A Novel Improved Grey Incidence Model for Evaluating the Performance of Supply Chain Resilience

Under uncertain conditions, stronger supply chain resilience can efectively reduce disruption risks and help enterprises achieve their goal of high-quality operations. Tis paper constructs a resilience evaluation index system for manufacturing enterprises from the perspective of the supply chain and uses the improved TOPSIS method to quantify the level of resilience. Taking into account that the resilience index is easily afected by nonconventional factors in the real environment, the WAWBO weakening bufer operator and the metabolism idea are introduced to improve the grey prediction method, so as to realize the dynamic prediction of the resilience index. In addition, a supply chain resilience early warning model is constructed by combining it with the quantifcation method of resilience. Using the data of a Chinese electronics manufacturing enterprise as a case study, the results demonstrate the efectiveness of the proposed resilience quantifcation method, and the improved grey prediction method has higher prediction accuracy. Te study provides a new idea for relevant enterprises to improve the early warning ability of their supply chain, thus promoting the sustainable development of the supply chain.


Introduction
With supply chains (SCs) spanning multiple countries, businesses have enjoyed cost advantages and access to rapidly growing markets.However, managing these complex networks has exposed frms to increase risks of disruptions.Te interconnection between global partners can cause disruptions to quickly spread and interrupt the supply chain.As disruptions become more frequent, experts suggest that supply chain resilience (hereafter SCR) capabilities should be developed [1].Resilience enables supply chains to be event-ready and respond efciently and efectively to recover from disruptions.Traditional risk management strategies are inadequate for the current highly dynamic environment.Terefore, frms should adopt a resilient orientation to mitigate disruptions amidst increasing uncertainties and associated challenges.
Resilience is defned as the adaptive capability of a system to respond better to disruptions or even gain advantages from such events [2].It is the property by which a supply chain can reduce, react to, and overcome potential risks and vulnerabilities.A resilient supply chain can quickly adapt to changes in demand, supply, and market conditions, allowing enterprises to respond to new opportunities, optimize their operations, and improve their competitiveness [3].Hence, a strong SCR can assist manufacturing companies in achieving robust operational performance and sustainable growth in unpredictable environments [4].
Existing literature suggests that certain attributes, known as enablers, are crucial for enhancing SCR and have a positive impact on the risk mitigation environment.Tese enablers include visibility, robustness, agility, fexibility, collaboration, organizational culture, innovation, and top management commitment [5][6][7].Tey have been shown to improve fnancial performance, situational awareness, quick response, adaptability, and recovery during disruptions.Quantitative assessments of resilience using enablers and their interdependencies are useful tools for managers to measure, manage, and control SC resilience [8,9].Employable quantitative measures of resilience are advantageous in computing the quality of SC resilience to mitigate disruptive events and provide a method for benchmarking and comparing resilience capabilities with other SCs.
In parallel, existing studies have well documented that the resilience level of a manufacturing enterprise supply chain can be measured by multiattribute decision-making (MADM) methods [10,11].Multiattribute decision-making (MADM) methods are a set of techniques used to evaluate and rank alternatives based on multiple criteria or attributes.Tese methods are commonly used in decision-making contexts where there are multiple, conficting objectives or criteria that must be considered.Tere are many diferent MADM methods, including weighted sum models, analytic hierarchy process (AHP), ELECTRE, PROMETHEE, and TOPSIS.For example, Pournader et al. [12] established a supply chain risk resilience evaluation framework by combining the fuzzy set theory and data envelopment analysis (DEA).Lotf et al. [13] utilized an improved fuzzy comprehensive evaluation method to assess the resilience of the healthcare supply chain.Te technique for order preference by similarity to an ideal solution (TOPSIS) method is widely employed as an efective approach in multiobjective decision analysis.It is not restricted by sample size or indicators, making it suitable for comprehensive evaluations across diverse scenarios.Ama et al. [14] proposed a fuzzy multiobjective programming model for green resilience and combined fuzzy AHP and TOPSIS methods to evaluate the resilience of the supply network.Menon and Ravi [15] employ a combined AHP-TOPSIS multiple criteria decisionmaking approach to consider the uncertainty involved in evaluating both quantitative and qualitative data and conclude that economic factors still dominate during sustainable supplier selection.
In an uncertain environment, SCR is not long-term stable, and through early warning signals, enterprises can timely make strategic adjustments to reduce the possibility of interruption.However, conventional quantitative analysis methods make it difcult to achieve accurate prediction in an uncertain environment.Moreover, enterprise resilience indicators are signifcantly impacted by recent data, and the grey system theory ofers higher accuracy in predicting uncertain information with a small database.Grey system theory is a mathematical framework for modeling and analyzing systems with incomplete or uncertain information.Te basic idea behind grey system theory is to use a small amount of available information to make predictions and decisions.In this way, the grey system theory provides a useful tool for dealing with problems that cannot be modeled using traditional mathematical methods.By incorporating both known and unknown information into the analysis, grey system theory can help researchers and practitioners make more informed decisions in complex and uncertain environments [16].
Te limitations of current research on SCR mainly lie in the following two aspects.First, most existing research regards resilience as a constant value, ignoring the characteristic of resilience fuctuating with time from a microperspective.Second, there is a lack of analysis of the evolution of resilience in manufacturing enterprises from the perspective of the supply chain and the use of scientifc methods to predict the resilience level for early warning.To address these concerns, this study selects resilience evaluation indicators from three perspectives of responsiveness, adaptability, and recovery according to the characteristics of manufacturing enterprise supply chains and quantifes the resilience level of the supply chain with the TOPSIS method.In the resilience warning model, the idea of weakening bufer operators and metabolism is introduced into the grey prediction method, and a resilience warning model of manufacturing enterprise supply chains is constructed.Te weakening bufer operators can efectively weaken the impact disturbance of the system and restore the original appearance of the system, and the advantage of the metabolism model for grey prediction is its ability to provide accurate forecasts even when there is limited data available, making it a useful tool for decision-making [17].Finally, a case study is conducted based on the data of an electronic manufacturing enterprise from 2020 to 2022 to provide implications for related manufacturing enterprises to achieve the goal of high-quality management.
Te rest of this paper is laid out as: Section 2 introduces the SCR evaluation index system.Section 3 establishes the SCR warning model.Section 4 provides a case study using the method proposed, while the last section concludes the paper.

