Fuzzy-FMEA Theory Approach for Prioritizing Supply Chain Nervousness Factors

Abstract

Global supply chain shocks and interruptions underscore the importance of supply chain nervousness (SCN). A clear understanding of nervousness in the event of a crisis allows an organization to make a good plan to deal with interruptions and future shocks. This study aims to develop a model for assessing nervousness parameters in the supply chains (SCs) by incorporating the fuzzy-FMEA theory and gray correlation approach to rank the SCN factors. The integrated model used in this study can improve the accuracy of outcomes when uncertainty exists in the SCN data. The results show that the most important nervousness factors are SC planning, visibility, stability, decision support systems, and SC flexibility. The developed SCN approach allows understanding and prioritizing SCN factors with more realistic and effective assessment. Findings offer beneficial insights for SCN prevention, and suggestions are made to identify nervousness mitigations. The outcomes of this research can be used by researchers and SC specialists to develop decision support systems.

1. Introduction

Supply chain nervousness (SCN) refers to the potential for events that negatively impact SC decisions, efficiency, and performance. Mitigating and eliminating nervousness will continue to be a major challenge in achieving long-term SC excellence. In today’s business environment, factors such as instability, uncertainty, complexity, and vagueness are significant sources of nervousness. Nervousness can arise from every activity or decision made within or along the SC. The SC’s stability is heavily dependent on nervousness management through applying proper actions and strategies.

The COVID-19 pandemic has altered business practices for the coming years, and continued development is essential for future crisis preparedness. Decision inputs, solutions, and evaluation tools are all required for continuous improvement. Making decisions necessitates revisiting global SC strategy, understanding the demand effect specific to the company, and enlisting the help of SC professionals. To preserve the stability of SCs, it is necessary to improve decision-making skills, take on analytical capabilities, as well as comprehend costs, restrictions, and business capabilities.

With SCN, making decisions is a complicated process that plays a significant role in promoting a sustainable SC. In this research, SCN is evaluated using an integrated fuzzy-FMEA–gray correlation technique. SCs confront threats such as natural disasters and government inconsistency. As a result, failure mode and effects analysis (FMEA) is used to assess SCN. In addition, a case study of a SC business demonstrates the efficacy and applicability of the proposed approach. Businesses and manufacturing industries can benefit from the current method. The proposed approach not only increases performance but also reduces the amount of nervousness imposed on long-term viability.

Existing research on SCN focuses more on two areas: MRP nervousness and the nervousness associated with schedule and planning systems in production planning; this research is often considered from a single dimension, like costs, planning processes, prediction errors, inventory management, or strategies. This, however, does not provide enough information to make proper decisions in this complex environment. The number of research papers focusing on SCN in recent years is small. Consequently, research articles published with the keywords “nervousness” and “SC” “MRP”, “demand”, “planning”, “and scheduling” are explored.

Table 1. Sample of SCN-related work.

Reference	Problem Addressed	Methodology
[1]	MRP nervousness	Order-up-to (OUT) policy and the proportional OUT policy (POUT).
[2]	Assessing internal nervousness in semiconductors SC planning system	Simulation-based analysis
[3]	Demand supply network nervousness	Experiential study
[4]	Evaluating the relationships between the different determinants of schedule nervousness	Statistical analysis
[5]	Studying the relationship between nervousness and the bullwhip effect	Vendor managed inventory (VMI) approach
[6]	Reducing demand nervousness	Mathematical modeling
[7]	System nervousness cost	Mathematical modeling
[8]	Exploring causes and effects of SCN in the MENA region	Delphi-based AHP
[9]	Identifying combinations of factors linked to GSCN	Delphi-FAHP
[10]	Examining setups added to production scheduling nervousness and costs	Wagner–Whitin algorithm
[11]	Scheduling stability and forecast errors	Simulation experiment
[12]	Reducing MRP system nervousness	Modified Wagner–Whitin algorithm
[13]	MRP nervousness	Simulation modeling
[14]	Investigating alternative strategies dealing with nervousness	Simulation experiments
[15]	Order nervousness	Simulation modeling
[16]	Lot-sizing rules and MRP nervousness	Simulation modeling
[17]	Nervousness in manufacturing firms	Simulation modeling
[18]	MRP nervousness	Simulation modeling
[19]	Cost-performance of the MRP system and forecast errors	Simulation modeling
[20]	Classifying nervousness-dampening procedures and their relative effectiveness	Static dampening procedure
[21]	Studying the schedule nervousness increased by uncertainty in the demand forecast	Empirical transfer function estimate (ETFE)
[22]	Reducing frequent revisions of the schedule, which leads to scheduling nervousness	Resource–task network (RTN)
[23]	Comparing the effectiveness of the planning policy for reducing demand uncertainty	Mixed-integer linear programming (MILP)
[24]	Quantifying nervousness in scheduling nervousness based on field observations	Mathematical modeling and analytical hierarchy process (AHP)
[25]	Nervousness in MRP systems under uncertainty	Simulation modeling
[26]	Quantify nervousness in stochastic inventory control demand	Rolling horizon planning procedure
[27]	Examining solutions for overcoming master production schedule nervousness	Simulation model
[28]	Exploring undesirable effects of nervousness master production scheduling	Simulation and mixed-integer programming model
[29]	Addressing the implications of the statistical findings compared to simulated MRP environments	Simulation model
[30]	Considering the economic effect of the production schedule caused by nervousness	Wagner–Whitin method
[31]	Stochastic lot sizing nervousness problem	Mixed-integer programming
[32]	Unveiling SCN and presenting a strategic framework for disruption management under a fuzzy environment	Fuzzy-DEMATEL
[33]	SCN analysis	Fuzzy-ELECTRE
[9]	Introduction of global supply chain nervousness (GSCN)	Delphi–fuzzy-AHP

displays the key literature articles that meet the search criteria.

To fulfill the needs of researchers and SC managers, this paper provides the basis for assessing several types of nervousness through an integrated framework addressing potential interruptions of logistics and SC systems. There are three novelties in this paper. First, SC-related nervousness elements are identified from the perspective of the entire SC. This includes multiple aspects such as interruptions, faults, and errors because of risks, uncertainties, vulnerabilities, and SC disruptions. Second, this study examines and considers more nervousness parameters. This will help better understand and model the SCN. Third, an integrated method is developed to effectively address the several types of uncertainty that exist in the SCN assessment. A joint fuzzy-FMEA–gray correlation method is used to incorporate an effective approach to nervousness assessment.

