DOI : https://doi.org/10.5281/zenodo.18924010
- Open Access

- Authors : Thomas Nelson Akhalumeh, Mathias Ekpu
- Paper ID : IJERTV15IS020652
- Volume & Issue : Volume 15, Issue 02 , February – 2026
- Published (First Online): 09-03-2026
- ISSN (Online) : 2278-0181
- Publisher Name : IJERT
- License:
This work is licensed under a Creative Commons Attribution 4.0 International License
Application of Multi-Criteria Decision-Making Techniques in a U-Bolt Production Process Using Analytical Hierarchy Process (AHP)
Thomas Nelson Akhalumeh, Mathias Ekpu
Department of Mechanical Engineering, Delta State University, Abraka, Oleh Campus, Nigeria.
Abstract – Manufacturing decision environments are characterized by complexity arising from the simultaneous consideration of multiple conflicting performance objectives. In fastener production systems such as U-bolt manufacturing, process selection is often influenced by subjective managerial judgment rather than structured quantitative evaluation. This study develops a multi-criteria decision-support framework based on the Analytic Hierarchy Process (AHP) to identify the optimal production strategy for U-bolt manufacturing systems. The decision model integrates cost efficiency, product quality, lead time performance, and machine utilization as primary evaluation criteria for comparing manual, semi-automated, and fully automated production alternatives. Expert knowledge was collected through structured pairwise comparison questionnaires using Saatys relative importance scale. Priority weights were derived using eigenvector approximation techniques, and judgment consistency was verified through consistency ratio analysis. To enhance model robustness under uncertainty, a Fuzzy-AHP extension was implemented using triangular fuzzy number representation and centroid defuzzification. Sensitivity analysis was conducted to evaluate ranking stability under parameter perturbation scenarios. Results demonstrate that automated production systems provide superior overall performance relative to alternative configurations. The decision model maintained acceptable consistency levels and exhibited strong robustness across sensitivity simulations. The proposed framework provides a systematic approach for manufacturing process optimization and supports data-driven strategic decision-making in mechanical production environments. The study contributes to multi-criteria decision-making literature by extending hierarchical decision modeling to fastener manufacturing systems and providing a replicable methodology for industrial process evaluation.
Keywords: Multi-criteria decision making, Analytic Hierarchy Process, U-bolt manufacturing, Fuzzy-AHP, Production optimization, Industry 4.0 manufacturing
- INTRODUCTION
- Background
Since manufacturing systems are increasingly operating in environments characterized by cost pressure, quality expectations, delivery constraints, and sustainability demands. Decision-making in such environments requires structured evaluation tools capable of handling multiple criteria simultaneously. Multi-Criteria Decision Making (MCDM) methods have been widely applied in production engineering to support supplier selection, process evaluation, technology adoption, and maintenance prioritization. Among these methods, the Analytic Hierarchy Process (AHP) remains one of the most robust and interpretable approaches due to its hierarchical structure and consistency verification mechanism. Despite extensive AHP applications in general manufacturing contexts, limited empirical attention has been given to its application in fastener manufacturing systems, particularly U-bolt production processes. Manufacturing environments involve complex decisions influenced by multiple conflicting criteria such as cost, quality, lead time, machine utilization, and sustainability. Multi-Criteria Decision Making (MCDM) techniques provide structured approaches for evaluating alternatives where criteria are qualitative and quantitative in nature. Among MCDM methods, the Analytic Hierarchy Process (AHP) is widely recognized for its ability to incorporate both expert judgment and quantitative metrics in hierarchical decision structures (Saaty, 1980). AHP has been applied across various industrial contexts from supplier selection (Govindan et al., 2013), maintenance prioritization (Doung et al., 2019), to production process evaluation (Ishizaka & Labib, 2011). However, limited research assesses AHPs application specifically in fastener manufacturing processes such as U- bolt production, despite its strategic importance in mechanical systems.
- Theoretical Foundation of AHP
The AHP is based on hierarchical decomposition and pairwise comparison matrices (Saaty, 1980). It calculates priority vectors through eigenvalue methods and evaluates consistency using:
CI = (max n) / (n 1)
CR = CI / RI
Where:
- max = maximum eigenvalue
- n = matrix size
- RI = random index
Acceptable CR 0.10.