SCR Evaluation Index System
Te extant literature on the evaluation of enterprise resilience is multifaceted, including collaboration, visibility, security redundancy, market position, partnership, etc. [18][19][20].For manufacturing enterprises, SCR is essential for their high-quality and sustainable development.Terefore, this study aims to uncover the factors afecting the level of resilience from the following aspects, namely, response ability, adaptation ability, and recovery ability.Tese three dimensions correspond to the pre-, in-, and postevent stages of the uncertain event, respectively.
(1) Response Capability.Response capability stresses the supply chain's capacity to respond quickly to unknown risks by promptly sensing changes in the external environment in the purchasing, production, and delivery processes.Te ability to respond quickly to changes in market demand or supply is crucial for supply chain response capability, and it is closely related to agility and collaboration.Enterprises need to be agile in order to efectively respond to uncertain risks, while collaboration is essential for achieving this goal.According to [21], agility can be proxied by two subindicators: delivery lead time and order response speed.Collaboration capability emphasizes the importance of reducing uncertain risks and enhancing service levels through the sharing of information and the use of technology among partners who work together.When collaboration capability is low, it suggests that the production and delivery capabilities of cooperating enterprises may not meet the necessary requirements, or that the organizational management of these enterprises may not be able to keep up with the demands of enterprise operations.In line with [22,23], we select information sharing, on-time delivery of materials, and material qualifcation rate as the three subindicators corresponding to the collaboration factor.(2) Adaptation Capability.Adaptation capability emphasizes the maximum bearing capacity of the supply chain to maintain normal operation under external disturbances, including two indicators: fexibility and safety redundancy.Supply chain fexibility refers to the capacity to swiftly adapt operational plans in response to emergencies, taking into account demand and environmental conditions.Te subindicators that make up fexibility include capacity utilization and regional warehouse fnished product inventory, according to [24,25].Te safety redundancy index refects the ability of enterprises to reduce interruption risks by strategically using excess reserve resources to improve the response to unexpected risks.Te subindicators that make up safety redundancy at the third level include fnished goods inventory and key material inventory [26] Drawing from the analysis above, we have identifed the SCR indicators for manufacturing enterprises and have developed a corresponding evaluation index system, which is presented in Table 1.Furthermore, when selecting resilience indicators, it is important to consider factors such as data availability and data analysis usability.Tis ensures that the chosen indicators not only accurately refect the SCR of enterprises, but also allow for predictions based on indicator data collected at diferent times.