The remainder of this paper is arranged as follows: Section 2 reviews the relevant literature and highlights research gaps. Section 3 presents the research methodology. A case study is presented in Section 4 with results and discussion. Section 5 presents the conclusions.

2. Literature Review

SCs relate to many risks that can affect their profitability. The high-level risks include political nervousness, disasters, and pandemics like COVID-19 [34]. Companies are striving to cope with risks, deal with unforeseen disruptions, and increase performance in an increasingly uncertain commercial environment. Operational performance of SCs can be improved through SC integration, risk management, and information processing [35]. To deal with various risk levels, advanced strategies for sustainable risk management are essential, especially for large companies [36]. Depending on SC risk factors, aspects of integration, flexibility, and coordination can improve resilience [37].

Previous research studies used different methodologies to study SC risks; a method was introduced to manage SC risks and uncertainties by combining simulation and optimization methods to assist decision-makers find the best risk reduction strategies [38]; other researchers have analyzed the relationship between uncertainty in a company’s business environment, vulnerability to SC risks, and conditions that can mitigate such risks [39]. Organizations with high environmental uncertainty are at increased risk in terms of supply disruptions [39].

Nervousness decreases the efficiency, stability, and resilience of SC performance with potential increases in cost and unstable relationships with suppliers and customers [8]. As partners recurrently change the scheduling and size of replenishments, replenishment decisions are modified based on stochastic requirements leading to system nervousness [7]. MRP nervousness refers to the extreme fluctuations sometimes seen in future order forecasts given to suppliers [1]. Recurrent variations in production schedules, known as “nervousness”, can be very confusing, especially when implementing MRP systems. This also leads to accelerated, postponed, or canceled orders, thus affecting both the internal system and the operation of the supplier, further impacting the SC’s performance in terms of operating costs, quality control, addressing SC partners, operational flexibility, and competitiveness in the global market [4].

As globalization progresses, SC systems that require powerful planning systems are becoming more complex. The plan should consider the whole SC. This might cause nervousness and customer dissatisfaction due to multiple uncertainties in the entire SC. External causes of SC planning system nervousness and instability have been previously discussed. Internal nervousness in planning complex networks within SCs results from interactions among the planning system’s subcomponents [2]. Nervousness in the planning process increases fluctuations in supply network and demand [3]. For instance, scheduling nervousness is a major issue for manufacturers [4]. Although changing production schedules is common in order to fulfill customer demands and maintain a certain level of service, it causes nervousness and costs to rise [6].

Even though there is little research on nervousness throughout SCs, some researchers have studied SCNs from different perspectives. For example, researchers explored SCN in the MENA region using the Delphi–analytic hierarchy process (AHP) [8]. The global SCN (GSCN) sources, impact, measurements, and solutions were investigated. A framework was proposed to discuss SCN and solutions [9]. Another study developed a nervous scale that geometrically weighs future prediction errors over time; they found that short-term prediction errors have higher weights than remote prediction errors [1]. The inner nervousness of demand fulfillment was investigated [2]. The results highlight the importance of maintaining transparency regarding the internal interactions between SC networks to reduce instability. The effects of batch size, buffer stock, backorder, production capacity, and variations in the initial order in a two-echelon SC system were considered when analyzing SCNs [6]. Two kinds of nervousness—facility-based and crowd-based—were studied [7]. Nervousness cost was calculated using the inventory–management–strategy, considering static, dynamic, and static–dynamic uncertainties.

Supply and demand uncertainties are mainly due to SC interruptions. SC interruptions from unexpected events caused great economic losses. Any increase in the probability of interruption will increase business interruption and, hence, the value of insurance [40]. An interruption is a failure or change in all or part of the SC over a specific period when wholesaler and warehouse products are not enough to meet demand and are not able to deliver the product to the store at a certain time. It is essential to utilize a strategy for resilience measures for SC operations in the interrupted environment with a quantitative indicator for assessing SC resilience [41]. In the event of a long-term supply interruption, SC resilience is reduced, and the greater the demand shock, the longer the supply interruption. There are potential causes of supply interruptions, such as changes in geopolitics around the world and natural disasters. The risk of interruption is directly affected by the supply of raw constituents [42].

An interruption experienced by a node’s location can move to another node in the SC. To improve enterprise performance, proper coordination between various layers and cross-chains is recommended to deal with various nodes’ interruptions [43]. The risk of distribution in closed SC is discussed from material flow and other perspectives [44,45]. If the demand in the market is uncertain, the manufacturer’s interruption of downstream supply is a disaster for the enterprise. Using fuzzy programming to model SC interruptions, the option of selecting from multiple manufacturing centers can effectively decrease SC costs and sustain business continuity [45].

Failure mode and effects analysis (FMEA) is a structured prophylactic and multipurpose analytical method that can be used in a variety of industries, in which a team of outsourced personnel can experience potential errors, defects, and problems within a system. Then, the relative impacts are analyzed and prioritized to decide what action to take to eliminate these faults [46,47]. To evaluate the risk level in the maritime SC, a superior model is proposed based on fuzzy Bayesian networks and FMEA [48]. Risks associated with green SCs are also assessed through a fuzzy-FMEA approach [49]. On the other hand, FMEA is used to identify, analyze, and assess product deletion risk in the SC and propose its impact on managing risk in dynamic industry scenarios. FMEA is utilized to identify, analyze, and assess product deletion risk in the SC and suggest its impact on managing risks in dynamic business scenarios [50]. The MOORA-FMEA-based model is proposed for selecting sustainable suppliers with insights into volume discounts, disasters, and governmental changes [51]. FMEA and fuzzy-VIKOR are used to explore risks in the food grain SC and suggest risk mitigation classifications to support decision-making [52]. The FMEA technique is employed to effectively analyze the security of gas station SC systems [53]. A comparative study of risk management strategies was conducted by incorporating FMEA with the hybrid AHP-PROMETHEE procedure to assess suppliers in an SC risk-based environment [54]. Firms can mitigate SC risks through proper utilization of FMEA in supplier selection [55]. Moreover, the integrated multi-criteria analysis–Saaty method joined with FMEA is proposed to identify and evaluate the related logistics chain constraints [56].