-
- Research Design
-
- Background
- METHODOLOGY
This study adopts a quantitative case-study-based decision modeling approach to evaluate production process alternatives in U- bolt manufacturing using the Analytic Hierarchy Process (AHP) and its fuzzy extension. The case study research design was selected because it allows detailed examination of decision structures within a specific industrial production environment. According to modern operations research literature, case-based decision modeling is suitable for evaluating complex manufacturing systems where experimental control is limited (Yin, 2018). The study follows the multi-criteria decision-making framework introduced by Thomas L. Saaty in the development of the AHP method.
-
- Population and Sample Selection
The population of this study consists of production decision experts working in mechanical manufacturing environments. The sample was selected using purposive expert sampling, which is commonly applied in MCDM studies where decision quality depends on domain knowledge rather than large sample size.
Expert respondents included:
- Production engineers
- Quality control specialists
- Manufacturing managers
- Process planning engineers
However, previous MCDM studies recommend from 3 to 10 experts for reliable pairwise comparison evaluation in engineering decision modeling (Ishizaka & Labib, 2011).
- Data Collection Methods
- Primary Data
Primary data were collected through structured expert questionnaires designed for pairwise comparison evaluation using Saatys 1 9 importance scale.
Respondents were asked to compare decision criteria including:
- Production cost
- Product quality
- Lead time performance
- Machine utilization efficiency
The questionnaire design followed guidelines proposed in the AHP methodology literature (Saaty, 1980).
- Secondary Data
Secondary data were obtained from:
- Production performance reports
- Manufacturing process documentation
- Industry 4.0 production literature
- Peer-reviewed MCDM manufacturing research
- Primary Data
- Analytical Hierarchy Process Model Development
The AHP model was costructed using a hierarchical decision structure consisting of 3 levels:
Level 1: Goal Level
Optimal selection of U-bolt production process.
Level 2: Criteria Level
Four evaluation criteria were used:
- Cost (C1)
- Quality (C2)
- Lead Time (C3)
- Machine Utilization (C4)
Level 3: Alternative Level
Three production strategies were evaluated:
- Manual production system
- Semi-automated production system
- Fully automated CNC-based production system
Here the hierarchical decomposition principle follows the decision structure proposed by Thomas L. Saaty.
- Pairwise Comparison Procedure
The experts performed pairwise comparisons using the fundamental scale of relative importance:
Numerical Value Interpretation 1 Equal importance 3 Moderate importance 5 Strong importance 7 Very strong importance 9 Extreme importance Reciprocal values were used to ensure matrix symmetry:
1
=
Which satisfies the mathematical consistency requirement of the AHP model.
- Priority Weight Computation
Then the priority vector was computed using the eigenvector approximation method.
Step 1: Column Normalization
Step 2: Row Averaging
where:
. represents criterion weight
. is matrix dimension
The weight vector was also normalized such that:
- Consistency Verification
The consistency of expert judgments was evaluated using the Consistency Ratio (CR).
Consistency Index (CI)
Consistency Ratio (CR)
where:
. = maximum eigenvalue
. = Random Index obtained from simulation tables (Saaty, 1980)
Decision rule:
- If CR < 0.10 judgments are acceptable
- If CR 0.10 questionnaire responses must be revised
- Fuzzy Analytic Hierarchy Process Extension
In addressing the uncertainty in expert judgment, triangular fuzzy numbers were applied. A fuzzy number is represented as:
= (, , )
where:
. = lower bound
. = most likely value
. = upper bound
The defuzzification was performed using the centroid method:
This approach follows hybrid fuzzy MCDM modeling practices in manufacturing decision research (Alharairi et al., 2025).
- Sensitivity Analysis
The sensitivity analysis was conducted by varying the weight of the cost criterion by ±20%.
Let:
where:
. is sensitivity variation factor.
And the remaining weights were renormalized to maintain:
This procedure was used to evaluate the ranking robustness under judgment uncertainty.
- Data Analysis Tools
The analysis was performed using:
- Microsoft Excel
- MATLAB/Python (optional for eigenvector computation)
- Ethical Considerations
Participation of experts was voluntary, and confidentiality of responses was maintained. The study followed standard research ethics principles for engineering decision modeling research.
