3.1. Simulation-related Policies in South Korea and Other Countries

Major countries are implementing various policies to realize manufacturing innovation powerhouses and improve national competitiveness through the digital transformation of manufacturing. They also try to respond quickly to environmental changes such as the expansion of non-face-to-face markets triggered by COVID-19. The United States has presented five strategic goals, including supercomputing-based simulations, in the “National Strategic Computing Initiative Strategic Plan (2016)” and has been ceaselessly implementing policies for smart manufacturing since then. A noteworthy example is the inclusion of M&S in the five strategic objectives in the “Strategy for American Leadership in Advanced Manufacturing (2018.10).” In particular, since 2015 the Department of Energy, Advanced Manufacturing Office, and national research institutes have been cooperating on High Performance Computing for Manufacturing (HPC4Mfg), a project to support manufacturing simulations using supercomputing, and are strengthening efforts to promote the use of simulation technology, including injecting a financial resource of $3.75 million into ten projects in 2021. Germany has emphasized technical sectors such as supercomputing, and digital design and simulation, to realize the digital innovation of manufacturing through Industrie 4.0 and “Plattform Industrie 4.0” policies at the pan-ministerial level. Furthermore, they are actively supporting simulation-oriented R&D through “AUTONOMIK 4.0 (simulation-based systems for small and medium-sized enterprises)” in connection with “Mittelstand 4.0” to encourage digital innovation in small and medium-sized companies. As of 2020, 26 regional competence centers and four agencies have been established and are under operation as R&D support programs for the proliferation of simulation-based manufacturing systems. The UK is expanding investment in simulation technology through government policies such as “High Value Manufacturing” and “Industrial Strategy Challenge Fund” for the digital transformation of manufacturing. China has also selected smart design and simulation technology development as one of the ten major projects in “Made in China 2025.”

In South Korea, government policies and investments for the digital transformation of manufacturing have been continuously strengthened, from the “Manufacturing Innovation 3.0” strategy, which aimed at the proliferation of smart factories in 2014, to the recent “Manufacturing Renaissance Vision and Strategy (2019)” and “Comprehensive Plan for Korean New Deal (2020).” However, it was the “Digital New Deal” in the 2020 comprehensive plan for a new deal that made people begin to directly mention the importance of supercomputing and simulation, and development of relevant technologies. Thus, manufacturing innovation through digitalization is fast becoming an essential element in securing national competitiveness and the importance of analysis-based strategy establishment is reiterated.

3.2. Simulation-related Technology Development Status

The demand for simulation-based manufacturing digitalization is on the rise because of the prolonged social distancing due to COVID-19 and the radical development of ICT, such as XR (eXtended Reality). Global companies recognize the use of simulation as a core technology that facilitates fast response to the market by dramatically reducing the time and costs required for new product development and improved productivity. The use of simulation is increasing not only in the design process but also across the whole product development process. Furthermore, its scale is expanding, and the field of complex simulation execution using supercomputing resources is gaining importance. In particular, as shown in Fig. 1, it corresponds mainly to the simulation (Computer Aided Engineering, CAE) part through product design (Computer Aided Design, CAD) in the product development processes of manufacturing companies. The key to simulation is the software that supports a series of processes such as preprocessing, analysis, and post-processing (Kim et al., 2016).

Fig. 1

Simulation positioning in production process. CAD, Computer Aided Design; CAE, Computer Aided Engineering; CAM, Computer Aided Manufacturing; NC, Numerical Control; CNC, Computer Numerical Control; CIM, Computer Integrated Manufacturing.

The application to the industry through simulation technology development enables the optimization of products and processes, which contributes greatly to the improvement of productivity, such as defect rate reduction, shortening of development period, and cost reduction. The Korea Institute of Science and Technology Information (KISTI) has supported 626 manufacturing companies since 2007 with simulation technology, and as of 2021, the product development time is reduced by 61.88% and cost by 73.94% (KISTI, 2021).

In recent years, the Reduced Order Model (ROM) has emerged. Based on advancements in supercomputing and simulation technologies, ROM enables increasingly stable and innovative designs by executing complex simulations in the design space and generating a large-scale optimization plan. ROM simplifies high-fidelity models and maintains essential behaviors by using a complex mathematical algorithm. More detailed models can be created, and sophisticated simulations can be performed if supercomputing resources and ROM are used together (Scientific Computing World, 2019). Siemens, a global company in the US, and Ansys in Germany are leading the simulation software market, including ROM. Although the ROM technology development activity in South Korean companies is insignificant, KISTI has recently developed a pilot program of ROM to assure quality. As the advantages of using simulation technology in the industry become visible and the sectors show expansion, efforts are made to develop relevant technologies.