The gray theory involves using known and unknown information. A gray theory is suitable for assessing SC risks as it can correctly and effectively define and monitor performance and the laws of evolution [57]. The weighting technique and gray theory are effective methods for SC risk assessment [41]. By combining the fuzzy theory and gray theory, it is possible to calculate the degree of correlation of each vulnerability index and improve the target of SC vulnerability [58].

The fuzzy arithmetic operation approach provides an acceptable fuzzy spread for analyzing fuzzy interconnection. Using this method, decision-makers usually want to accurately estimate uncertain influencing aspects in uncertain environments [59]. The fuzzy-AHP method is proposed to determine the local and global weights to evaluate alternatives [60]. The fuzzy-AFDEMATEL model is constructed to deal with potential fuzziness that exists in sustainable SC management (SCM) systems [61]. A fuzzy-based model is offered for SC design and network resilience evaluation and analysis [59]. An integrated model composed of fuzzy-DEMATEL and ANP is proposed to prioritize food SC performance measures [62].

Given the cost and quality of SC, the crisis requires rapid decision-making in complex and vague environments [63]. Companies should improve the decision-making process and assist SC managers in choosing solutions depending on their significance and effect on business. SCs need to continue to use technology to withstand future risks and interruptions [64], consider the SC vulnerable and vulnerability drivers [65], and secure supply in crises like the COVID-19 pandemic situation [66].

To fill the gap in previous studies, this research first explores the SCN parameters and then proposes the integrated fuzzy-FMEA–gray correlation approach to rank the SCN-related factors based on their impact and priorities. This can be attained by the inclusion of important SC system nervousness parameters. The suggested nervousness assessment methodology consistently processes diverse types of information from multiple sources, whether it is quantitative or qualitative, to address nervousness input uncertainties. It can offer accurate results while maintaining a certain level of easiness and acceptable operation simplicity.

3. Research Methodology

Multiple elements affect SCN and these elements can be interrelated. Therefore, there is a need for a systematic methodology to evaluate nervousness given the inherent complexities. The FMEA method is a widely used technique in industries because of its effectiveness in the assessments of safety and reliability. FMEA, the gray correlative approach, as well as fuzzy theory, can be integrated to assess, prioritize, and rank SCN parameters [58]. The proposed method has ten main components as shown in Figure 1.

Interruption modes and risk priority numbers (RPNs) are determined using FMEA to identify nervousness priority. Such priority values are derived through expert judgments, which may be prone to biases, resulting in an inaccuracy in the SCN assessment process. Fuzzy logic is integrated into traditional FMEA in this study to solve the problem of assigning risk (nervousness) priority numbers.

3.1. Assessment of SCN

SCN is affected by threats like the COVID-19 pandemic, trade war, terrorism activities, partners’ bankruptcy, and suppliers’ capability. The COVID-19 pandemic reveals the nervousness of global SCs. Efficiency is the main driver of SCs with little focus on nervousness understanding and mitigations. SC is studied and analyzed in terms of errors and failures using the reviewed literature and collected surveys. This is to identify interruptions, errors, and faults that could lead to nervousness in the SC. A total of eleven experts with experience in SC participated in SCN assessment. They identify SCN’s main strategies (main factors) as follows: planning, visibility, stability, decision support systems (DSS), and flexibility.

Table 2. Valuation index and interruption of mean analysis.

Level I Elements	Level II Elements	Interruption Mode
Planning (P)	Demand (P1)	P1I1: Reduced satisfaction
		P1I2: Excess inventory
	Supply (P2)	P2I1: Increased disruptions
		P2I2: Governmental interventions
	Risk (P3)	P3I1: Increased vulnerability
		P3I2: Raise of safety and security issues
Visibility (V)	Collaboration (V1)	V1I1: Less transparency
		V1I2: Competitiveness among partners
	Integration (V2)	V2I1: Lack of consistent decision-making
		V2I2: Lack of trust and willingness
	Communication (V3)	V3I1: Shortages/lack of exchange information
		V3I2: Low employees confidence
Stability (S)	Policies (S1)	S1I1: Lack of prioritization
		S1I2: Design change
	Disaster recovery (S2)	S2I1: Mismatch between supply and demand
		S2I2: Long recovery time
	Stable roles and regulations (S3)	S3I1: Difficulties of regulatory compliance
		S3I2: Changes in government policies
DSS (D)	Expertise (D1)	D1I1: Variations in skills
		D1I2: Scarcity of special competencies
	Powerful tools (D2)	D2I1: Selecting the right tool
		D2I2: Criteria, process mapping, and flow problems
	Technology (D3)	D3I1: Technological constraints (implementation)
		D3I2: Digital transformation (SC transformation)
Flexibility (F)	Awareness (L1)	L1I1: Lack of trends and situational awareness
		L1I2: Deficiencies in traceable and sustainable awareness
	Resilience (L2)	L2I1: Lack of resistance, recovery, and redundancy systems (plans)
		L2I2: Unexpected changes (external changes)
	Innovation (L3)	L3I1: Slow reaction to modern innovations
		L3I2: Adoption of significant changes

shows the three layers of decomposition and the SCN evaluation index.

3.2. SCN Model

The integrated fuzzy-FMEA–gray correlation approach is used to rank the SCN factors based on their impacts and priorities. The proposed integrated FMEA model described in [58,67] is applied in this study to analyze the nervousness modes estimation as follows:

Step 1: Forming a rating index system. Based on Table 2, the following sets are defined:

$$\begin{gathered} \mathrm{Set} \mathrm{of} \mathrm{the} \mathrm{level} \mathrm{I} \mathrm{elements}: l=\left\{P, V, S, D, F\right\}, \\ \mathrm{Set} \mathrm{of} \mathrm{the} \mathrm{level} \mathrm{II} \mathrm{elements}: \\ {l}_i=\left\{P_1, P_2, P_3,V_1, V_2, V_3,S_1, S_2, S_3,D_1, D_2, D_3,F_1, F_2, F_3\right\} \forall i=1,2,3 \\ \mathrm{Set} \mathrm{of} \mathrm{the} \mathrm{level} \mathrm{III} \mathrm{elements}: l_i{I}_j=\left\{P_1{I}_1, \cdots , L_3{I}_2\right\} \forall i=1,2,3 \& j=1,2. \end{gathered}$$

Step 2: Defining the evaluation sets as shown in

Table 3. The corresponding denotation of semantic elements.

