Redefining supply chain management with Fuzzy TOPSIS

By Jing Yang Li and Yingying Gu from Grid Dynamics

Supply chain management requires precision and efficiency, and the quest for optimization knows no bounds. As the heartbeat of global commerce, supply chains pulse with data, decisions, and complexities that demand a sophisticated approach to management. For the discerning supply chain engineer, finding the latest technological innovations to orchestrate seamless operations and unlock untapped potential is critical.

At the forefront of this technological frontier stands multi-criteria decision-making (MCDM), a framework that optimizes supply chain management with precision and foresight. Within MCDM, one method shines as a beacon of innovation: Fuzzy Technique for Order of Preference by Similarity to Ideal Solution (Fuzzy TOPSIS). This approach leverages the power of fuzzy logic to tackle the inherent uncertainties and complexities of supply chain decision-making, offering a powerful toolkit to optimize operations, mitigate risks, and drive strategic growth.

In this article, we delve into the transformative potential of Fuzzy TOPSIS within supply chain management, exploring how this advanced decision-making methodology is redefining the benchmarks of operational excellence and competitive advantage.

Applications of multi-criteria decision-making

MCDM stands at the crossroads of complex decision-making, weaving through the fabric of daily life, social sciences, engineering, medicine, and beyond. This field specializes in dissecting and evaluating the myriad choices present in diverse scenarios, leveraging a blend of quantitative and qualitative factors to navigate the labyrinth of possibilities.

MCDM serves as a foundational tool in enterprise contexts, offering a structured approach to dissecting and prioritizing alternatives across a broad spectrum of applications. From refining supply chain management strategies to guiding project prioritization, informing investment decisions, streamlining talent management, and fostering product development, MCDM’s versatility shines brightly.

Enter Fuzzy TOPSIS, a nuanced variant of the multi-criteria decision-making methodology, renowned for its adeptness in evaluating and ranking options by their proximity to an ideal solution versus a worst-case scenario. This technique marries the precision of mathematical models with the fluidity of fuzzy logic, presenting a refined lens through which to assess and make decisions.

This article ventures into the practical application of Fuzzy TOPSIS within the domain of supply chain management, articulated through:

• A detailed exploration of the supplier selection challenge,
• A numerical example of TOPSIS in action for supplier evaluation, and
• Insights into the implementation nuances of TOPSIS.

Introduction of TOPSIS

Developed by Hwang and Yoon [1], TOPSIS is one of the most popular methods for solving MCDM problems.

TOPSIS uses the basic mathematical approach to find the optimal alternative amidst a sea of possibilities. The crux of its methodology lies in its pursuit of alternatives that exhibit the closest proximity to the positive ideal solution while maintaining a considerable distance from the negative ideal solution. By leveraging the Euclidean distance metric, TOPSIS navigates the geometric landscape of decision-making, systematically evaluating alternatives against a predetermined set of criteria. The positive ideal solution (X+) is represented as the total of all best-obtained values for each alternative. In contrast, the negative ideal solution (X−) includes all the worst attainable values for each alternative considered. Both solutions are hypothetical and are obtained within the process.

The extension of the classical TOPSIS method with fuzzy logic, namely fuzzy TOPSIS, has also been successfully implemented in various application areas [2,3,4], including supply chain management, defense, energy, personnel selection, healthcare, and environmental sustainability.

In the pursuit of resolving practical dilemmas, the application of TOPSIS often necessitates collaboration, where the collective expertise of a diverse group of individuals proves invaluable. Recognizing the complexity inherent in decision-making, particularly when confronted with nuanced criteria and weighted preferences, proper group decision-making processes emerge as a cornerstone of success. This collaborative approach ensures a holistic and robust evaluation of alternatives, minimizing the risks associated with individual biases and errors.

Tackling the supplier selection problem

In the context of supply chain resilience, supplier selection is a critical problem that involves choosing the best suppliers to provide the necessary materials or products to a company. The goal of supplier selection is to identify suppliers that can meet the company’s needs and expectations in terms of quality, price, delivery time, reliability, and sustainability.