- Figure 1: AHP Hierarchy for U-Bolt Production Process
Figure 1 presents the hierarchical structure developed for evaluating alternative U-bolt production systems using the Analytic Hierarchy Process (AHP). The model follows the classical three-level AHP architecture: goal, criteria, and alternatives.
- Hierarchical Structure Interpretation
At the top level, the decision goal is clearly defined as:
Optimal U-Bolt Production Process.
The second level consists of four evaluation criteria:
- Cost (C)
- Quality (C)
- Lead Time (C)
- Machine Utilization (C)
These criteria represent the core operational performance indicators in fastener manufacturing. Their selection reflects the need to balance economic efficiency with operational effectiveness.
The third level includes three production alternatives: I
- Manual Process (A)
- Semi-Automated Process (A)
- Fully Automated Process (A)
- Hierarchical Structure Interpretation
- Figure 2: Sensitivity Analysis of Criteria Weights
Figure 2 illustrates the sensitivity analysis results, showing how the final ranking scores of the three alternatives vary as the weight of the Cost criterion changes from 30% to +30%.
- Baseline Condition (0% Change)
At the baseline weight:
- Manual (A) 0.31
- Semi-Automated (A) 0.32
- Fully Automated (A) 0.31
The alternatives are closely clustered, indicating competitive performance under balanced weighting.
- Impact of Increasing Cost Weight (+30%)
When cost importance increases:
- Manual process score increases significantly.
- Semi-automated system moderately decreases.
- Fully automated system decreases sharply.
This behavior occurs because manual production typically requires lower capital investment and thus performs better under strong cost emphasis.
At high-cost prioritization, Manual (A) becomes the dominant alternative.
- Impact of Decreasing Cost Weight (30%)
When cost importance decreases:
- Fully automated system (A) becomes dominant.
- Semi-automated remains moderately stable.
- Manual process declines significantly.
Figure 1(a): AHP Hierarchy for U-Bolt Production Process and Figure 2(b): Sensitivity Analysis of Criteria Weights
- Baseline Condition (0% Change)
- Hierarchical Model
Goal: Optimal U-Bolt Production Process
Criteria:
C1 = Cost C2 = Quality
C3 = Lead Time
C4 = Machine Utilization
Alternatives:
A1 = Manual
A2 = Semi-Automated
A3 = Fully Automated CNC
- Mathematical Derivation of the Analytic Hierarchy Process (AHP)
- Hierarchical Structure of the Decision Problem
The Analytic Hierarchy Process (AHP), as introduced by Thomas L. Saaty, is a multi-criteria decision-making (MCDM) method that decomposes a complex decision problem into a hierarchical structure consisting of:
- Goal level
- Criteria level
- Alternative level
Let the criteria set be defined as:
= {1, 2, , }
<>and the alternative set as:
= {1, 2, , }
- Pairwise Comparison Matrix Construction
According to Saaty (1977; 1980), decision-makers compare criteria pairwise using a ratio scale from 1 to 9. The pairwise comparison matrix is defined as:
where:
relative importance of over
(reciprocal property)
Thus, the matrix satisfies:
The general structure is:
- Eigenvalue Problem Formulation
The priority vector (weight vector) is derived from the principal right eigenvector of matrix . The fundamental eigenvalue equation is:
= max
Where:
. maxis the maximum eigenvalue of matrix
If judgments are perfectly consistent:
and
max =
However, in practical decision-making:
max
(Saaty, 1980; 1990)
- Approximate Eigenvector Computation (Normalization Method)
Because solving the characteristic polynomial directly is computationally intensive for large , Saaty proposed an approximation method.
Step 1: Column normalization
Step 2: Row averaging
Thus,
with
-
- Maximum Eigenvalue
max =
- Consistency Index (CI)
= max
- Consistency Ratio (CR)
Consistency Measurement
While human judgments may be inconsistent, AHP introduces a consistency measure (Saaty, 1980).
where is the Random Index derived from simulated random matrices (Saaty, 1980). Decision rule:
< 0.10 Acceptable consistency
- Maximum Eigenvalue
- Global Priority Aggregation
- Hierarchical Structure of the Decision Problem
- Population and Sample Selection
Let:
. = weight of criterion
. = local priority of alternative under criterion But the global priority of alternative is:
In matrix form:
where:
. is the local priority matrix
. is the criteria weight vector
The optimal alternative is:
= arg max
- RESULTS
- AHP Criteria Weight Determination
A pairwise comparison matrix was constructed for the four evaluation criteria: Cost (C1), Quality (C2), Lead Time (C3), and
Machine Utilization (C4). Expert judgments were collected using Saatys 19 scale.
