing is not possible due to
military security issues. Programming code and simulation models also
contain content that must be protected militarily.

\textbf{Ethics approval}

Not applicable

\textbf{Consent to participate}

Not applicable

\textbf{Consent for publication}

Not applicable

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