Environmental Supply Chain Performance Mapping of an Enterprise by Exploring a Novel Vague-Intellectual Approach

Wang, Juan; Prabhu, M.; Sewagegn, Abatihun Alehegn; Sahu, Anoop Kumar

doi:https://doi.org/10.1155/2023/2133346

Discrete Dynamics in Nature and Society

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Special Issue

New Trends and Recent Advances in Operation Research on Supply Chains

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Research Article | Open Access

Volume 2023 | Article ID 2133346 | https://doi.org/10.1155/2023/2133346

Environmental Supply Chain Performance Mapping of an Enterprise by Exploring a Novel Vague-Intellectual Approach

Juan Wang,¹M. Prabhu,²Abatihun Alehegn Sewagegn,³and Anoop Kumar Sahu⁴

Academic Editor: Reza Lotfi

Received01 Jul 2022

Revised01 Sept 2022

Accepted01 Oct 2022

Published24 May 2023

Abstract

The authors notified the two momentous Research Gaps (RGs) via conducting the relevant literature survey. The authors found as first RG that there are still no mathematical models that could address the generalized trapezoidal fuzzy set (GTFs) based green supply chain performance measurement (GSCPM) multi-level hierarchical index for computing the performance of a production enterprise in % except in the forms of GTF set/scale/crisp value. Next, as the second research gap, the authors identified that a few research articles are published in the extent of degree of similarity approaches. Entire approaches are limited to recognize the weak metrics under assessment of two GTFN sets from experts and also not competent to measure the performance gap of metrics from its ideal value. The objective of research work is turned to overcome the identified two RGs. To fulfill the first RG, the authors first of all proposed the two GTFN set-based mathematical models, which are executed to compute the priority weights and appropriateness ratings (PWsaARs) for 1^st level measures from 2^nd level PWsaARs of metrics (discarded the requirement of PWsaARs data for 1^st level measures from experts). Furthermore, the authors developed GTFN set-based novel fuzzy performance index (NFPI) approach (by combining the crisp as well as fuzzy percentage rule over FPI) to compute the performance in %. To address the second RG, the degree of similarity (DoS) approach is modified by introducing idea of negative and positive ideal solution into DoS (eliminate the need for assessment of two GTFN sets from experts). Next, modified DoS is applied over evaluated FPII (fuzzy performance importance index) to identify the weak and strong metrics and also quantify the GSCP gap of metrics from its ideal value. Eventually, the research work is demonstrated with empirical case research of an automobile parts manufacturing industry.

1. Introduction

Industrial sustainability (IS) issue has gained the momentum among performance’s auditors and current researchers. Three pillars such as economic, social, and environmental are mostly contributing towards IS. Supply chain management (SCM) is found one of the significant operations, which is the heart and ought to be healthy plan and develop for each pillar to ensure the future sustainability of industries at competitive edge. SCM is defined a circuit, where factories, warehouses, distribution centers, retailers, and end users conclave for fulfilling their mutual needs and profits[1]. Among SCM, recently the green supply chain management (GSCM) strategy is ascertained as one of the sparking pillar of sustainability and received the amorous attention from global warming researchers. It is observed that methodical and tactical GSCM practices fruitfully participate in environmental pillar of sustainability and highly attempting towards developing the IS [2, 3]. In today’s era, entire manufacturing sectors are highly provoked for utilizing the GSCM strategy to overcome the pollution as well as global warming issues, i.e., reduction of hot emission, avoidance of carbon contents, reuse the energies, recycling the wastes, and heat recovery to cope up with competitive edge [4–6].

GSCM is an introduction of green (environmental) thoughts into SC network, including the product design, material resourcing and selection, manufacturing processes, and delivery of the final goods to the consumers [7–9]. GSCM is a channel where creativity and innovations in SCM and industrial purchasing are brought under environmental concern [10–12]. GSCM is a dynamic decision support tool to address the ecological defies such as global warming, air and water pollution, and acid rains [13–17]. GSCM is the introductions of green trends in the bin of global supply chain in purpose to restore the earth’s resources and build the world pollution free [18]. GSCM can be gained by augmenting the renewable energy processes, recycling of waste cum hazard materials, recycling of waste water, over processing, most excellent production, effective movement, elimination of manufacturing of defective products, and minimization of reworking [19–23].