SCR Warning Model
3.1.Fuzzy Analytical Hierarchy Process.When the number of indicators is large, the traditional AHP method is more likely to cause consistency problems in subjective weighting.Terefore, a stream of studies has extended the AHP method to fuzzy conditions and presented the fuzzy analytic hierarchy process (FAHP) to construct a fuzzy consistency judgment matrix [29].Te FAHP procedure is an efective way to address the issue of inconsistency among experts when determining weightings.Tis helps to ensure that weight distribution is more reasonable and accurate.According to Chamoli [30], the typical FAHP model mainly includes the following four steps: set up the hierarchical structure model, establish the fuzzy complementary judgment matrix, solve the weight of fuzzy complementary judgment matrix, and test the consistency.
3.2.TOPSIS Method.TOPSIS (technique for order preference by similarity to an ideal solution) method proposed by Hwang and Yoon is a commonly used efective method in multiobjective decision analysis, also known as the superiority-inferiority distance method [31].Tis method is an ordering method that approximates an ideal solution.Te method only requires each utility function to have monotonically increasing (or decreasing) properties.Te TOPSIS method involves quantifying evaluation objects by measuring the Euclidean distance between each solution and the positive/negative ideal solution.Te determination of the positive/negative ideal solution is typically based on the optimal and worst values of each indicator.However, in realworld enterprise environments, resilience indicators may not always reach the ideal state.To address this issue, we have improved the model by manually setting the optimal and worst values.Tis allows the model to better refect the current SCR levels of enterprises.Te improved TOPSIS method can be described as follows.
To begin with, the optimal and worst solution sets for the indicators need to be determined based on industry standards and expert opinions, respectively, denoted as A � [y + 1 , y + 2 , . . ., y + j ] and B � [y − 1 , y − 2 , . . ., y − j ], j � 1, 2, . . ., n, where for the negative indicator j, the optimal solution y + j should not be larger than y − j .Second, normalize matrix P m×n (p ij ) to obtain the feature matrix N m×n (n ij ), where p ij denotes the value of index j for enterprise at time i: Tird, the weighted feature matrix V m×n (v ij ) can be calculated by V m×n � N m×n × W m×n , where W m×n is the index weight matrix obtained through the fuzzy analytic hierarchy process (FAHP).
Fourth, compute the Euclidean distance between each index, and we can obtain the positive and negative ideal solutions as follows: where V + j and V − j denote the maximum and minimum values of each column of the feature matrix V m×n , respectively.
Lastly, score the indicators at the time i by , where c i ∈ [0, 1], the higher c i is, the stronger the resilience at time i is.

Improve Grey Prediction Method.
From a macro perspective, enterprise supply chains tend to remain fairly stable in terms of resilience.However, when we zoom in and examine things on a smaller scale, SCR can be more susceptible to fuctuations caused by unconventional factors.Furthermore, traditional prediction methods like neural networks, which heavily rely on historical data to forecast future states, are unable to provide accurate predictions for enterprise resilience due to the relatively minor impact of historical data on future states.In comparison, the grey prediction method allows the modeller to predict future states of SCR with limited grey information under the circumstance of information uncertainty and a relatively small sample set.
Te enterprise resilience index is usually subject to interference from uncertain factors, which often results in faster or slower evolution trends.However, the grey prediction method has low accuracy for predicting nonsmooth sequences.Hence, by incorporating a weakened bufer operator to adjust the original sequence, it becomes feasible to predict the random fuctuation patterns of the sequence, thereby signifcantly enhancing the prediction accuracy.Te improved grey prediction method can be described as follows: Step 1: Given a time series X � (x (0) (1), x (0) (2), . . ., x (0) (n)) of the resilience index r, where x (0) (i) > 0(i � 1, 2, . . ., n), r represents the resilience index to be predicted, and n represents the number of prediction samples.Te ratio σ(k) is calculated to determine whether the sequence data can be used for grey prediction, where σ(k) � x (0) (k − 1)/x (0) (k), k � 1, 2, . . ., n.If σ(k) ∈ (e − (2/(n+1)) , e 2/(n+1) ), the ratio test is passed.
Step 2: If the original sequence does not pass the ratio test, the weighted average weakness bufering operator (WAWBO) D is introduced to modify the raw database.
Estimate the parameters of the equation using the least squares method, then, the parameters a and μ to be estimated satisfy  u � (a, μ) T � (B T B) − 1 B T M. Solve the parameter, take x (1) (0) � x (0) (1), we can obtain the time response sequence of the grey diferential equation as follows: x (1) To obtain the fnal prediction result, perform a cumulative subtraction reduction on the acquired sequence: Step 4: Metabolic grey prediction.Te conventional grey prediction method is based upon the historical static data before t time for prediction.However, under realistic conditions, with the continuous addition of new grey information into the prediction system, the amount of information contained in the longer data is less, so the use of grey theory for prediction will cause the accumulation of errors.Te metabolic grey prediction model can dynamically incorporate real-time information into the grey prediction, enabling dynamic sequence prediction and reducing prediction errors efectively.
To predict the original data with a quantity of n, a metabolic grey prediction model needs to select the data of time t to predict the data of time t + 1.By dropping the oldest data x (0) (1) and adding the new data x (0) (t + 1), an updated model is obtained, and then Step 3 is repeated to obtain a metabolic renewal.By continuously updating the data sequence to predict the data at t + 1 time, a new prediction sequence is established.When t + 1 � n, the predicted data x (0) (n + 1) can be added to the original sequence and using the available information, the subsequent data can be predicted to determine the developmental trend of the data.Tis can help enterprises adjust their strategies in a timely manner.
Step 5: Testing the model prediction error.Since the model requires multiple iterations, the mean absolute percentage error (MAPE) model is chosen for testing its efectiveness.
where n is the number of predicted samples, and x i and  x i are the real value and the predicted value of the SCR index at time i.