Semantic Element	Severity (Se)	Occurrence (Oc)	Detection (De)
EU	SC is not affected	Interruptions barely occur	Almost all interruptions are detected
VU	SC is slightly affected	Interruptions infrequently/rarely occur	The probability that an error is not recognized is low
UL	Some SC processes are slightly affected, but the flows work appropriately	Interruptions occur less	The probability that a fault will not be detected is quite low
NE	The flows fairly work, but some important processes are affected as long as there is no unsatisfied customer	Interruptions occur occasionally/intermittently	The error is not recognized infrequently
LK	The flows fairly work, but some important processes are seriously affected, and some customers are not satisfied	Interruptions occur often/in moderate amounts	Not being recognized is a common occurrence
VL	The process and flows have problems and have lost their basic functions	Interruptions occur recurrently	Most of the time, errors cannot be recognized
EL	SC operations completely lose their basic functions and endanger personal safety or violate laws	Interruptions are almost unpredictable	Errors are almost undetectable

. The evaluation is based on seven semantic items: extremely unlikely (EU), very unlikely (VU), unlikely (UL), neutral (NE), likely (LK), very likely (VL), and extremely likely (EL). The experts give fuzzy scores for the semantic elements. Then, each interruption failure mode is given a semantic value for each measure of severity (Se), occurrence (Oc), and detection (De).

Let $u=\left\{EU, VL, UL, NE, LK, VL, EL\right\}$ be the set of the semantic elements and $k_e^u=\left(a_e^u, b_e^u, c_e^u\right)$ be the triangular fuzzy evaluation of the semantic value $u$ given by expert $e$. Then, $k^u=\left(a^u,b^u, c^u\right)$ represent the weighted fuzzy evaluations on semantic value $u$. $k^u$ can be obtained by means of the following equations:

$$\begin{gathered} a^u={\sum }_{e=1}^n{\rho }_e{a}_e^u, b^u={\sum }_{e=1}^n{\rho }_e{b}_e^u, c^u={\sum }_{e=1}^n{\rho }_e{c}_e^u, \\ {\sum }_{e=1}^n{\rho }_e=1, 0\le {\rho }_e\le 1, \mathrm{for} \mathrm{each} u=\left\{EU, VL, UL, NE, LK, VL, EL\right\}, \end{gathered}$$

where ${\rho }_e$ is a weight given to reflect the importance of evaluation made by expert $e, e=1,\cdots , n$.

The following formula [68] is used for the defuzzification process to obtain the clear number or the crisp value $H\left(k_e^u\right)$ of semantic element $u$:

$$H\left(k^u\right)=\frac{a^u}{2\left(1+N\right)}+\frac{\left(N+2NM+M\right)b^u}{2\left(1+N\right)\left(1+M\right)}+\frac{c^u}{2\left(1+M\right)} ,$$

(1)

where $N$ and $M$ are numbers identified based on the triangular fuzzy values $a^u$, $b^u$, and $c^u$, such that $N$ and $M$ indicate how large $b^u$ is relative to $a^u$ and $c^u$, respectively.

Step 3: Forming the FMEA and level of nervousness. The weights of the elements of levels I, II, and III (interruption modes), denoted by ${\phi }^l$, ${\phi }^{l_i}$, ${\phi }^{l_i{I}_j}$, respectively, are calculated as the average values, such that we have the following:

$${\phi }^l=\frac{1}{n}{\displaystyle \sum }_{e=1}^n{\phi }_e^l, {\phi }^{l_i}=\frac{1}{n}{\displaystyle \sum }_{e=1}^n{\phi }_e^{l_i}, {\phi }^{l_i{I}_j}=\frac{1}{n}{\displaystyle \sum }_{e=1}^n{\phi }_e^{l_i{I}_j},$$

where ${\phi }_e^l$, ${\phi }_e^{l_i}$, and ${\phi }_e^{l_i{I}_j}$ are the weights given by expert $e,e=1,\cdots , n$, on elements of sets $l$, $l_i$, and $l_i{I}_j$, respectively.

The above weights are used to calculate the RPN’s coefficient of each interruption failure mode, ${\mathsf{\lambda }}_{l_i{I}_j}$, as follows:

$${\mathsf{\lambda }}_{l_i{I}_j}={\phi }^l{\phi }^{l_i}{\phi }^{l_i{I}_j}.$$

Then the RPN number of each failure mode, ${\mathrm{RPN}}_{l_i{I}_j}$, can be represented as a weighted RPN, as follows:

$${\mathrm{RPN}}_{l_i{I}_j}={\mathsf{\lambda }}_{l_i{I}_j}\times {\mathrm{Se}}_{l_i{I}_j}\times {\mathrm{Oc}}_{l_i{I}_j}\times {\mathrm{De}}_{l_i{I}_j},$$

where ${\mathrm{Se}}_{l_i{I}_j}$, ${\mathrm{Oc}}_{l_i{I}_j}$, and ${\mathrm{De}}_{l_i{I}_j}$ are the average crisp values of Se, Oc, and De, respectively, given for failure mode $l_i{I}_j$. Se, Oc, and De for each failure mode is assessed by each expert using one of the semantic elements. Then, the average of all assessments, i.e., the average crisp values, are used to calculate the values of ${\mathrm{Se}}_{l_i{I}_j}$, ${\mathrm{Oc}}_{l_i{I}_j}$, and ${\mathrm{De}}_{l_i{I}_j}$.

Step 4: Calculating the gray correlations and ranking. Define $F$ and $F_0$ as the comparison and reference matrices, respectively. In $F$ matrix, the evaluations of Se, Oc, and De are listed with the corresponding interruption failure mode. These evaluations are benchmarked to the corresponding ratings in the reference matrix $F_0$. Usually, the elements of $F_0$ should be either the best or the worst ratings, i.e., UL or EL. In this study, EL is used as the benchmark.