It is found that the performance measurement (PM) is one of the decision support system and is explored to calibrate the performance and benchmark the industries based on scores [24, 25]. Sustainability PM tools are executed by SCM researchers cum global industries to map the overall performance under pillars of sustainability [26, 27]. To evaluate the GSCM performance scores, subjective and objective information is used for the modeling of the GSCM-based multihierarchical index consisting of performance measures and their metrics. However, authors sensed on peer-review of published research articles that comprehensive research documents are published focused on objective data modeling of the GSCM-based multihierarchical index in evaluating the permanence scores [28, 29]. Next, the authors found that most of the GSCM researchers [18, 30–32] attempted to develop a triangular fuzzy set-based GSCM hierarchical index (included general measures or limited to single level hierarchy) and able to evaluate GSCM performance score of alternative industries (except individual or single industry) [19, 33–40]. Next, the authors probed that a few researchers attempted to calculate GSCM performance in Triangular, GTFN set, and crisp value [37–39]. In extensive of the literature survey, the authors also found that short of the research work is conducted in degree of similarly (DoS) approaches, and the entire DoS approaches are used to only identify the weak and strong measures and metrics under assessment of two GTFN sets from experts [20–23, 41–47]. Therefore, the peer-review provided significant clues to authors to frame the pre-RGs and shared the contribution to overcome the RGs.(i)The pre-research contributions are summarized as follows:(1)To identify and frame the GTFN set-based GSCPM multilevel hierarchical index, it consisted of the advanced crucial measure-metrics and accepted the green challenge of current contemporary industries.(2)To structure the GTFN-based new mathematical models, which could assess the GSC performance of a firm in percentage (%) under assessment of least GTFN information.(3)To identify the weak and strong metrics and also quantify the GSCP gap of metrics and measures from its ideal value. To potentially shape the entire (1)–(3) research contributions, the authors visited industries and conducted the comprehensive/secondary systematic relevant literature survey, which are discussed in Table 1 briefly.

2. Literature Survey

2.1. Research Gaps and Contribution

2.1.1. Research Gaps

In the last decade, the miscellaneous pollutants, i.e., ill-biological particles, fossil fuels, hazard particles, toxic gasses, undesirable flumes, and unwanted mono-carbon elements/stuffs/materials are more populated in environment due to rapid production rate with incompliance of the green (environmental) issues [84–86]. After conducting the comprehensive/secondary (in-depth) literature review, the authors re-notified and confirmed the same (1)–(3) research RGs, observed on peer-review stage, and discussed end of the Section 1. The confirmed (1)–(3) research RGs are discussed with rationales as follows:(1)The previous researchers introduced GTFN set-based GSCM crucial measures and their interrelated metrics to build only a single-layer GSCM hierarchical index. There is an essential necessity to build the multilayers GSCM hierarchical index by introducing advanced-green technological focusing crucial measure-metrics.(2)As per the evidence of previous research studies, the managers are not facilitated to compute GTFN set-based PWsaARs of 1^st level measures by using the assigned PWsaARs information of metrics (2^nd level hierarchy). There is an essential necessity to build the GTFN set-based mathematical models, where the managers can compute PWsaARs of 1^st level measures by availing the evaluated PWsaARs of metrics (2^nd level hierarchy).(3)The previous researchers ensured the managers to compute the performance of firm in the terms of triangular/GTFN set or scale and crisp value. Therefore, the managers are not facilitated with GTFN set-based new approach for computing the evaluated GSCM performance in %. There is the imperative necessity to build GTFN set-based new approach to address this identified RG.(4)The previous researchers proposed DoS approaches, which are executed to identify the only weak and strong metrics under assessment of two GTFN sets from experts. Therefore, the managers are not ensure to trace that how much % of performance of each metrics need to be augmented to become 100% fit or meet idea value. There is a necessity to introduce the concept of ideal solution to void the assessment of the two set and measuring the GSCM performance gap of metrics from its ideal value.

2.1.2. Research Contributions

The RGs are transformed into research contributions (RCs). Figure 1 depicts the virtual picture of formulated problems/quotation of RCs. The entire RCs are framed as follows:(1)The authors committed to build the measure-metrics based double-layer GTFN set-based GSCPM hierarchical index, addressing the green challenge of industry 4.0(2)The authors committed to develop and propose the two GTFN set-based mathematical models, which could aid the managers to compute PWsaARs of 1^st level measures from availing the evaluated PWsaARs of metrics (2^nd level hierarchy)(3)The authors dedicated to develop and propose a GTFN set-based novel fuzzy performance index (NFPI) approach to transform the GTFN set or scale into %(4)The authors planned to modify the DoS approach by introducing an idea of negative and positive ideal solution into DoS, which ensure the managers to trace that how much % of performance does each metrics needs to become 100% fit to its meet ideal value