SCR Early Warning Model.
Based on the resilience evaluation index system, the fuzzy hierarchical analysis method is used to determine the weight of the index, and the improved TOPSIS method is performed to accurately quantify the resilience level of the supply chain.To timely perceive the change in SCR, we propose an improved grey prediction model to forecast the resilience features in the future time and combine it with the resilience quantifcation method to analyze the dynamic of enterprise SCR.Tis can assist decision-makers in making timely supply chain strategy adjustments, thereby mitigating the risk of disruptions.In addition, through the feedback on the implementation results of the supply chain strategy, it also helps decision-makers realize the dynamic optimization process of the supply chain.Te process of the manufacturing enterprise SCR early warning framework is illustrated in Figure 1.

Case Study
Tis study takes a Chinese electronics manufacturing company as a case to verify the efectiveness of the proposed early warning model.Tis company is a worldwide leader in security product manufacturing, but has faced challenges due to the rapidly changing external environment, including international supply chain disruptions and the COVID-19 crisis.To tackle this issue, the company requires an early warning mechanism for SCR that can monitor and forecast changes in real-time and support decision-makers in adapting operations as needed.
Trough interviews with supply chain directors, we discovered that data on resilience indicators was available.We then selected a representative product line and collected data on 13 resilience indicators from 30 monthly time nodes.We replaced some indicators with relevant ones and determined optimal and worst solutions for each index based on industry expertise.Te data was then preprocessed through normalization.

Measure for SCR.
For the sake of simplicity, only twolevel hierarchy structure consisting of dimensions and second-level indicators is considered here due to the complexity of the three-level structure.According to the scoring method of the fve-level method, an expert questionnaire is designed to compare the importance of each indicator.Ten, the weights of each indicator are calculated using the FAHP method, as shown in Table 2.
Ten, the resilience distribution of the enterprises from 2020 to 2022 is obtained by using the improved TOPSIS method, as illustrated in Figure 2.
As illustrated in Figure 2, the SCR of the considered enterprise is relatively strong, with the resilience distribution ranging from 0.45 to 0.70 in 2020-2022, and the majority of the time nodes having resilience levels higher than 0.5.However, the enterprise's SCR performance is relatively weak, with approximately one-third of the total sample falling within the 0.55-0.60range across multiple time nodes.Tis may be attributed to the combined pressures of domestic and foreign environmental factors during the past two years and the impact of uncertain factors, which highlights the need for further improvements in enterprise resilience.

Grey Prediction.
Since some fexibility indicators are relatively stable over a certain period of time, we focus on predictive indicators that are easily afected by external factors and forecast the fexibility indicators for the next three months based on two years of historical data.Te selection of fexibility features and some raw data are shown in Table 3.
After preliminary analysis of the data sequence, it suggests that the database is a nonsmooth sequence and the range of data change is large, resulting in the failure of the model to pass the class-compare verifcation.However, we are able to successfully address this issue by introducing the weakened bufer operator to modify the original data sequence.Subsequently, we employed three diferent traditional GM (1, 1), WAWBO with bufer operator GM (1, 1), and improved GM (1, 1) based on metabolism to predict the related resilience indicators.Te metabolism cycle t is set to 6 months, and the accuracy of the model is tested by the mean absolute percentage error (MAPE).Te specifc results are shown in Table 4.
According to Table 4, the prediction accuracy of the grey prediction method can be greatly improved by using the WAWBO weakening bufer operator to modify the raw database.We fnd that the prediction results of the modifed grey prediction model were signifcantly lower than those of the traditional grey prediction method in terms of mean absolute error, from 24.11% to 4.13%.Furthermore, the implementation of the metabolism method can eliminate the impact of long-term data on prediction results and lead to improved prediction performance.

