Becoming the world&#;s leading enabler of intelligent transformation often means Lenovo must pioneer new technology and processes across our own operations. Teams across the enterprise transform rapidly adapt to not only better serve customers and partners, but to internally push the limits of innovation.
In Lenovo&#;s manufacturing hub in Shenzhen, China, this full-scale transformation manifests as the new Lenovo South Smart Campus (LSSC). The state-of-the-art facility, which opened on May 6, is affectionately called a &#;global mother factory.&#;
&#;We are at the forefront of the most advanced technologies, where we can develop replicable and scalable solutions that can be exported to all our overseas factories, empower the industry, and foster innovative ideas and products,&#; explained Guan Wei, senior vice president of Lenovo and head of the global supply chain ranked eighth in the world by Gartner.
In a sense, this means the LSSC &#;mother factory&#; creates powerful transformations that cascade to her &#;children&#; around the world. New ways of working&#;from AI-assisted acceleration of quality assurance to bespoke employee training&#;are pioneered at LSSC and directly impact the full supply chain.
With a total investment of $300 million USD, LSSC will be capable of rolling out more than 16 million intelligent products annually, potentially creating hundreds of thousands of jobs among Lenovo&#;s partners and customers, both up and downstream along the supply chain.
&#;LSSC can improve the efficiency, product quality, and resilience of our entire supply chain,&#; Guan added. &#;It can also serve as an incubation center, helping small- and medium-sized enterprises achieve significant improvements in intelligent manufacturing.&#;
To further increasing efficiency and reducing waste, LSSC features automatic collection and transparent visualization of energy consumption data such as water, electricity and gas, as well as environmental data such as temperature, humidity and discharge in the park and production line. Analysis and optimization across these data points helps create a smarter and more sustainable industrial park.
According to the stability theorem of differential equation, the stable state of the probability that the government selects the incentive must satisfy F(q)&#;=&#;0 and F&#;(q)&#;<&#;0. The derivative of the government's replication dynamic Eq. (7) can be obtained:
$$F^{\prime}\left( q \right) = \left( {1 - 2q} \right){\mkern 1mu} \left\{ {\left( {1 - {\mkern 1mu} \theta_{2} } \right)S_{1} + \theta_{2} {\mkern 1mu} w + p\left[ {\left( {S_{1} {\mkern 1mu} - w} \right)\left( {\theta_{2} - {\mkern 1mu} \theta_{1} } \right) - G} \right]} \right\}$$
(9)
When \(p = p^{*} = \frac{{\left( {1 - {\mkern 1mu} \theta_{2} } \right)S_{1} + \theta_{2} {\mkern 1mu} w}}{{G + \left( {S_{1} {\mkern 1mu} - w} \right)\left( {{\mkern 1mu} \theta_{1} - \theta_{2} } \right)}}\), F(q) &#; 0 and F&#;(q) &#; 0 can be obtained. At this time, any strategy formulated by the government is stable.
If \(\left( {S_{1} {\mkern 1mu} - w} \right)\left( {\theta_{2} - {\mkern 1mu} \theta_{1} } \right) - G > 0\), when p&#;>&#;p*, \(\left. {F^{\prime}\left( q \right)} \right|_{q = 0} > 0\), \(\left. {F^{\prime}\left( q \right)} \right|_{q = 1} < 0\), q&#;=&#;1 is in an evolutionary stable state, the government's strategy is incentive. When p&#;<&#;p*, \(\left. {F^{\prime}\left( q \right)} \right|_{q = 0} < 0\), \(\left. {F^{\prime}\left( q \right)} \right|_{q = 1} > 0\), q&#;=&#;0 is in an evolutionary stable state, the government's strategy is no incentive.
If \(\left( {S_{1} {\mkern 1mu} - w} \right)\left( {\theta_{2} - {\mkern 1mu} \theta_{1} } \right) - G < 0\), when p&#;>&#;p*, \(\left. {F^{\prime}\left( q \right)} \right|_{q = 0} < 0\), \(\left. {F^{\prime}\left( q \right)} \right|_{q = 1} > 0\), q&#;=&#;0 is in an evolutionary stable state, the government's strategy is no incentive. When p&#;<&#;p*, \(\left. {F^{\prime}\left( q \right)} \right|_{q = 0} > 0\), \(\left. {F^{\prime}\left( q \right)} \right|_{q = 1} < 0\), q&#;=&#;1 is in an evolutionary stable state, the government's strategy is incentive.