Let $Y=F-F_0$ be the difference matrix, such that

$$Y_{z\times t}=F-F_0=\left[\begin{array}{ccc}{\mathrm{Se}}_{l_1{I}_1}& {\mathrm{Oc}}_{l_1{I}_1}& {\mathrm{De}}_{l_1{I}_1}\\ ⋮& ⋮& ⋮\\ {\mathrm{Se}}_{l_i{I}_j}& {\mathrm{Oc}}_{l_i{I}_j}& {\mathrm{De}}_{l_i{I}_j}\\ ⋮& ⋮& ⋮\end{array}\right]-\left[\begin{array}{ccc}EL& EL& EL\\ ⋮& ⋮& ⋮\\ EL& EL& EL\\ ⋮& ⋮& ⋮\end{array}\right],$$

(2)

where $z$ and $t$ denote the number of rows and columns, respectively, in the matrix $Y$. Therefore $z$ is equal to the number of interruption failure modes, and $t=1, 2, \mathrm{and} 3$ represent the columns of Se, Oc, and De, respectively. The gray correlation coefficients correspond to matrix $F$ are calculated using the following equation:

$${\omega }_{l_i{I}_j,t}=\frac{{\min }_t\left|Y_{l_i{I}_j}\right|+\upsilon · {\max }_t\left|Y_{l_i{I}_j}\right|}{\left|Y_{l_i{I}_j}\right|+\upsilon · {\max }_t\left|Y_{l_i{I}_j}\right|} \mathrm{for} t=1,2,3,$$

(3)

where ${\omega }_{l_i{I}_j, t=1}$, ${\omega }_{l_i{I}_j, t=2}$, and ${\omega }_{l_i{I}_j, t=3}$ are the gray correlation coefficients of Se, Oc, and De of failure mode $l_i{I}_j$, respectively. $\upsilon \in \left(0, 1\right)$ is and usually equals to 0.5.

Considering the influences of Se, Oc, De, the degree of correlation of each failure mode,${\gamma }_{l_i{I}_j}$, is calculated using the following equation [69]:

$${\gamma }_{l_i{I}_j}={\displaystyle \sum }_{t=1}^3{Ƚ}_t{\omega }_{l_i{I}_j,t},$$

(4)

where $\sum _{t=1}^3{Ƚ}_{l_i{I}_j,t}=1$, and ${Ƚ}_{l_i{I}_j,1}$, ${Ƚ}_{l_i{I}_j,2}$, and ${Ƚ}_{l_i{I}_j,3}$ are the importance weights of ${\mathrm{Se}}_{l_i{I}_j}$, ${\mathrm{Oc}}_{l_i{I}_j}$, and ${\mathrm{De}}_{l_i{I}_j}$ of failure mode $l_i{I}_j$, respectively.

The last step is to rank the interruption failure modes based on their correlation grades. The degree of correlation (or correlation grade) of each interruption mode, ${\mu }_{l_i{I}_j}$, can be calculated as follows:

$${\mu }_{l_i{I}_j}={\mathsf{\lambda }}_{l_i{I}_j}\times {\gamma }_{l_i{I}_j}$$

(5)

Also, elements of levels I and II in Table 2 can be ranked based on their correlation grades as follows:

$${\mu }_{l_i}=\sum {\mu }_{l_i{I}_j} \mathrm{for} \mathrm{each} l_i, {\mu }_l=\sum {\mu }_{l_i} \mathrm{for} \mathrm{each} l,$$

where ${\mu }_{l_i}$ and ${\mu }_l$ are the correlation grades that correspond to each element in sets $l_i$ and $l$, respectively.

4. Illustrative Application of the SCN Model

Recently, organizations have started to pay greater attention to the nervousness of the SC because of the impact of disruptions and crises like COVID-19. As a result of the complication in the SCs, an integrated FMEA approach is used to evaluate the SCN. Due to the difficulties of obtaining accurate elements, the semantic variables are utilized to score the interruption modes. The FMEA evaluation team, called the expert team, consists of eleven multifunctional evaluation members, and is mainly asked for scoring and evaluation. The expert team comprises industry, academic, and SC specialists, who are aware of SC disruptions, interruptions, fears, and risks. The expert team should score the weights of each factor between 0 and 1. The total weights of the elements in a process must equal one. For instance, the sum of weights of P, V, S, D, and F must equal one; the total weights of V1, V2, and V3 must also equal one, as should the sum of the weights of V1I1 and V1I2. Furthermore, the total weights of related severity, occurrence, and detection for each level III element must equal one.

Each expert can select one of the seven semantic levels, EU, VU, UL, NE, LK, VL, and EL for the three items Se, Oc, and De. Due to the diverse experiences and different backgrounds of the experts, their importance and skills are also dissimilar. For these reasons, an important weight ${\rho }_e$ is given as follows to each expert: 0.15, 0.14, 0.11, 0.097, 0.089, 0.086, 0.078, 0.077, 0.066, 0.059, and 0.048. To check the effectiveness of the construction index and the scoring results, the experts’ team is asked to re-evaluate and approve the scoring results after summarizing their results.

To establish a rating index system, a thorough initial evaluation with a total of 30 factors from the third layer and 15 factors from the second layer are selected. The expert team receives questionnaires to determine the most important variables. After that, the experts summarize a series of nervousness rating index systems for SCs. The index system is then presented to the same team for model validation. The final most suitable index system for the SCN is shown in Table 2.

Then, the fuzzy evaluation set is established to obtain clear numbers of the corresponding fuzzy semantic elements. The experts’ team evaluates the fuzzy decision of each interruption type.

Table 4. TFN expert scores for semantic evaluation.

