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A Fuzzy AHP Approach for Supplier Selection Problem: A Case Study in a Gear Motor Company
Mustafa Batuhan Ayhan
TL;DR
Supplier selection becomes difficult when suppliers, criteria, and expert judgments are numerous, conflicting, or imprecise. The paper applies Fuzzy AHP to a gear motor company case, where Alternative 3 is recommended as the best supplier. It also reviews related methods and presents the Fuzzy AHP steps numerically.
Problem
Supplier selection must address multiple conflicting criteria and vague expert judgments when identifying the best supplier.
Method
The paper applies Fuzzy AHP, combining hierarchical AHP analysis with fuzzy numbers for pairwise comparisons, to evaluate suppliers in a gear motor company.
Results
Alternative 3 has the largest total score and is suggested as the best supplier among three alternatives evaluated against five criteria.
Takeaways & Limitations
Fuzzy AHP provides the company with a supplier recommendation based on fuzzy preferences of decision makers.
Takeaways & Limitations
The study addresses a single-sourcing problem; more complex multi-sourcing cases may require mathematical programming models.
Abstract
from arXiv · showhide
Suuplier selection is one of the most important functions of a purchasing department. Since by deciding the best supplier, companies can save material costs and increase competitive advantage.However this decision becomes compilcated in case of multiple suppliers, multiple conflicting criteria, and imprecise parameters. In addition the uncertainty and vagueness of the experts' opinion is the prominent characteristic of the problem. therefore an extensively used multi criteria decision making tool Fuzzy AHP can be utilized as an approach for supplier selection problem. This paper reveals the application of Fuzzy AHP in a gear motor company determining the best supplier with respect to selected criteria. the contribution of this study is not only the application of the Fuzzy AHP methodology for supplier selection problem, but also releasing a comprehensive literature review of multi criteria decision making problems. In addition by stating the steps of Fuzzy AHP clearly and numerically, this study can be a guide of the methodology to be implemented to other multiple criteria decision making problems.
1. INTRODUCTION
Supplier selection is a multi-criteria decision problem involving conflicting objectives, multiple supplier types, and extensive prior criteria and methodological research.
- Supplier selection seeks suppliers offering the right quality, price, timing, and quantities across multiple conflicting criteria.Purchased goods and services can constitute up to 70% of product cost.
- Manufacturers may use single sourcing when one supplier meets all needs or multiple sourcing when orders must be divided among suppliers.
- Dickson identified 23 supplier-selection criteria, including quality, delivery, performance history, warranties, price, technical capability, and financial position.
- Prior research classifies supplier-selection methods into linear weighting, mathematical programming, and statistical approaches, alongside staged selection processes.
- The paper reviews supplier-selection criteria and methods, then explains Fuzzy AHP and applies it in a manufacturing-firm case study.
2. LITERATURE REVIEW
The literature review surveys supplier-selection criteria and decision methods, motivating Fuzzy AHP as a suitable approach for vague expert judgments in multi-criteria settings.
- Earlier reviews by Dickson, Weber et al., De Boer et al., and Sanayei et al. provide established classifications of supplier-selection criteria and methods.
- Quality, price, and delivery performance are suggested as the most important supplier-selection criteria in the reviewed literature.
- Supplier-selection methods are grouped into value measurement, goal/aspiration/reference, and outranking models.Examples include AHP and MAUT, goal programming and TOPSIS, and ELECTRE and PROMETHEE.
- AHP decomposes complicated problems into hierarchies and integrates expert opinions with evaluation scores.
- Fuzzy AHP extends standard AHP by using fuzzy numbers to represent uncertain and vague human judgments.
- Prior supplier-selection applications used Fuzzy AHP alone, with screening, with fuzzy objective programming, or within interactive multi-objective optimization.
- The paper selects Fuzzy AHP because supplier selection has a multi-criteria structure and real-world expert opinions are vague.
3. FUZZY ANALYTIC HIERARCHY PROCESS (F-AHP)
F-AHP combines hierarchical AHP analysis with fuzzy linguistic comparisons, then calculates, defuzzifies, and normalizes criterion and alternative weights to rank suppliers.
- F-AHP embeds fuzzy theory into AHP, which compares alternatives pairwise under criteria arranged in an objective-criteria-subcriteria-alternatives hierarchy.
- F-AHP represents pairwise comparisons through linguistic variables mapped to triangular fuzzy numbers rather than precise numerical judgments.
- When multiple decision makers participate, their fuzzy preferences are averaged and used to update the pairwise comparison matrix.
- For each criterion, the method calculates a fuzzy geometric mean, derives fuzzy weights, and then defuzzifies them using the centre-of-area method.
- The resulting non-fuzzy weights are normalized for both criteria and alternatives before final alternative scores are calculated.
- The highest-scoring alternative is recommended to the decision maker, and the paper demonstrates the procedure in a gear motor company case study.
4. APPLICATION IN A GEARMOTOR COMPANY
The study applies Fuzzy AHP to select a bearing supplier for a gear motor company, using five criteria and three anonymous alternatives. It calculates criterion and alternative weights through fuzzy pairwise comparisons and identifies Alternative 3 as the preferred supplier.
- Case setup: The case evaluates three alternative suppliers for the company’s most frequently used raw material, bearing, against five criteria.The company produces frequency inverters and decentralized Drive Engineering motors in Turkey; supplier and company names are withheld.
- Criterion weighting: Criterion weights are computed through fuzzy comparison matrices, geometric means, fuzzy weights, defuzzification, and normalization.The procedure calculates geometric means, reverses the summed fuzzy vector, derives fuzzy weights, then obtains normalized non-fuzzy criterion weights.
- Alternative weighting: The same calculations are repeated for alternatives under each criterion, with the Quality criterion shown as an example.Alternative pairwise comparisons are performed separately for each of the five criteria, followed by geometric-mean and fuzzy-weight calculations and centre-of-area defuzzification.
- Results: Alternative 3 has the largest aggregated total score and is suggested as the best supplier among the three alternatives.The recommendation reflects the five criteria and the fuzzy preferences of the decision makers.
- Results: Alternative 3 also outperforms the other alternatives in the earlier Fuzzy TOPSIS study of the same case.The comparison reports that Alternative 3 again ranks first, while the relative ordering of the other alternatives differs between studies.
5. CONCLUSION
The Fuzzy AHP model evaluates three suppliers across five criteria, and the case study identifies the third supplier as outperforming the others. The study is limited to a single-sourcing problem, with other models and more complex sourcing settings proposed for future work.
- The Fuzzy AHP model inspects three alternative suppliers using Quality, Origin of the raw material, Cost, Delivery Time, and After Sales Services.
- The case study finds that the third supplier outperforms the other suppliers.
- The study addresses a single-sourcing problem, so models for splitting order quantities among multiple suppliers are not required here.The paper identifies multi-sourcing as a more complex setting in which mathematical programming can split order quantities.
- Future studies could apply Fuzzy ANP or ELECTRE, compare results, or develop hybrid models for the same problem.