4.1. Significance and Structure of Input-Output Analysis

In a national economy, each industry enters into a relationship with the other directly or indirectly through the process of purchasing and selling goods and services for production activities. Input-output tables are statistical tables that record these trading relationships among industries for a certain period (usually one year) in the form of a matrix, following a certain principle, as shown in Table 1. In Table 1, the total input is the sum of intermediate inputs and value-added, and the total output is the sum of intermediate demand and final demand, minus imports. The total input refers to the total output. The vertical direction explains the input structure, which consists of production costs incurred by each industrial sector. The horizontal direction refers to the allocation structure, which shows how much of each industrial sector’s products have been sold to fulfill intermediate or final demands.

Input-output analysis is a method of quantitatively analyzing the relationship among industries based on the input-output tables. Input-output analysis is used to establish economic policies and measure policy effects because various ripple effects such as the production, employment, and income induced by the final demand can be analyzed by classifying them for each industry. To estimate the ripple effects such as production, value-added, and employment inducement of supercomputing-based simulations, we use the 2019 input-output tables (extended tables) released by the Bank of Korea on June 21, 2021 and calculate various coefficients and decipher the inducement effects (Bank of Korea, 2021).

4.2. Calculation of Various Coefficients

The coefficient calculated by dividing the intermediate input—such as raw materials purchased by each industrial sector from others for use in the production of goods and services—by the total input is the input coefficient. A matrix that arranges input coefficients in the same manner as the endogenous sectors of the input-output table is described as an input coefficient table. As the production effects induced by imported goods or services must be excluded to calculate the economic ripple effect of supercomputing-based simulations, the domestic input coefficient excluding the import transaction amount is the same as Eq. (1).

Domestic input coefficient between industries i and j $a_{ij}=\frac{X_{ij}-M_i}{X_j}$-- Eq. (1)

◦ X_ij: intermediate input between industries i and j, Mi: imports, X_j: total input

The production inducement coefficient is calculated by using Eq. (2) after converting the sectors corresponding to the integrated sub-categories into exogenous variables by using Eq. (1).

Production inducement coefficient= $A_s^d{\left(I-A^d\right)}^{-1}$-- Eq. (2)

◦ $A_s^d$: Domestic input coefficient row vector of supercomputing-based M&S

◦ I: diagonal matrix composed of 1

◦ A_d: matrix of domestic input coefficients (a_ij)

The value-added coefficient shows the proportion of value-added in total output, and it is obtained by dividing the sum of value-added of each industry by total output in the input-output table, as shown in Eq. (3).

Value-added coefficient of industry i $v_i=\frac{V_i}{X_i}$-- Eq. (3)

◦ V_i: sum of value-added, X_i: total input

The labor coefficient is calculated by dividing the amount of labor put into production activity for a certain period by total input, and it refers to the amount of labor required directly for the production of one unit. It is classified into the employment coefficient and hiring coefficient depending on whether self-employed owners and unpaid family workers are included in the amount of labor.

Employment coefficient $l_w=\frac{L_w}{X}$, hiring coefficient $l_e=\frac{L_e}{X}$ ---- Eq. (4)

◦ L_w: number of employees, L_e: number of employees, X: total output

The labor inducement coefficient includes not only the amount of labor required directly for the production of one unit of product in a certain industry but also the amount of labor required indirectly in the production ripple process. It is represented by Eq. (5), and in this study, the employment inducement coefficient is used to analyze the employment inducement effect.

Employment inducement coefficient $\stackrel{⏜}{l_w}{(I-A^d)}^{-1}$

Hiring inducement coefficient = $\stackrel{⏜}{l_e}{(I-A^d)}^{-1}$---Eq. (5)

◦ $\stackrel{⏜}{l}$: diagonal matrix of labor coefficients, I: unit matrix, A_d: domestic input coefficient matrix

The “degree of sensitivity” coefficient is calculated as a ratio for the industrial average of the unit that the i^th industry must produce to increase the final demands of all sectors by one unit each. The coefficient of influence refers to the ratio of the production inducement coefficient of each sector to the average production inducement coefficient of all industries.

4.3. Analysis of Economic Ripple Effects

Input-output analysis is used to analyze economic ripple effects in various disciplines such as social sciences, engineering, and natural sciences (Hong et al., 2010; Jee et al., 2011; Park, 2018; Park & Hahn, 2011). Based on the fact that the flow of goods and services among economic sectors is relatively stable, the input-output analysis examines the economic system statistically in more detail, thus explaining economic phenomena. In particular, input-output analysis is widely used in fields related to economic policy establishments and effect analysis of a country, which means that it can be used to ascertain the economic ripple effects of domestic simulations.

First of all, we apply supercomputing-based simulations to the “Information Service,” “Software Development and Distribution,” “Research and Development,” “Other Scientific and Technical Services,” and “Other Business Support Services,” as shown in Table 2, to apply the input-output analysis. The result is derived as the output element of supercomputing-based simulations through the input element of the government R&D budgets.