Evolution of SCR.
Using the improved grey model discussed earlier, we predicted the resilience indicators for the period from October 2022 to December 2022 and quantifed the future enterprise SCR.Tis enables us to track the evolution of enterprise SCR since January 2020, as depicted in Figure 3.  demonstrated in Figure 3, the SCR of the enterprise has been unstable due to factors such as international product competition and economic conditions, resulting in signifcant variations in resilience at certain points.We particularly notice that the SCR of the enterprise reaches its lowest point in August 2021, due to the infuence of the government demand side of the security industry.Despite the short-term sharp fuctuations, the main trend of the SCR of the enterprise has been rising, reaching a new high in March 2022.Tis highlights the fact that decision-makers can efectively enhance the enterprise's ability to deal with uncertain risks by making operational strategy adjustments aimed at improving the resilience level.
It also suggests that the resilience of the enterprise has been on a downward trend since March 2022.Tis can be mainly attributed to the international further policy sanctions that businesses were facing at that time as well as the impacts of the COVID-19 pandemic on the supply chain on both the supply and sales sides.However, with the relatively stable epidemic situation in China since June 2022, the release of government demand accelerated, while the enterprise also adjusted its supply chain strategy, gradually increasing the resilience of the enterprise supply chain since July.Terefore, this paper explores the evolution trend of resilience from the three dimensions of reaction ability, adaptation ability, and recovery ability, as shown in Figure 4.
Since March 2022, the rapid decline in responsiveness has led to a gradual decrease in SCR, however, with the rapid recovery of responsiveness since July, the level of resilience has improved signifcantly.Tis appearance indicates that responsiveness is the main reason for the variation in SCR.In addition, it suggests that the performance of adaptability is relatively stable.At the start of 2021, the enterprise signifcantly improved its adaptability by adjusting its inventory strategy to mitigate supply chain risk through high inventory levels, as depicted in the adaptability curve in Figure 4.By comparing the recovery curves in Figures 3 and  4, we can observe that when the enterprise's resilience begins to decline, the recovery level is typically higher, indicating that recovery capability plays a crucial role after a risky event has occurred.
Although the resilience level of the supply chain is gradually increasing in the next three months, the overall resilience performance is not strong enough.Terefore, enterprises still need to maintain a high level of crisis awareness, retain high responsiveness through improving supply chain strategies, such as improving order processing speed and improving supplier quality.Besides, measures such as inventory adjustment and the risk response plan should be taken to enhance the adaptive capacity and recovery capacity of the supply chain, so as to further enhance the resilience level of the supply chain of the enterprise.Te prediction results and strategy recommendations above were validated through subsequent visits to the enterprise.During the most recent visit on September 26, 2022, the supply chain director provided feedback that the company is currently experiencing a decrease in response speed on both the demand and supply side due to measures taken for epidemic prevention and control, as well as changes in the international business environment.However, the enterprise is actively making strategic adjustments to address these challenges.Tis feedback further confrmed the practicality and feasibility of the study.

Conclusion
Te resilience theory provides a valuable complement to traditional risk management, allowing enterprises to proactively identify potential supply chain risks.Tis study has quantitatively calculated enterprise SCR by establishing an evaluation indicator system for manufacturing enterprises.Unlike prior studies, this research evaluates SCR and predicts future enterprise resilience based on historical data, while analyzing the time-varying of resilience level across multiple dimensions.By establishing an early warning model for manufacturing enterprises' SCR, changes in resilience and their causes can be identifed in real-time, providing decisionmakers with a basis for adjusting operational strategies promptly to improve their capacity to react to market condition changes and avoid the risk of disruption.
We conducted a case study based on actual data from a Chinese electronic manufacturing company and found that this method achieved excellent results in practical applications.Te analysis indicates that the company's supply chain resilience was severely afected during the COVID-19 pandemic and urgently needs improvement.Further analysis also shows that the FAHP-TOPSIS method proposed in this paper can efectively measure and evaluate supply chain resilience.Moreover, our method can handle data fuctuations better, making it suitable for predicting resilience indicator data.In summary, this study expands the application of grey forecasting models in the feld of supply chain resilience (SCR) and proposes solutions for SCR early warning, prevention, and response.

Table 1 :
Manufacturing enterprise SCR evaluation index system.

Table 3 :
Raw data for resilience indicators.

Table 4 :
Comparison of prediction errors among diferent models.