Expert	${\mathit{\rho }}_{\mathit{e}}$	EU	VU	UL	NE	LK	VL	EL
1	0.15	(0, 1.1, 2.7)	(0.9, 2.5, 3.6)	(2.9, 4.6, 6.4)	(3.1, 5.6, 7.4)	(5.8, 7.5, 8.7)	(7.1, 8.9, 9.8)	(9.6, 10, 10)
2	0.14	(0, 1.3, 2.8)	(0.7, 2.4, 3.9)	(2.8, 4.5, 6.3)	(3.4, 5.8, 7.8)	(6.1, 7.1, 8.3)	(7.7, 8.8, 9.9)	(9.4, 10, 10)
3	0.11	(0, 1.2, 2.8)	(0.6, 2.3, 3.2)	(3.1, 4.5, 6.3)	(3.6, 5.9, 7.9)	(5.7, 7.8, 8.7)	(8.3, 8.9, 9.7)	(9.3, 10, 10)
4	0.097	(0, 1.4, 2.4)	(0.8, 2.6, 3.5)	(2.7, 4.7, 6.6)	(3.2, 6.2, 7.6)	(5.4, 7.9, 8.2)	(8.2, 8.7, 9.9)	(9.4, 10, 10)
5	0.089	(0, 1.5, 2.3)	(0.7, 2.7, 3.7)	(2.9, 4.2, 6.2)	(3.9, 6.3, 8.1)	(5.8, 8.1, 9.1)	(7.9, 9.1, 9.8)	(9.5, 10, 10)
6	0.086	(0, 1.7, 3.1)	(0.7, 2.8, 3.6)	(2.5, 5.2, 6.7)	(3.1, 5.7, 8.3)	(6.3, 6.9, 7.8)	(7.7, 9.3, 9.9)	(9.6, 10, 10)
7	0.078	(0, 2.1, 2.2)	(0.9, 2.5, 3.8)	(2.4, 4.1, 6.6)	(3.2, 5.4, 7.5)	(4.8, 7.6, 8.6)	(7.4, 8.6, 9.7)	(9.7, 10, 10)
8	0.077	(0, 1.3, 2.7)	(1.1, 3.1, 4.2)	(2.6, 4.5, 7.1)	(3.3, 5.3, 7.8)	(6.5, 7.8, 8.7)	(8.4, 9.1, 9.8)	(9.7, 10, 10)
9	0.066	(0, 1.2, 2.8)	(0.8, 2.4, 3.3)	(2.5, 4.7, 6.1)	(4.1, 5.6, 7.9)	(6.6, 7.7, 8.5)	(7.5, 8.7, 9.9)	(9.8, 10, 10)
10	0.059	(0, 1.1, 2.6)	(0.8, 2.3, 3.4)	(2.5, 4.1, 6.2)	(3.4, 5.8, 7.6)	(6.4, 7.9, 8.8)	(7.6, 8.8, 9.9)	(9.9, 10, 10)
11	0.048	(0, 1.4, 2.5)	(1.2, 2.1, 3.5)	(2.6, 4.6, 6.3)	(3.5, 5.7, 7.7)	(6.8, 7.6, 8.6)	(7.8, 8.9, 9.9)	(9.8, 10, 10)
Total/Average	1.00	(0, 1.4, 2.6)	(0.8, 2.5, 3.6)	(2.7, 4.5, 6.4)	(3.4, 5.8, 7.8)	(5.9, 7.6, 8.5)	(7.8, 8.9, 9.8)	(9.6, 10, 10)

lists the expert ratings based on triangular fuzzy numbers (TFNs).

Using Equation (1) and the values given in Table 4, the weighted crisp values can be computed from fuzzy semantics, as shown in

Table 5. Crisp values of the semantic items.

Evaluation Rate	EU	VU	UL	NE	LK	VL	EL
Crisp value	1.34	2.37	4.56	5.68	7.42	8.84	9.89

.

Next, the FEMA and the weighting tables are prepared. Furthermore, the FEMA classifications and weights for all SCN levels are listed. A sample of calculations of Se evaluations for interruption failure modes of factor P is illustrated in

Table 6. Experts’ Se scoring for failure modes of factor P.

Factor/Expert	Se											Avg.
	1	2	3	4	5	6	7	8	9	10	11
P1I1	EL	NE	VL	LK	EL	VU	LK	VL	EL	NE	VL	7.7
	9.9	5.7	8.8	7.4	9.9	2.4	7.4	8.8	9.9	5.7	8.8
P1I2	VL	NE	LK	VL	VL	NE	UL	VL	UL	LK	NE	6.9
	8.8	5.7	7.4	8.8	8.8	5.7	4.6	8.8	4.6	7.4	5.7
P2I1	VL	EL	VL	LK	EL	LK	VL	VL	LK	EL	NE	8.4
	8.8	9.9	8.8	7.4	9.9	7.4	8.8	8.8	7.4	9.9	5.7
P2I2	EL	VL	LK	UL	VU	NE	VL	LK	VL	EL	VL	7.4
	9.9	8.8	7.4	4.6	2.4	5.7	8.8	7.4	8.8	9.9	7.4
P3I1	VL	EL	VL	UL	NE	NE	UL	LK	NE	UL	VL	6.7
	8.8	9.9	8.8	4.6	5.7	5.7	4.6	7.4	5.7	4.6	7.4
P3I2	NE	LK	LK	NE	EU	VU	UL	VU	VL	NE	UL	5.1
	5.7	7.4	7.4	5.7	1.3	2.4	4.6	2.4	8.8	5.7	4.6

, whereas

Table 7. Sets of weights of SCN’s model.

Level I Factors	${\mathit{\phi }}^{\mathit{l}}$	Level II Factors	${\mathit{\phi }}^{{\mathit{l}}_{\mathit{i}}}$	Failure Mode	${\mathit{\phi }}^{{\mathit{l}}_{\mathit{i}}{\mathit{I}}_{\mathit{j}}}$	Se Weight Ƚ1%	Oc Weight Ƚ2%	De Weight Ƚ3%	${\mathbf{\lambda }}_{{\mathit{l}}_{\mathit{i}}{\mathit{I}}_{\mathit{j}}}$
P	28%	P1	40%	P1I1	61%	51%	12%	37%	0.068
				P1I2	39%	44%	21%	35%	0.044
		P2	38%	P2I1	68%	53%	11%	36%	0.072
				P2I2	32%	54%	8%	38%	0.034
		P2	22%	P3I1	72%	52%	27%	23%	0.044
				P3I2	28%	38%	29%	33%	0.017
V	24%	V1	54%	V1I1	66%	65%	7%	28%	0.086
				V1I2	34%	43%	31%	26%	0.044
		V2	30%	V2I1	52%	38%	42%	20%	0.037
				V2I2	48%	32%	34%	34%	0.035
		V3	16%	V3I1	49%	56%	9%	35%	0.019
				V3I2	51%	39%	8%	53%	0.020
S	21%	S1	35%	S1I1	53%	40%	11%	49%	0.039
				S1I2	47%	41%	14%	45%	0.035
		S2	33%	S2I1	78%	56%	26%	18%	0.054
				S2I2	22%	34%	21%	45%	0.015
		S3	32%	S3I1	36%	47%	15%	48%	0.024
				S3I2	64%	58%	7%	35%	0.043
D	17%	D1	40%	D1I1	57%	39%	35%	26%	0.039
				D1I2	43%	29%	18%	53%	0.029
		D2	28%	D2I1	59%	31%	22%	47%	0.028
				D2I2	41%	59%	29%	22%	0.020
		D3	32%	D3I1	33%	42%	23%	35%	0.018
				D3I2	67%	57%	27%	16%	0.036
F	10%	L1	19%	L1I1	55%	41%	16%	43%	0.010
				L1I2	45%	38%	15%	47%	0.009
		L2	46%	L2I1	51%	58%	22%	20%	0.023
				L2I2	49%	62%	10%	28%	0.023
		L3	35%	L3I1	53%	58%	7%	35%	0.019
				L3I2	47%	59%	15%	26%	0.016