In this study, the production inducement coefficient, value-added inducement coefficient, and employment inducement coefficient are calculated through Eq. (1)-(5), as summarized in Table 3. Each inducement coefficient explains the inducement effect that occurs directly/indirectly in all the industries when the final demand for supercomputing-based simulations increases by one unit.

Assuming that “Information Service,” “Software Development and Distribution,” “Research and Development,” “Other Scientific and Technical Services,” and “Other Business Support Services,” which belong to the integrated sub-category in Table 3, affect the supercomputing-based simulation equally, the production inducement coefficient is 1.54 and the value-added inducement coefficient is 0.89.

In the national economy, the outputs from a particular industry group are used by other industries, and production activities are carried out as ripple effects in a value chain. In the value chain of our analysis, the effect of supercomputing-based simulations on the industries in front is called the forward linkage effect, and the effect on the industries on the rear side of the value chain is called the backward linkage effect. Here, the degree of sensitivity is 1.07, and the coefficient of influence is 0.80. Since the degree of sensitivity is greater than 1, there is a forward linkage effect. As the coefficient of influence is smaller than 1, it is interpreted that the backward linkage effect is small.

However, for each one of the five variables belonging to the integrated sub-category, we summarize the weight through the focus group interviews targeting ten experts from the industry, universities, and research institutes. The ten experts are three university professors (Hanbat National University, Gyeongsang National University, Chonnam National University), five people from government-funded research institutes (KIST, KRICT, KIMM, DISTEP, NAFI), and two persons from companies (INNOPLUS Company, Beyond Lab). The weight of each variable corresponding to the integrated sub-category is derived from the experts. The results show that the variables of “Information Service,” “Software Development and Distribution,” “Research and Development,” “Other Scientific and Technical Services,” and “Other Business Support Services” have effects with weights of 3:1:3:2:1, respectively. We then obtained the adjusted coefficient values reflecting them, as shown in Table 4.

An examination of the inducement coefficient values adjusted by reflecting the experts’ opinions revealed that values of the production inducement coefficient and coefficient of influence are larger than the average coefficient values, and the value-added inducement coefficient and degree of sensitivity are smaller, thus showing that the results vary. Furthermore, when the employment inducement coefficients are calculated through the values of “Information Service,” “Software Development and Distribution,” “Research and Development,” “Other Scientific and Technical Services,” and “Other Business Support Services,” as in the coefficients given above, the results are as shown in Table 5. However, the average coefficient value—the evenly assumed coefficient value—indicates an inducement effect of 10.2934 persons per billion won, and the adjusted coefficient value is a value calculated reflecting the expert opinions and demonstrates an inducement effect of 9.9893 persons per billion won.

To calculate the economic ripple effect of supercomputing-based simulations, we must determine which input variable is the most important factor. Therefore, the national R&D budget of the government is used as an input variable to calculate the economic ripple effect of supercomputing-based simulations. A total of 28.3 billion won is injected into the supercomputing-based simulations from 2007 to 2020; detailed information related to the budget is shown in Table 6.

To calculate the economic ripple effects based on the inducement coefficients of supercomputing-based simulations obtained in Tables 3, 4, and 5, we first estimate the production inducement effect by multiplying the production inducement coefficient calculated through the input-output table of supercomputing-based simulations. The value-added inducement effect is the net value of the national economy, which can be obtained through supercomputing-based simulations, and the portion attributed to the value-added in the production inducement effect can be estimated through the value-added inducement coefficient. The employment inducement effect can be assessed from the perspective that an increase in the related market of supercomputing-based simulations leads to a rise in employment, and it can be calculated by multiplying the employment inducement coefficient.

The fact that merely the input-output table of the Bank of Korea was used for the economic ripple effects of supercomputing-based simulations for budget input for a total of 14 years from 2007 to 2020 is a factor that needs to be improved in follow-up research. Nevertheless, this analysis is significant in that there has been no study or report that analyzes the economic ripple effects of supercomputing-based simulations for the past 14 years, and we have done it for the first time. Furthermore, our analysis is differentiated from other studies as we used the inducement coefficients adjusted by reflecting the opinions of ten experts from the industry, universities, and research institutes.

Table 7 describes the economic ripple effects induced by supercomputing-based simulations over the past 14 years.

Assuming that the coefficients of the variables of supercomputing-based simulations are equal, the analysis results show that the total production inducement effect of supercomputing-based simulations over the last 14 years is 43.6 billion won, the value-added inducement effect is 25.1 billion won, and the employment inducement effect is 291 persons per billion won.

The inducement effects based on the coefficients adjusted by reflecting the opinions of the experts are as follows: The total production inducement effect of supercomputing-based simulations over the past 14 years is 45.1 billion won, the value-added inducement effect is 24.8 billion won, and the employment inducement effect is 282 persons per billion won.