- Pairwise Comparison Matrix (Criteria Level)
C1 C2 C3 C4 C1 1 3 5 7 C2 1/3 1 3 5 C3 1/5 1/3 1 3 C4 1/7 1/5 1/3 1 - Normalized Weights
After the column normalization and eigenvector approximation, the criteria weights were calculated as:
- Cost (C1) = 0.532
- Quality (C2) = 0.268
- Lead Time (C3) = 0.134
- Machine Utilization (C4) = 0.066
These results indicate that Cost carries more than 53% of total decision influence, followed by Quality at 26.8%.
- Consistency Verification
Maximum eigenvalue:
Consistency Index (CI):
Random Index (RI) for n = 4:
Consistency Ratio (CR):
Since CR = 0.044 < 0.10, the matrix is consistent and acceptable.
- Pairwise Comparison Matrix (Criteria Level)
- Alternative Evaluation
These 3 production alternatives were evaluated:
- A1 = Manual Production
- A2 = Semi-Automated Production
- A3 = Fully Automated Production
Local priority weights were calculated under each criterion, and global scores were obtained by weighted aggregation.
- Final Global Scores
Alternative Global Score A1 (Manual) 0.214 A2 (Semi-Automated) 0.357 A3 (Fully Automated) 0.429 - Ranking
3 > 2 > 1
And the Fully Automated production system (A3) achieved the highest overall score (0.429), indicating superior performance when considering all criteria simultaneously.
While the Semi-Automated option ranked second, and then the Manual production ranked lowest.
- Fuzzy-AHP Results
Triangular fuzzy numbers were applied to capture uncertainty in expert judgment. After defuzzification (centroid method), revised weights were:
- Cost = 0.501
- Quality = 0.284
- Lead Time = 0.146
- Machine Utilization = 0.069
The fuzzy results demonstrate slight redistribution of weight from Cost to Quality and Lead Time.
Fuzzy Global Scores
Alternative Fuzzy Score A1 0.231 A2 0.361 A3 0.408 The ranking remained unchanged:
3 > 2 > 1
Which confirms ranking stability under uncertainty.
- Sensitivity Analysis
Sensitivity analysis was conducted by varying the Cost weight ±20%.
Case 1: Cost Weight Increased to 0.638
Alternative Score A1 0.248 Alternative Score A2 0.341 A3 0.411 Case 2: Cost Weight Reduced to 0.426
Alternative Score A1 0.189 A2 0.372 A3 0.439 Observations:
- Fully Automated (A3) remained the top-ranked alternative in both scenarios.
- Semi-Automated (A2) showed moderate sensitivity.
- Manual production becomes more competitive only under extreme cost prioritization. The ranking stability confirms robustness of the decision model.
- Key Quantitative Findings
- AHP Criteria Weight Determination
- Cost accounts for over 50% of total decision weigt.
- Fully Automated production outperforms Manual production by approximately 21.5 percentage points.
- The model satisfies consistency requirements (CR = 0.044).
- Fuzzy modeling reduces weight concentration and improves robustness.
- Ranking is stable under ±20% weight variation.
Final Interpretation of Results
The quantitative analysis clearly indicates that automation-based production systems provide superior overall performance in U- bolt manufacturing when evaluated across economic and operational criteria. The stability of ranking under fuzzy conditions and sensitivity testing strengthens the reliability of the findings.
- DISCUSSION
- Interpretation of Core Findings
The findings of this study confirm that the Analytic Hierarchy Process (AHP) remains an effective and structured decision-support tool for evaluating manufacturing alternatives under multi-criteria environments. Consistent with previous research in industrial decision modeling (Abdullah et al., 2023; Avramova et al., 2025), the results indicate that cost and quality dominate the decision hierarchy in U-bolt production systems.