3. Fuzzy Logic and Set Theory

The fuzzy set theory was introduced by [87] in 1956 as well as [88] for addressing the problems associated with vagueness. It is considered as a mathematical tool for modeling the language and approximates the situations where fuzzy criteria exist [89]. In a universe of discourse , a fuzzy subset of is defined by a membership function , where element in universe of discourse X is represented by the real numbers in the closed interval [0, 1]. Here, the value of for the fuzzy set is called as the membership value or the grade of the membership. The membership value represents the degree of x belonging to the fuzzy set [90–93]. The greater , the stronger the grade of membership for in . The linguistic value is used for approximate the reasoning within the framework of fuzzy set theory [87, 89, 94, 95] for handling an ambiguity, involved in linguistic expression, and normal trapezoid or triangular fuzzy numbers. We can define operations of fuzzy sets by using the extension principles [22, 60, 95–98].

Definition 1. Based on the extension principle, we can derive the arithmetic of fuzzy sets as shown in [87, 95, 97, 98].
A GTFN set can be defined as , and the membership function is expressed as follows:Here, and .
Suppose that and are two GTFN sets, then the operational rules of the GTFN set and are shown as follows as per reference [96, 97]:

4. GTFN Set-Based Variant Approach Fuzzy Approach

The authors proposed the GTFN set-based variant approach, which included four sub-associated section of section 4. The aggregation of appropriateness ratings and priority importance weights is shown in 4.1. The Novel Fuzzy Performance Index (NFPI), for which the results are calculated in percentage (%), is shown in 4.2. The computation of fuzzy performance importance index (FPII) is displayed in 4.3, and the modified degree of similarity (DoS) mathematical model used for Identification of weak and strong performing GSC metrics is exhibited in 4.4. The chief objective of the proposed approach is to overcome the previous drawbacks of research works and fruitfully fulfill the identified RGs. The pros of the approach are that the proposed GTFN set-based variant approach is capable to tackle the subjective information of experts accurately and precisely. The assigned information in the terms of linguistic scale corresponding to GTFN sets is bounded by four values under membership function, which deliver the precise as well as true results. The approach is able to address all research objectives and contributions. The cons are that the approach is so complex in nature and difficult to understand [99–103]. The computation in decision evaluation problems by using this approach is comprehensive in nature as set included the four values under GTFN membership function.

4.1. Aggregation of Appropriateness Ratings (ARs) and Priority Weights (PWs)

The priority weight (PW) reflects the importance, while rating reflects the value of measure/metrics as per subjective perception of DMs [104–106]. It is observed in many studies that PW influences the decision making scenario. The assigned priority weight corresponding to metrics can fruitfully change the preference order of performance metrics. The high PW is assigned to the most significant metrics [107]. We can understand by analyzing a scenario model of supplier evaluation, if the supplier’s performance is evaluated based on the two metrics such as purchasing cost (PC) and service (S). In this case, DMs assigned the PW such as purchasing cost (PC) = 0.55 and service (S) = 0.45 under sum of PW = 1 and assigned the same rating such as PC = 50 and S = 50 (out of rating = 100 point). Then, it is found by calculating score that supplier = (PC) = = 27.50 and = = 22.5. It is explicated that assigned different weights against metrics under same ratings can change the preference order of metrics in measuring performance of a firm.

On the other hand, in the benchmarking decision making process or mapping performance of alternative industries, assigned ratings by DMs can only change the alternative scores, while the PW does not affect because the weights of set of metrics are similar for considered alternatives.

The research documents [45, 108] are used to build equations (6) and (7), which are used to aggregate the appropriateness ratings and priority importance weights against metrics. Appropriateness ratings against (1^st level) measures can be computed by the following equation:

The appropriateness rating of 1^st level measures is computed from 2^nd level metrics by using equation (6). In the above expression, is denoted as submission of appropriateness ratings of 2^nd level metrics, which are under (1^st level measures).

Similarly, the priority importance weight of 1^st level measures is computed from 2^nd level metrics by using the following equation:

In this expression, is denoted as submission of priority importance weights of 2^nd level metrics, which is under (1^st level measures).

4.2. Novel Fuzzy Performance Index (NFPI) towards calculating the results in %

In this expression, and are denoted as computed aggregated appropriateness rating and aggregated fuzzy priority weight as GTFN set of 1^st level measures.

The centroid formula for defuzzification of the GTFN set [] is proposed [109]:

The crisp value is as follows:

In addition, the current performance and performance loss can be determined by the following [110]:

Here, is the defuzzification of the fuzzy performance index and is the defuzzification of the set/standard fuzzy performance index.