displays the weights of the SCN model’s elements.

In

Table 8. Comparison matrix elements.

Element	${\mathit{\phi }}^{{\mathit{l}}_{\mathit{i}}{\mathit{I}}_{\mathit{j}}}$	Ƚ1%	$\mathbf{S}{\mathbf{e}}_{{\mathit{l}}_{\mathit{i}}{\mathit{I}}_{\mathit{j}}}$	Ƚ2%	$\mathbf{O}{\mathbf{c}}_{{\mathit{l}}_{\mathit{i}}{\mathit{I}}_{\mathit{j}}}$	Ƚ3%	$\mathbf{D}{\mathbf{e}}_{{\mathit{l}}_{\mathit{i}}{\mathit{I}}_{\mathit{j}}}$	${\mathbf{\lambda }}_{{\mathit{l}}_{\mathit{i}}{\mathit{I}}_{\mathit{j}}}$
P1I1	61%	51%	7.7	12%	6.1	37%	7.4	0.068
P1I2	39%	44%	6.9	21%	5.3	35%	6.8	0.044
P2I1	68%	53%	8.4	11%	7.2	36%	7.2	0.072
P2I2	32%	54%	7.4	8%	4.2	38%	8.1	0.034
P3I1	72%	52%	6.7	27%	5.5	23%	6.5	0.044
P3I2	28%	38%	5.1	29%	4.2	33%	7.4	0.017
V1I1	66%	65%	8.6	7%	7.1	28%	6.8	0.086
V1I2	34%	43%	6.2	31%	6.2	26%	6.6	0.044
V2I1	52%	38%	7.2	42%	8.4	20%	5.8	0.037
V2I2	48%	32%	6.1	34%	6.8	34%	7.8	0.035
V3I1	49%	56%	8.9	9%	2.8	35%	7.6	0.019
V3I2	51%	39%	6.3	8%	2.6	53%	8.6	0.020
S1I1	53%	40%	8.4	11%	3.4	49%	8.4	0.039
S1I2	47%	41%	5.2	14%	4.4	45%	8.1	0.035
S2I1	78%	56%	7.4	26%	5.4	18%	4.6	0.054
S2I2	22%	34%	6.4	21%	4.8	45%	4.4	0.015
S3I1	36%	47%	8.9	15%	3.6	48%	5.1	0.024
S3I2	64%	58%	5.1	7%	2.6	35%	6.8	0.043
D1I1	57%	39%	7.5	35%	6.6	26%	5.8	0.039
D1I2	43%	29%	6.8	18%	4.8	53%	8.2	0.029
D2I1	59%	31%	8.2	22%	5.2	47%	7.8	0.028
D2I2	41%	59%	5.6	29%	6.4	22%	5.1	0.020
D3I1	33%	42%	7.6	23%	5.3	35%	6.6	0.018
D3I2	67%	57%	6.8	27%	6.1	16%	4.4	0.036
L1I1	55%	41%	8.8	16%	4.8	43%	7.4	0.010
L1I2	45%	38%	6.2	15%	4.2	47%	7.8	0.009
L2I1	51%	58%	8.2	22%	5.2	20%	5.1	0.023
L2I2	49%	62%	6.2	10%	2.8	28%	6.2	0.023
L3I1	53%	58%	7.4	7%	2.6	35%	6.4	0.019
L3I2	47%	59%	5.1	15%	3.4	26%	6.2	0.016

, the crisp values of Se, Oc, and De of each failure mode are listed. These values are used for constructing the comparison matrix in order to calculate the gray correlation coefficients of each failure mode, ${\omega }_{l_i{I}_j, t}$. Based on the calculated values of ${\omega }_{l_i{I}_j, t}$ and the values of ${\mathsf{\lambda }}_{l_i{I}_j}$, ranking the level I, II, and III factors are determined based on the computed gray correlation grades ${\mu }_{l_i{I}_j}$, ${\mu }_{l_i}$, and ${\mu }_l$, as displayed in

Table 9. Nervousness element ranking based on the FMEA–gray correlation approach.