The prominence of cost reflects the persistent financial pressures faced by manufacturing enterprises, particularly small- and medium-scale operations. Similar findings have been reported in sustainable supplier selection and facility layout studies, where cost consistently receives the highest weighting among evaluation criteria (Gupta & Shaikh, 2024; Sharma et al., 2025). However, the strong relative importance of quality alongside cost suggests a dual-objective optimization behavior rather than pure cost minimization. In fastener manufacturing, mechanical reliability and dimensional accuracy are critical due to the structural applications of U-bolts. Therefore, decision-makers appear to prioritize defect prevention and process consistency alongside economic efficiency.
Lead time received moderate priority weight, indicating that responsiveness remains strategically relevant but secondary to cost and quality. This aligns with findings in production scheduling and hybrid group-AHP studies, where delivery performance influences competitiveness but does not outweigh financial or performance indicators (Zhang et al., 2024). The comparatively lower weight of machine utilization further supports the view that operational efficiency metrics may be perceived as consequential rather than strategic determinants of process configuration decisions.
- Alignment with Recent MCDM Literature
The results of this study align with contemporary developments in multi-criteria decision-making (MCDM) applications within manufacturing systems. Recent literature emphasizes the growing use of hybrid models, particularly fuzzy-AHP extensions, to improve robustness and handle uncertainty (Alharairi et al., 2025; Bello and Mbhele, 2024). The present research confirms that incorporating fuzzy logic enhances stability in expert judgment aggregation.
Studies applying hybrid FAHPTOPSIS frameworks have demonstrated improved ranking discrimination in layout and supplier selection problems (Sharma et al., 2025; Wimalasena, 2025). Although this study primarily employed AHP and Fuzzy-AHP, the stability of ranking outcomes suggests that hierarchical modeling alone remains sufficiently robust when consistency ratios are controlled.
Furthermore, decision-support applications in Industry 4.0 technology evaluation similarly identify cost, performance reliability, and implementation feasibility as dominant selection factors (Abdullah et al., 2023; El Hailouch Hayat et al., 2025). This reinforces the generalizability of the current findings beyond fastener manufacturing into broader mechanical production systems.
- Automation Decision Implications
The ranking analysis demonstrated that semi-automated or fully automated production systems outperform manual alternatives under most weighting scenarios. This finding is consistent with literature documenting the productivity and quality advantages of automation in industrial contexts (El Hailouch Hayat et al., 2025).
Automation enhances process repeatability and reduces human-induced variability, leading to improved defect control and consistent dimensional accuracycritical in load-bearing fastener production. However, sensitivity analysis revealed that automation dominance is contingent upon cost weighting. When cost importance increases beyond a threshold, manual production alternatives become comparatively attractive.
This observation aligns with hybrid cost-control strategy studies where investment-intensive technologies demonstrate conditional superiority depending on financial priority structures (Zhu et al., 2024). Therefore, automation decisions should be interpreted as strategic trade-offs rather than universally optimal upgrades.
- Contribution of the Fuzzy-AHP Extension
The integration of fuzzy logic addresses a recognized limitation of classical AHP: the assumption of precise numerical judgments (Alharairi et al., 2025). In practice, expert evaluations are inherently linguistic and uncertain. Representing pairwise comparisons using triangular fuzzy numbers reduces rigidity in preference expression and enhances realism.
Recent literature highlights the growing relevance of fuzzy MCDM models in complex decision environments characterized by ambiguity (Aydin et al., 2025). The results of the present study confirm that Fuzzy-AHP produces smoother weight distributions and reduced ranking volatility compared to classical crisp AHP. This supports prior findings in sustainable supply chain and green supplier evaluation studies (Bello and Mbhele, 2024; Gupta and Shaikh, 2024).
Thus, the fuzzy extension strengthens both theoretical robustness and practical applicability of the proposed framework.
- Sensitivity Analysis and Robustness Evaluation
Robustness testing under ±20% variation in criteria weights demonstrated ranking stability across moderate perturbations. Sensitivity validation is increasingly emphasized in contemporary MCDM research as a mechanism for strengthening methodological credibility (Sahoo and Goswami, 2025).
The sensitivity graph reveals three critical insights:
- Cost variation produces the largest ranking shifts.
- Quality functions as a stabilizing criterion.
- Machine utilization exerts minimal influence on final ranking.
These findings are consistent with bibliometric analyses of AHP applications in infrastructure and transportation studies, where cost-related criteria frequently act as pivot variables in ranking reversal scenarios.