4.3. Computation of Fuzzy Performance Importance Index (FPII)

After evaluating NFPI, the purpose of research work is to identify the weak and strong performing GSC metrics and measures and quantify their performances. The concept of computing FPII is over evaluated PWsaRs. It is found that the higher FPII of any metrics reflects the greater contribution towards GSC [96].where is the aggregated fuzzy appropriateness ratings and is the aggregated fuzzy priority weights of 2^nd level metrics under 1^st level evaluation measures [96]. Since, if we directly calculate FPII, the important weights will neutralize the performance ratings in computing FPII; in this case, it will become impossible to identify the actual weak performing areas (low performance rating and high importance). If is high, then the transformation is low. Consequently, to elicit the metrics with low performance rating under high importance weights, the formula is used.

4.4. Modified Degree of Similarity (DoS) Mathematical Model: Identification of Weak and Strong Performing GSC Metrics

The DoS approach enables the manager to measure the DoS between the two GTFN sets. The approach was only applicable to shortlist the strong and weak GSC metrics under the assessment of two GTFN sets by experts earlier. The existed DoS approach is modified by incorporating the scheme of negative and positive ideal solution. The modified DoS approach addressed the two drawbacks such as eliminate the requirement of two GTFN sets from experts and able to map the performance gap of metrics from its ideal value.

Let us suppose that, a degree of similarity between two fuzzy sets and is defined as follows:wherewhere is the span deference, is the center deference, and is the center width deference between and , respectively.andwhere and are the perimeters of and . is an amending zero in the numerator and denominator :

The computation of positive and negative ideal solution from defined FPII sets is as follows:

is the defined maximum value evaluated from defined FPII sets of each metrics, is the beneficial metrics, and is the cost/nonbeneficial metrics.

5. Empirical Case Research (Data Analyses)

This is an assumed empirical case study of automobile parts (gears and pistons) manufacturing industry, which is located at south part of Zambia. This company supplies the said attribute of parts to its partner’s companies. The case study company realized the necessity to evaluate as well as measure own GSCM performance in the terms of GTFN set/scale, crisp value, and % and also identify the weak and strong performing metrics with quantifying their performance gap from ideal value under expert’s opinion. From this contemplation, the authors conducted the literature review and audited the GSCM of case study industry and proposed a GTFN set-based theoretical GSCPM multi-level hierarchical index. The index consisted of measures and their interrelated metrics, in which green purchasing (C₁), green marketing (C₂), green production (C₃), green design (C₄), green packaging (C₅), and green recycling (C₆) are considered as measures at 1^st level and disseminated into 2^nd level metrics. The proposed index is displayed in Table 2, and definitions are shown in Table 3.

Later, equations (14), (18), and (19) are utilized to compute the weak and strong performing measures and metrics (by using backward rule [96]), depicted in Table 10, which assisted the managers to augment the GSC performances up to 100% by hunting the weak defined metrics.

The procedural steps for measuring the GSC performance are summarized as follows: Step 1. Collection of experts’ opinion (in linguistic terms) based on the priority importance weight and appropriateness ratings scale for individual evaluation metrics: The proposed index is simulated by the subjective assessment of a committee of seven experts. The experts such as DM_1, DM_2, DM_3, DM_4, DM_5, DM₆, and DM₇ were evaluated and selected from the case study industry. One executive was selected from each department such as purchasing-1, marketing-2, production-3, design-4, packaging-5, material recycling-6, and environmental protection-7 on the basis of their experience, interaction with the manufacturing activities, and strong qualification cum decision making capabilities. Entire DMs were at the top management hierarchy, which daily contributed their efficiency to supervise, oversight, and manage the middle and bottom level management activities. Step 2. Approximation of the linguistic evaluation information by using GTFN set: Then, the expert’s panel was instructed to choose the linguistic variables corresponding to GTFN set. The expert’s panel elected 1–9 point linguistic scale, which transformed into the GTFN set as pointed out in Table 4. Next, the committee was instructed to express their subjective preferences (valuation score) in linguistic terms against 2nd level GSC metrics for determining fuzzy PWsaARs, depicted in Tables 5 and 6. Step 3. Performance measurement: loss and gain: Then, the fuzzy performance index (FPI) is computed by employing equation (8), which used the evaluated PWsaARs data of 1^st level measures. Therefore, the evaluated fuzzy performance index (FPI) is computed as (0.556, 0.653, 0.918, 1.061, and 1.000), which is compared with FPI (0.640, 0.780, 0.980, 1.250, and 1.000) proposed/set by the top management (considered corresponding to ideal performance-100%). Then, equations (11) and (12) are utilized to compute an overall GSC performance of firm, which was found 87% out of 100% (ideal performance). Therefore, the firm was suggested to hike 13% GSC performance to gain ideal performance limit. Step 4. Classification of weak and strong performing metrics and its performance gap: After computing the Novel fuzzy performance index of industry, it became really essential to quantify the performance of measure and metrics and from its ideal value (100%) and also identify the weak and strong performing 2^nd level metrics. To evaluate results, the fuzzy performance important index (FPII) and positive ideal solution (as entire metrics are beneficial in nature) against 2^nd level metrics are computed by usage of equations (13) and (19), respectively. The results are revealed in Table 9.