The steady state for the selection of smart production in an assembled steel plant needs to satisfy F(p)&#;=&#;0 and F&#;(p)&#;<&#;0. The derivative of the replication dynamic Eq. (8) can be obtained:
$$F^{\prime}\left( p \right) = {\mkern 1mu} \left( {1 - 2p} \right)\left\{ {C_{2} - C_{1} + R_{1} - R_{2} + {\text{D}}\left( {\theta_{2} - {\mkern 1mu} \theta_{1} } \right) + {\mkern 1mu} q\left[ {G + w\left( {\theta_{2} - {\mkern 1mu} \theta_{1} } \right)} \right]} \right\}$$
(10)
When \(q = q^{*} = \frac{{R_{2} - R_{1} + C_{1} - C_{2} + {\text{D}}\left( {{\mkern 1mu} \theta_{1} - {\mkern 1mu} \theta_{2} } \right)}}{{G + w\left( {\theta_{2} {\mkern 1mu} - \theta_{1} {\mkern 1mu} } \right)}}\), F(p) &#; 0 and F&#;(p) &#; 0 can be obtained. At this time, any strategy formulated by the government is stable.
According to the parameter relationship it is known that \(G + w\left( {\theta_{2} - {\mkern 1mu} \theta_{1} } \right) > 0\), if q&#;>&#;q*, then \(\left. {F^{\prime}\left( p \right)} \right|_{p = 0} > 0\), \(\left. {F^{\prime}\left( p \right)} \right|_{p = 1} < 0\), at this time p&#;=&#;1 is in an evolutionary stable state and the strategy of the assembled steel plant is to choose the smart plant strategy. If q&#;<&#;q*, then \(\left. {F^{\prime}\left( p \right)} \right|_{p = 0} < 0\), \(\left. {F^{\prime}\left( p \right)} \right|_{p = 1} > 0\), at this time p&#;=&#;0 is in an evolutionary stable state and the strategy of the assembled steel plant is to choose the traditional plant strategy.
This part performs stability analysis on the two-dimensional system of the game. Combining Eqs. (7) and (8) gives the following evolutionary dynamical system for both sides of the game.
$$\left\{ \begin{gathered} F\left( q \right) = q{\mkern 1mu} \left( {1 - q} \right){\mkern 1mu} \left\{ {\left( {1 - {\mkern 1mu} \theta_{2} } \right)S_{1} + \theta_{2} {\mkern 1mu} w + p\left[ {\left( {S_{1} {\mkern 1mu} - w} \right)\left( {\theta_{2} - {\mkern 1mu} \theta_{1} } \right) - G} \right]} \right\} = 0 \\ F\left( p \right) = p{\mkern 1mu} \left( {1 - p} \right)\left\{ {C_{2} - C_{1} + R_{1} - R_{2} + {\text{D}}\left( {\theta_{2} - {\mkern 1mu} \theta_{1} } \right) + {\mkern 1mu} q\left[ {G + w\left( {\theta_{2} - {\mkern 1mu} \theta_{1} } \right)} \right]} \right\} = 0 \\ \end{gathered} \right.$$
(11)
Five equilibrium points can be obtained by solving equation system (11): E1 (0,0), E2 (0,1), E3 (1,0), E4 (1,1), E5 (q*, p*), where \(p^{*} = \frac{{\left( {1 - {\mkern 1mu} \theta_{2} } \right)S_{1} + \theta_{2} {\mkern 1mu} w}}{{G + \left( {S_{1} {\mkern 1mu} - w} \right)\left( {{\mkern 1mu} \theta_{1} - \theta_{2} } \right)}}\), \(q^{*} = \frac{{R_{2} - R_{1} + C_{1} - C_{2} + {\text{D}}\left( {{\mkern 1mu} \theta_{1} - {\mkern 1mu} \theta_{2} } \right)}}{{G + w\left( {\theta_{2} {\mkern 1mu} - \theta_{1} {\mkern 1mu} } \right)}}\). According to Friedman's study42, the stability of the evolutionary system can be obtained from the local stability analysis of the Jacobian matrix. The Jacobian matrix of the two-dimensional system is as follows:
$$J = \left[ {\begin{array}{*{20}c} {\frac{\partial F\left( q \right)}{{\partial q}}} & {\frac{\partial F\left( q \right)}{{\partial p}}} \\ {\frac{\partial F\left( p \right)}{{\partial q}}} & {\frac{\partial F\left( p \right)}{{\partial p}}} \\ \end{array} } \right] = \left[ {\begin{array}{*{20}c} {a_{11} } & {a_{12} } \\ {a_{21} } & {a_{22} } \\ \end{array} } \right]$$
(12)
Among them:
$$\left\{ \begin{gathered} a_{11} = \left( {1 - 2\,q} \right)\,\left\{ {\left( {1 - \,\theta_{2} } \right)S_{1} + \theta_{2} \,w - p\left[ {G + \left( {S_{1} - w} \right)\left( {\theta_{1} - \theta_{2} } \right)} \right]} \right\} \hfill \\ a_{12} = - q{\mkern 1mu} \left( {1 - q} \right){\mkern 1mu} \left[ {G + \left( {S_{1} - w} \right){\mkern 1mu} \left( {\theta_{1} - {\mkern 1mu} \theta_{2} } \right)} \right] \hfill \\ a_{21} = p{\mkern 1mu} \left( {1 - p} \right){\mkern 1mu} \left[ {G - w\left( {\theta_{1} {\mkern 1mu} - \theta_{2} {\mkern 1mu} } \right)} \right] \hfill \\ a_{22} = \left( {1 - 2\,p} \right)\,\left\{ {R_{1} - R_{2} + C_{2} - C_{1} - {\text{D}}\left( {\,\theta_{1} - \,\theta_{2} } \right) + q\left[ {G\, - w\left( {\,\theta_{1} \, - \,\theta_{2} \,} \right)} \right]} \right\} \hfill \\ \end{gathered} \right.$$