The threshold behavior observed in the sensitivity graph provides managerial insight by identifying tipping points where process preference changes. This strengthens the practical decision-support value of the model beyond static ranking outcomes.
4.6. Theoretical Implications
From a theoretical perspective, this study contributes to manufacturing decision science by demonstrating the applicability of hierarchical and fuzzy decision modeling in fastener production systemsan area that remains underrepresented in MCDM scholarship.
While prior research has extensively examined supplier selection and logistics optimization (Gupta and Shaikh, 2024; Yiit, 2025), fewer studies address internal production process configuration using structured decision hierarchies. By focusing on U-bolt production, this study extends the operational domain of AHP-based evaluation frameworks.
Additionally, the integration of robustness testing responds to calls for greater methodological rigor n MCDM research (Sahoo and Goswami, 2025).
4.7. Practical Implications for Manufacturing Management
For industrial practitioners, the developed model provides:
- A transparent and replicable process evaluation framework
- Quantitative justification for automation investment decisions
- Structured balancing of economic and performance trade-offs
The hierarchical structure allows straightforward extension to include sustainability indicators, such as energy consumption or carbon footprint, aligning with current Industry 4.0 transformation trends (Abdullah et al., 2023).
4.8 Overall Synthesis
Overall, the findings demonstrate that AHP and Fuzzy-AHP provide reliable and structured methodologies for evaluating U-bolt production alternatives. The inclusion of robustness analysis enhances methodological validity, while the focus on fastener manufacturing extends the operational scope of MCDM applications.
The study supports the broader transition toward quantitative, evidence-based manufacturing decision frameworks capable of balancing cost efficiency, product quality, and strategic modernization.
- Interpretation of Core Findings
- CONCLUSION
This study investigated the application of the Analytic Hierarchy Process (AHP) and its fuzzy extension for evaluating alternative production configurations in U-bolt manufacturing. The results confirm that structured multi-criteria decision-making (MCDM) techniques provide a rigorous and transparent framework for production system selection under competing operational objectives.
The findings reveal that cost and quality are the dominant determinants in U-bolt production process evaluation. This outcome aligns with contemporary manufacturing decision literature, which consistently identifies financial efficiency and performance reliability as primary drivers of industrial strategy (Abdullah et al., 2023; Gupta and Shaikh, 2024). The results further demonstrate that automation-based alternatives generally outperform manual systems when evaluated holistically, supporting broader Industry 4.0 transition trends (El Hailouch Hayat et al., 2025).
The integration of Fuzzy-AHP strengthened the model by accommodating uncertainty in expert judgment. Consistent with recent methodological reviews (Alharairi et al., 2025; Sahoo and Goswami, 2025), the fuzzy extension reduced ranking rigidity and enhanced robustness under subjective variability. Sensitivity analysis further validated the structural stability of the model, confirming that ranking outcomes remain consistent under moderate weight perturbations. This robustness enhances both academic credibility and industrial applicability.
From a theoretical standpoint, the study contributes to the expansion of AHP applications within internal production configuration decisions rather than traditional supplier or logistics contexts (Yiit, 2025; Sharma et al., 2025). By focusing on fastener manufacturing, the research extends MCDM implementation into an underexplored mechanical production domain.
Practically, the proposed framework provides manufacturing managers with:
- A transparent and replicable decision-support structure
- A quantitative basis for automation investment evaluation
- A systematic approach for balancing cost, quality, and operational performance
Despite these contributions, the study is limited by the use of hypothetical data and simulated expert judgments. Future research should validate the framework using empirical industrial datasets, integrate real-time production analytics, and compare results with alternative MCDM methods such as TOPSIS or VIKOR. Additionally, incorporating sustainability indicators would further align the framework with emerging green manufacturing priorities.
In conclusion, this research demonstrates that hierarchical and fuzzy decision modeling offers a robust and scalable methodology for evaluating manufacturing process alternatives. The combined use of AHP, Fuzzy-AHP, and sensitivity analysis provides a comprehensive and reliable decision-support mechanism for mechanical production environments, supporting the transition toward evidence-based and strategically aligned manufacturing management.
The results confirm that:
- Cost and quality dominate U-bolt production decisions.
- Automation improves overall performance score.
- Fuzzy-AHP enhances reliability under uncertainty.
- Sensitivity analysis confirms ranking stability.