${\mathit{l}}_{\mathit{i}}{\mathit{I}}_{\mathit{j}}$	${\mathbf{\lambda }}_{{\mathit{l}}_{\mathit{i}}{\mathit{I}}_{\mathit{j}}}$	${\mathit{\mu }}_{{\mathit{l}}_{\mathit{i}}{\mathit{I}}_{\mathit{j}}}$	Rank	${\mathit{l}}_{\mathit{i}}$	${\mathit{\phi }}^{{\mathit{l}}_{\mathit{i}}}$	${\mathit{\mu }}_{{\mathit{l}}_{\mathit{i}}}$	Rank	$\mathit{l}$	${\mathit{\phi }}^{\mathit{l}}$	${\mathit{\mu }}_{\mathit{l}}$	Rank
P1F1	0.068	0.0177	3	P1	0.4	0.0286	2	P	0.28	0.0707	1
P1F2	0.044	0.0109	6
P2F1	0.072	0.0198	2	P2	0.38	0.0286	3
P2F2	0.034	0.0088	12
P3F1	0.044	0.01	9	P3	0.22	0.0135	10
P3F2	0.017	0.0035	26
V1F1	0.086	0.023	1	V1	0.54	0.0331	1	V	0.24	0.062	2
V1F2	0.044	0.0101	8
V2F1	0.037	0.0105	7	V2	0.3	0.0185	5
V2F2	0.035	0.008	15
V3F1	0.019	0.0052	21	V3	0.16	0.0104	13
V3F2	0.02	0.0052	20
S1F1	0.039	0.0111	5	S1	0.35	0.0192	4	S	0.21	0.049	3
S1F2	0.035	0.0081	14
S2F1	0.054	0.0116	4	S2	0.33	0.0144	8
S2F2	0.015	0.0028	29
S3F1	0.024	0.0063	18	S3	0.32	0.0154	7
S3F2	0.043	0.0091	11
D1F1	0.039	0.0095	10	D1	0.4	0.0171	6	D	0.17	0.0412	4
D1F2	0.029	0.0076	16
D2F1	0.028	0.0072	17	D2	0.28	0.0113	11
D2F2	0.02	0.0041	23
D3F1	0.018	0.0041	24	D3	0.32	0.0128	9
D3F2	0.036	0.0087	13
L1F1	0.01	0.0029	28	L1	0.19	0.005	15	L	0.1	0.0233	5
L1F2	0.009	0.0021	30
L2F1	0.023	0.0057	19	L2	0.46	0.0105	12
L2F2	0.023	0.0048	21
L3F1	0.019	0.0046	22	L3	0.35	0.0078	14
L3F2	0.016	0.0032	27

.

Discussion

As shown in Table 9, the ranks of the five main elements are SC planning, visibility, stability, DSSs, and SC flexibility. The nervousness of SC is mainly reflected in three aspects: SC’s future planning, stability of the sources and destinations, and the availability of the right DSS. The risk of planning is the highest; therefore, SC managers should pay great attention to supply, demand, and risk planning. Planning is the main strategy that helps mitigate the impact of SCN. The most important interruptions in demand include low satisfaction and oversupply of inventories, while the main interruptions to the supply are increased disruption and government intervention, but the basic nervousness factors for interruptions are increased vulnerability and the occurrence of security issues. The second source element rank is SC visibility. Cooperation with SC partners, integration at all levels, and communication with employees within the chain are considered to be the most important visibility strategies that can undermine SCN. The most important interruptions in cooperation include reduced transparency and increased competitiveness of partners. However, the main sources of turmoil in SC integration are the lack of consistent decision-making, trust, and motivation. Instead, the lack of information exchange and low employee trust are the basic causes of communication interruptions.

SC stability, as it is ranked third, is one of the key policies to mitigate SCN through appropriate disaster recovery policies, plans, systems, and government support, as well as stable roles and regulations. Major policy interruptions include a lack of product and process prioritization and design changes. While the main disruptions in SC disaster recovery are supply and demand discrepancies and long recovery times, regulatory compliance issues and government policy changes are the most important causes of unstable aspects and disruptors of regulations. The fourth rank goes to the SC’s DSS. One of the key strategies for dealing with SCN is the use of DSSs, especially with the development of technology and information systems. The success of DSS depends on technical-expertise capabilities and availability, powerful tools that fit the company’s SC system, and the use of technology in the company. The main disruption to professional capability stems from the lack of different skills and specialized skills. However, the main slipup in powerful SC tools stems from the selection of the right tools and criteria, process mapping, and flow issues. Technology constraints, implementations, digital transformations, and SC transformations, on the other hand, are the most important sources of technology interruptions. SC flexibility, which represents the SC’s ability to adapt to changes, ranks fifth. Situational awareness, SC resilience, and innovation are considered to be key strategies for increasing SC flexibility and thereby reducing nervousness. The main interruptions to awareness include a lack of tendency to situational awareness and a lack of understandable and sustainable awareness. Alternatively, the main disruptions to SC resilience include a lack of resilience, recovery, redundant systems and plans, and unexpected changes, especially external changes. In comparison, the most important factors contributing to the disruption of innovation include responding slowly to innovation, digital transformation, and the adoption of major changes.

COVID-19 has severely disrupted SCs around the world. GSC managers need to maintain business operations, meet urgent requirements, and mitigate supplier challenges in the face of significant disruption. Initial efforts focus on managing supply interruptions and readjusting SCs to account for supply network constraints. Now, more focus should be directed toward securing supply bases and building resilience for the future. This approach helps in dealing with the SCN as well as in building a stronger, more resilient, and flexible company that is ready to succeed when the economy grows again. The GSC needs to make the planning process more important, requiring accurate strategic planning and effective GSCN mitigation systems.

5. Conclusions

During pandemic events, a clear understanding of SCNs can help organizations create the right plans to deal with interruptions and future disruptions. New technologies enable SC decision-makers to establish tools to explore potential risks and provide corrective action plans. Organizations that consider SCN will have better opportunities to identify the impacts of disruptions and risky events on their SCs, providing an opportunity to evaluate and respond to threatening circumstances.

The complexity of GSC systems and the uncertainty of different types of nervousness necessitate the need to create flexible and effective ways to assess SCNs. In this research, an integrated fuzzy-FMEA–gray correlation approach is applied to model and rank the SCN’s factors. The results reveal that planning followed by visibility, stability, DSSs, and SC flexibility should be the primary focus when considering the SCN. The outcomes show contributions to identifying factors that can be used to understand and prioritize SCN elements. The findings can be utilized by researchers, SC specialists, and practitioners for the development of DSSs. Also, the results may be utilized to construct a nervousness mitigation strategy for better SC resilience.

There are several shortcomings in this work as well. First, the main informants come from different businesses. The experts from different industries may have different perspectives, which could affect the obtained results. Second, this study is based on the experts’ assessment and qualities without considering their risk attitudes. Third, thirty interruption modes are considered in this study. However, further failure modes can be studied. Although the selected case is demonstrative, information from other worldwide SC businesses located in other locations will assist in increasing the generality of the results. The applied approach can be extended to other industries in the future to prove its feasibility in a broader context. Additional research can focus on assessing nervousness solution plans.