(13)
According to Lyapunov stability theory, a sufficient necessary condition for the game system to achieve ESS is that all eigenvalues of the Jacobian matrix have negative real parts. That is, the system stable state in the Jacobian matrix should satisfy the determinant \(detJ = \lambda_{1} \lambda_{2} > 0\) and trace \(trJ = \lambda_{1} + \lambda_{2} < 0\) (λ1 and λ2 are the two eigenvalues of the Jacobian matrix). Because of the instability of the mixed strategy point in the evolution process&#;the trace \(trJ = 0\) of (q*, p*), only the local stability of the remaining four equilibrium points as pure strategy points in the Jacobian matrix is considered. By substituting the equilibrium point into the Jacobian matrix, the eigenvalue of each equilibrium point can be obtained and summarized in Table 3.
Table 3 Stability analysis of the equilibrium points.Full size table
In order to facilitate the subsequent analysis, the equation is simplified in this paper,
$$\left\{ \begin{gathered} K = \left( {1 - \theta_{2} } \right)S_{1} + \theta_{2} w \hfill \\ L = \left( {1 - \theta_{1} } \right)S_{1} - G + \theta_{1} w \hfill \\ M = R_{1} - R_{2} - C_{1} + C_{2} + D\left( {\theta_{2} - \theta_{1} } \right) \hfill \\ N = R_{1} - R_{2} - C_{1} + C_{2} + G + \left( {D + w} \right)\left( {\theta_{2} - \theta_{1} } \right) \hfill \\ \end{gathered} \right.$$
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(14)
Since \(\left( {1 - \theta_{2} } \right)S_{1} - \theta_{2} S_{2} + \theta_{2} w > - \theta_{2} S_{2}\), which is K&#;>&#;0, it can be judged that E1 (0,0) must not be a stable point of the evolution system. Based on the four situations shown in Table 3, there are three parameter relationships satisfying \(detJ > 0\) and \(trJ < 0\).
Condition I: When N&#;<&#;0, it is known that M&#;<&#;0. Both sides of the game evolve to (1,0) under this condition, that is, the government chooses the incentive strategy and the assembled steel plant chooses the traditional plant strategy.
Condition II: When L&#;<&#;0, M&#;>&#;0, N&#;>&#;0, (0,1) is the only stable point of the system. At this time, the government chooses the no incentive strategy and the assembled steel plants choose the smart plant strategy.
Condition III: When L&#;>&#;0, N&#;>&#;0, (1,1) is the only stable point of the system. Under this condition, the government chooses the incentive strategy, and the assembled steel plants chooses the smart plant strategy.
Specifically, the stability analysis results corresponding to the three parameter relationships are shown in Table 4.
Table 4 Stability analysis under different conditions.Full size table
Based on the above stabilization strategies and conditions, the following conclusions can be drawn:
&#;The government's subsidy policy is an important initiative to promote the manufacturing industry to achieve intelligent transformation and help traditional factories to move towards smart production. &#;Regardless of whether or not the government sets up incentive strategies, plants will participate in smart production as long as the net benefits derived by assembled steel plants choosing smart plants are greater than those generated by the traditional model. In short, investors seek advantage and avoid disadvantage. Therefore, for the government, reasonable subsidy incentives can satisfy the revenue needs of assembled steel plants and help stimulate investors' participation. In addition, the setting of negative penalty mechanism is conducive to enhancing the safety awareness of steel plants, thus eliminating opportunistic behavior in the cooperation process.