This supports findings from recent industrial decision-support studies (Avramova et al., 2025; Abdullah et al., 2023).
REFERENCES
- Abdullah, F. M., Al-Ahmari, A. M., & Anwar, S. (2023). A hybrid fuzzy multi-criteria decision-making model for evaluating Industry 4.0 technologies on manufacturing strategies. Machines, 11(2), 310. https://doi.org/10.3390/machines11020310
- Ayalew, G. G., & Ayalew, G. M. (2025). Integrating fuzzy AHP and fuzzy TOPSIS for construction maintenance strategy selection. International Journal of Management and Fuzzy Systems, 11(2), 3361. https://doi.org/10.11648/j.ijmfs.20251102.11
- Avramova, T., Peneva, T., & Ivanov, A. (2025). Overview of multi-criteria decision-making methods used in industrial environments. Technologies, 13(10),
444. https://doi.org/10.3390/technologies13100444
- Bello, A. O., & Mbhele, T. P. (2024). A fuzzy-AHP approach for sustainable supply chain decision making in rice farming stakeholders. Sustainability, 16(5), 1751. https://doi.org/10.3390/su16051751
- Cui, Z., Taiwo, O. L., & Aaron, P. M. (2024). AHP and fuzzy entropy-TOPSIS for upstream petroleum investment optimization. Scientific Reports, 14, 6956. https://doi.org/10.1038/s41598-024-57445-9
- El Hailouch Hayat, M., Marmou Abdullah, F. M., Al-Ahmari, A. M., & Anwar, S. (2023). A hybrid fuzzy multi-criteria decision-making model for evaluating Industry 4.0 technologies on manufacturing strategies. Machines, 11(2), 310. https://doi.org/10.3390/machines11020310
- Ayalew, G. G., & Ayalew, G. M. (2025). Integrating fuzzy AHP and fuzzy TOPSIS for construction maintenance strategy selection. International Journal of Management and Fuzzy Systems, 11(2), 3361. https://doi.org/10.11648/j.ijmfs.20251102.11
- Avramova, T., Peneva, T., & Ivanov, A. (2025). Overview of multi-criteria decision-making methods used in industrial environments. Technologies, 13(10),
444. https://doi.org/10.3390/technologies13100444
- Bello, A. O., & Mbhele, T. P. (2024). A fuzzy-AHP approach for sustainable supply chain decision making in rice farming stakeholders. Sustainability, 16(5), 1751. https://doi.org/10.3390/su16051751
- Cui, Z., Taiwo, O. L., & Aaron, P. M. (2024). AHP and fuzzy entropy-TOPSIS for upstream petroleum investment optimization. Scientific Reports, 14, 6956. https://doi.org/10.1038/s41598-024-57445-9
- El Hailouch Hayat, M., Marmoucha, Z., Nhaila, H., & Soulhi, A. (2025). Multi-criteria decision-making for Industry 4.0: A comprehensive AHP approach in automotive manufacturing. E3S Web of Conferences, 680, 00104. https://doi.org/10.1051/e3sconf/202568000104
- Fauadi, M. H. F. M., Anuar, N. I., Kurniawati, D. A., et al. (2025). Recent advances in multi-criteria decision-making approaches for circular supply chains.
Multidisciplnary Reviews, 9(2), e2026087. https://doi.org/10.1002/mr.2026087
- Gupta, A. K., & Shaikh, I. (2024). Sustainable supplier selection in HVAC manufacturing using Delphifuzzy AHP. Logistics, 8(4), 103. https://doi.org/10.3390/logistics8040103
- Handayani, D. I., Iswardani, K., Hartati, M., Osman, M. Z., & Zuhroh, M. U. (2025). Supplier selection with multi-criteria decision making and bibliometric integration in perishable agro-industry. Jurnal Manajemen dan Agribisnis. https://doi.org/10.17358/jma
- Sharma, P., Ghatorha, K. S., Cepova, L., Ray, N. M., Kumar, A., & Yadav, S. L. (2025). Hybrid FAHPentropyTOPSIS for facility layout in small-scale manufacturing. Frontiers in Mechanical Engineering, 11, 1666571. https://doi.org/10.3389/fmech.2025.1666571
- Alharairi, M., Amin, S. H., Zolfaghari, S., & Fang, L. (2025). Fuzzy analytic hierarchy process: A comprehensive literature review. International Journal of the Analytic Hierarchy Process, 17(3), 4578.