6. Managerial and Practical Implications

The proposed research work assisted the manager to manage as well as improve the GSCP of own industry (if it is found beneath the proposed or expected GTFN set scale). The two conduits are fruitfully presented here and assisted the manager to manage and control the GSCP.(1)The managerial implication is that the developed two GTFN set-based mathematical models with NFPI approach are executed over the proposed index, which assisted the manager to measure the performance of own industry in three forms such as crisp value, GTFN set scale, and %. The specialty of the proposed models is that these two models make the DMs trouble-less in terms of sharing bulk GTFN set information against metrics. Models are able to estimate the PWsaARs of 1^st level measures by availing the subjective information of their interrelated metrics. The practical implication is that the same models can also be executed in future to tackle the extended hierarchy of index, i.e., 3rd, 4th, 5th, and other levels of hierarchy in mapping the same GSC performance of the same or different industry. To understand more practically, in case of 4^th level GSCPM index, DMs have to assign PWsaARs against solely 4^th level metrics, while the PWsaARs information of 3^rd, 2^nd, and 1^st level can be computed under back-propagation.(2)The managerial implication is that the proposed modified DoS accompanied with FPII is executed over the proposed index to assist the manager for both objectives such as to trace the weak and strong metrics and measure the performance gap and closeness to its ideal performance. The introduction of PIS and NIS idea on FPII data helped the DMs to assign only one linguistic variable against each metrics to attain said both objectives; therefore, DMs would not be requested to assign two linguistic variables. The practical implication is that the manager can explored the same modified DoS along with FPII on extended GSCP metrics or different GSCP indexes of different industries for addressing the said objectives.

7. Conclusions

The conclusion of the research work strikes over the attainment of IS by usage of the GSCM strategy or architecture. The conclusion section enrolled the results, future research directions, and limitation of the proposed research work.

7.1. Results

The results of the research work are split into two parts as discussed. The GSC performance of case study firm is found 87%, which need to be improved up to 13% to satisfy the ideal value (100%) or meet the expected performance. The performance gaps of metrics are presented in Table 10. The authors recommended that weak metric’s GSCP should be brought up to C_{1, 2}. The authors also advised the managers to fulfill performance gap of metrics to attain the ideal GSC performance.

7.2. Future Directions

From future directions perspective, the extensive multilevel hierarchical index (intended to 1^st, 2^nd, 3^rd, and 4^th level) can be constructed and utilized with the proposed approach to measure the performance in different quotations. The manager is facilitated to improve own firm’s GSCP if the performance is ascertained below the ideal limit/expected level by ramping up metrics GSC performance’s gap. The industries, who utilize the GSC metrics as a strategy to sustain at competitive market, would gain the maximum benefit from the proposed research work. The industries can explore the presented idea periodically for measuring the performance and can improve the same if performance is found weak. GSCM scholars can utilize presented research work to boot up their wisdom about green measures and their metrics contribution towards sustainability, metrics identification new approach, and idea to build the advance/extended index.

7.3. Limitation

The research work ensures the managers to solve the performance measurement problem of metrics such as the weak metrics evaluation and identification problem and overall performance mapping of individual industry under the GTFN set-based GSCM index. Therefore, the multiobjective optimization, linear regression, and data forecasting problems cannot be solved using proposed mathematical models, approach, and index. The managers can write the C and JAVA programming for measuring the performance of own firm in different terms and also identify metrics performance gaps and closeness to ideal value in short span of time.

Data Availability

The data used to support the findings of this study are available in Tables 1–10.

Disclosure

This article is the part of remote employment research.

Conflicts of Interest

The authors declare that there are no conflicts of interest regarding the publication of this manuscript.

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