Numerical simulation is helpful to directly reflect the results of theoretical research and can continuously and dynamically show the development rule of things. Therefore, numerical simulation is often used as a supplementary argument to game analysis. In order to test the effectiveness of the theoretical game model, this part is based on MATLAB to carry out numerical simulation analysis of the Fuzhou X Steel Structure Plant project. The first part of this section describes the case background of the Fuzhou X Steel Structure Plant project, and sets the parameters corresponding to the model. The second part obtains the dynamic evolution process of the decision-making behavior of each stakeholder in the initial state of the project through MATLAB simulation. The third part carries out numerical simulation on the sensitivity of the relevant parameter changes (including costs, subsidies, etc.) of the project participants in the initial state to provide case reference for the government to actively promote the intelligent transformation of the manufacturing industry and enhance the internal upgrading power of enterprises.
According to the policy of Fuzhou, assembled construction bidding requires one bid and one component plant. Therefore, the steel plant will seize the opportunity of the policy dividend "window". With the first-mover advantage of the steel structure production base and the "EPC&#;+&#;industrialization" bidding policy, Company X has vigorously expanded the steel structure assembly EPC business and realized the accelerated growth of the marketing contract amount.
The X Steel Structure Plant project is located in the suburb of Fuzhou City, Fujian Province, about 45 km away from the urban area of Fuzhou. The transportation is convenient, and the plant can be reached through the highway G70 or the national highway G316. The project covers Putian, Ningde, Nanping, Sanming, Quanzhou, Pingtan Comprehensive Experimental Zone and other central cities in Fujian Province. The project covers a land area of about 88 mu, and two steel structure production lines (heavy steel line and light steel line) are operated at the same time, with an annual capacity of 25,000 tons. The total project investment is about 49,956,700 yuan, with payback period of 7.38 years (including 1-year construction period) and internal rate of return of 11.52%. The capital contribution of Company X is in the form of fixed assets such as land after evaluation and Company Y is in cash. After the project is put into operation, both parties will share the dividends according to their respective equity ratios. In order to lead the development of the steel structure green ecological industry in Haixi region, the project is positioned as an industrial base of steel structure assembled building integrating research and development, design, production, manufacturing, sales and construction. The GS-Building and ME-House assembled steel structure building product systems with independent intellectual property rights of Y Company are introduced, forming a complete integrated solution. Through the project feasibility study report and relevant policy data, this paper makes theoretical assignments to the relevant parameters, which are detailed in Table 5.
Table 5 Initial parameter values of the evolutionary game model.Full size table
According to the initial parameter value setting of the evolutionary game model in Table 5, the parameters of the project are obtained to satisfy \(\left( {1 - \theta_{1} } \right)S_{1} - G + \theta_{1} w < 0\), \(R_{1} - R_{2} - C_{1} + C_{2} + G + \left( {D + w} \right)\left( {\theta_{2} - \theta_{1} } \right) < 0\). Based on MATLAB Ra, 81 different groups of (q,p) initial strategy points can be randomly generated to test the stability of the equilibrium point E4 (1,1) in the game process. The lines with different colors in Fig. 1 represent the evolution process of 81 groups of different initial strategic points randomly produced by MATLAB in the game between the two sides. As shown in Fig. 3, as the evolution time grows, after continuous iteration, the strategies of both parties will converge to (1,1). At this time, the ESS of the government and assembled steel plants is {incentive, assembled steel smart plant}. The simulation process illustrates that the initial strategy choosing states of both sides of the game do not affect the evolutionary outcome when the constraints are satisfied. With sufficient evolutionary time, the final behavioral strategies of each stakeholder will gradually evolve into optimal solutions. Thus, the theoretical analysis in the previous section is effectively tested, while providing a basis for the initial state setting of the subsequent sensitivity analysis.
Figure 3Evolutionary results of 81 times satisfying the E4 condition.
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Sensitivity analysis, as a quantitative analysis method, aims to observe the change of the target through the adjustment of factors, so as to find out the rules. Based on the parameter setting of the case, the initial strategy of both sides of the game can be set as (q0, p0)&#;=&#;(0.5, 0.5). This part will simulate and analyze the relevant influencing factors in turn.
Firstly, numerical simulation is carried out for the policy subsidy limit G, the penalty limit w for safety accidents and the improvement of government credibility S1.