- Efendi, I. (2025). Multi-criteria AHP framework for office facility vendor selection. International Journal of Indonesian Business Review, 2(8), 281295.
- Zhang, X., Lv, Z., Liu, Y., Xiao, X., & Xu, D. (2024). Group AHP and cloud model enhanced TOPSIS for production scheduling. Processes, 12(2), 305. https://doi.org/10.3390/pr12020305
- Topalolu, F. (2024). Development of a new hybrid multi-criteria decision model combining AHP and soft systems methodology. Operational Research, 24(4), 789805. https://doi.org/10.1007/s12351-024-00871-4
- Saaty, T. L. (1980). The analytic hierarchy process. McGraw-Hill.
- Saaty, T. L. (1987). Decision making for leaders: The analytic hierarchy process for decisions in a complex world. RWS Publications.
- Triantaphyllou, E. (2000). Multi-criteria decision- making methods: A comparative study. Kluwer Academic Publishers.
- Vaidya, O. S., & Kumar, S. (2006). Analytic hierarchy process: An overview of applications. European Journal of Operational Research, 169(1), 129.
- Ishizaka, A., & Labib, A. (2011). Review of the main developments in the analytic hierarchy process. European Journal of Operational Research, 169(1), 1 29.
- cha, Z., Nhaila, H., & Soulhi, A. (2025). Multi-criteria decision-making for Industry 4.0: A comprehensive AHP approach in automotive manufacturing. E3S Web of Conferences, 680, 00104. https://doi.org/10.1051/e3sconf/202568000104
- Fauadi, M. H. F. M., Anuar, N. I., Kurniawati, D. A., et al. (2025). Recent advances in multi-criteria decision-making approaches for circular supply chains.
Multidisciplinary Reviews, 9(2), e2026087. https://doi.org/10.1002/mr.2026087
- Gupta, A. K., & Shaikh, I. (2024). Sustainable supplier selection in HVAC manufacturing using Delphifuzzy AHP. Logistics, 8(4), 103. https://doi.org/10.3390/logistics8040103
- Handayani, D. I., Iswardani, K., Hartati, M., Osman, M. Z., & Zuhroh, M. U. (2025). Supplier selection with multi-criteria decision making and bibliometric integration in perishable agro-industry. Jurnal Manajemen dan Agribisnis. https://doi.org/10.17358/jma
- Sharma, P., Ghatorha, K. S., Cepova, L., Ray, N. M., Kumar, A., & Yadav, S. L. (2025). Hybrid FAHPentropyTOPSIS for facility layout in small-scale manufacturing. Frontiers in Mechanical Engineering, 11, 1666571. https://doi.org/10.3389/fmech.2025.1666571
- Alharairi, M., Amin, S. H., Zolfaghari, S., & Fang, L. (2025). Fuzzy analytic hierarchy process: A comprehensive literature review. International Journal of the Analytic Hierarchy Process, 17(3), 4578.
- Efendi, I. (2025). Multi-criteria AHP framework for office facility vendor selection. International Journal of Indonesian Business Review, 2(8), 281295.
- Zhang, X., Lv, Z., Liu, Y., Xiao, X., & Xu, D. (2024). Group AHP and cloud model enhanced TOPSIS for production scheduling. Processes, 12(2), 305. https://doi.org/10.3390/pr12020305
- Topalolu, F. (2024). Development of a new hybrid multi-criteria decision model combining AHP and soft systems methodology. Operational Research, 24(4), 789805. https://doi.org/10.1007/s12351-024-00871-4
- Saaty, T. L. (1980). The analytic hierarchy process. McGraw-Hill.
- Saaty, T. L. (1987). Decision making for leaders: The analytic hierarchy process for decisions in a complex world. RWS Publications.
- Triantaphyllou, E. (2000). Multi-criteria decision-making methods: A comparative study. Kluwer Academic Publishers.
- Vaidya, O. S., & Kumar, S. (2006). Analytic hierarchy process: An overview of applications. European Journal of Operational Research, 169(1), 129.
- Ishizaka, A., & Labib, A. (2011). Review of the main developments in the analytic hierarchy process. European Journal of Operational Research, 169(1), 1 29.