Subsidy G under the government incentive strategy is set as 5, 10, and 15, respectively. Based on the two-dimensional dynamical system, the results are shown in Fig. 4. The government's punishment w for safety accidents is set at 10, 30, 60, and the simulation results under the two-dimensional system are shown in Fig. 5. In Fig. 4, it is shown that when G&#;=&#;15, p evolves fastest toward 1, while q evolves slowest toward 1. This suggests that a reasonable subsidy setup can, to some extent, facilitate a win&#;win situation&#;satisfying both the revenue needs of the assembled steel plant as an investor and the government's smooth promotion of smart manufacturing initiatives. In addition, Fig. 4 also shows that excessive subsidies can cause financial burden on government departments, which leads to the tendency of disincentive. From Fig. 5, it is clear that increased government punishment for safety accidents will enhance the speed of evolution to the stability point for both sides of the game. Strict punishment mechanism is the key to promote the healthy development of smart manufacturing.
Figure 4Effect of parameter G change.
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Figure 5Effect of parameter w change.
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Then, in order to analyze the impact of the improvement of government credibility on the evolution process and results, this paper will assign values of 20, 10, and 2, respectively. The simulation results of replication dynamic equations evolving over time are shown in Fig. 6. At this point, S1 in the steady state should satisfy \(S_{1} > \frac{{G - \theta_{1} w}}{{1 - \theta_{1} }}\), that is, when ESS is (1,1), S1&#;>&#;4.44 (4.44 is the critical value meeting the stability conditions of (1,1), which is calculated based on the above Eq. (14) and Table 5 parameters. At this critical value, the government behaves as a horizontal line and is in a mixed strategy state. However, the change of initial value can break this state and make it evolve to pure strategy.). From Fig. 6, it can be seen that as S1 decreases, the probability of government incentives becomes lower. When S1&#;<&#;4.44, the evolutionary stable state of both sides of the game will become (0,1). As can be seen, when the project background changes, the evolutionary stability state of both sides of the game changes accordingly. Therefore, the government's incentive strategy should also be flexible to adjust with changes in project benefits, costs, safety governance capacity, and other conditions.
Figure 6Effect of parameter S1 change.
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In order to explore the evolution of the behavioral decisions of the game subjects in the smart production model, this section conducts numerical simulations of the project's cost C1, benefit R1, the probability of a safety accident in the smart plant θ1 and the accident loss D.
Assign the values of C1 as C1&#;=&#;., ., ., and the results are shown in Fig. 7. Assign the values of R1 as R1&#;=&#;.304, .718, .339, and the results are shown in Fig. 8. From Fig. 7, it can be seen that with the increase of the cost of assembled steel smart plant, q will evolve in the direction of 1, while p will evolve in the direction of 0. At this time, the critical value condition of C1 is \(C_{1} = R_{1} - R_{2} + C_{2} + G + \left( {D + w} \right)\left( {\theta_{2} - \theta_{1} } \right)\), that is, C1&#;=&#;.46. This system stability state changes from (1,1) to (1,0) when the parameter change is greater than .46. Figure 8 shows that the considerable benefits of the assembled steel smart plant project are the key to attracting assembled steel manufacturers to invest in it. Based on this condition, R1 satisfies \(R_{1} > C_{1} + R_{2} - C_{2} - G - \left( {D + w} \right)\left( {\theta_{2} - \theta_{1} } \right)\), i.e., the critical value of R1 is .8. When R1 changes less than .8, the system steady state (1,1) will change to (1,0).
Figure 7Effect of parameter C1 change.
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Figure 8Effect of parameter R1 change.
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Next, the accident probability and the amount of loss generated by the accident are analyzed. Set θ1&#;=&#;0.1, 0.25, 0.5 and the simulation results of replication dynamic equations evolution over time as shown in Fig. 9. Set D&#;=&#;20, 60, 100 and the simulation results of replication dynamic equations evolution over time as shown in Fig. 10. Figure 9 shows that with the increase of θ1, the mood of the government to set incentives becomes stronger, and the assembled steel plant will prefer the traditional production mode. When \(\theta_{1} > \frac{{R_{1} - R_{2} - C_{1} + C_{2} + G}}{D + w} + \theta_{2}\), i.e., θ1&#;>&#;0., the assembled steel plant will change the original strategy. Figure 10 shows that as the loss amount D increases, the assembled steel plant prefers to choose the smart production option.
Figure 9Effect of parameter θ1 change.
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Figure 10Effect of parameter D change.
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