For example, consider a manufacturing company that needs to select a supplier for a critical component used in its products. The company may evaluate potential suppliers based on criteria such as:

1. Price: The price of the product or service offered by the supplier, including transportation costs and tariffs.
2. Quality: The ability of the supplier to provide high-quality products or services that meet the company’s requirements and specifications.
3. Delivery time: The ability of the supplier to deliver products or services on time and according to the agreed-upon schedule.
4. Reliability: The ability of the supplier to consistently provide products or services of the desired quality and quantity.
5. Environmental sustainability: The environmental, social, and ethical impact of the supplier’s operations and practices.

TOPSIS can be used to evaluate and rank potential suppliers based on multiple criteria. In order to use the qualitative factors in TOPSIS, we have to first convert them into numerical scores or rankings. There are several ways to do this, including:

1. Assigning scores based on expert judgment: You can ask subject matter experts or stakeholders to rate the alternatives on each qualitative factor using a scale or ranking system. For example, you can ask them to rate the suppliers on their reputation from 1 to 5, with 5 being the best.
2. Using surveys or customer feedback: You can collect feedback from customers or stakeholders on each qualitative factor and use the results to assign scores or rankings to the alternatives.
3. Using secondary data: You can collect information from external sources such as industry reports, market surveys, and social media to evaluate the alternatives on each qualitative factor.

Numerical example using TOPSIS for supplier selection

The computational procedure of the fuzzy TOPSIS method is summarized and illustrated as follows.

Step 1: Choose a linguistic model with fuzzy weights

For this example, we use triangular fuzzy numbers with 7 linguistic variables.

Table 1

Step 2: Collect evaluations of decision-makers for each criterion

In the context of supplier selection, for example, we could use four criteria:

1. Quality (C1)
2. Reliability (C2)
3. Price (C3)
4. Delivery time (C4)

Table 2

Here, C1 and C2 are positive criteria while C3 and C4 are negative criteria. D1, D2, and D3 are the experts.

Step 3: Convert linguistic evaluations to triangular fuzzy numbers

Each linguistic evaluation is mapped to three numerical values based on the linguistic model selected in Step 1.

Table 3

Step 4: Calculate aggregate fuzzy weights

The individual fuzzy weights provided by the decision-makers are aggregated to obtain the overall fuzzy weights for each criterion.

Table 4

L-FW is the average of D1-L, D2-L, and D3-L.

M-FW is the average of D1-M, D2-M, and D3-M.

U-FW is the average of D1-U, D2-U, and D3-U.

Step 5: Normalize the decision matrix

The decision matrix is normalized to be in [0,1].

Table 5

A1, A2, … and A5 are possible alternatives that decision makers can choose from based on the criteria C1, C2, …, and C4.

Step 6: Construct a weighted normalized decision matrix

The normalized decision matrix is then weighted using the aggregated fuzzy weights from the previous step.

Table 6

C1-L = C1 * L-FW

C1-M = C1 * M-FW

C1-U = C1 * U-FW

C1 is the column in Table 5.

L-FW, M-FW, and U-FW are the values of C1 in Table 4.

The other columns are calculated in the same way.

Step 7: Find fuzzy positive/negative ideal solutions (FPIS/FNIS)

The fuzzy positive ideal solution (FPIS) and fuzzy negative ideal solution (FNIS) are identified based on the values in the weighted normalized decision matrix.

Table 7

C1-L, C1-M, and C1-U of Table 7 are the maximum values of columns C1-L, C1-M, and C1-U in Table 6 since C1 is a positive criterion.

Similarly, C3-L, C3-M, and C3-U of Table 7 are the minimum values of columns C3-L, C3-M, and C3-U in Table 6 since C3 is a negative criterion.

Table 8

C1-L, C1-M, and C1-U of Table 8 are the minimum values of columns C1-L, C1-M, and C1-U in Table 6 since C1 is a positive criterion.

Similarly, C3-L, C3-M, and C3-U of Table 8 are the maximum values of columns C3-L, C3-M, and C3-U in Table 6 since C3 is a negative criterion.

Step 8: Calculate the Euclidean distance of each alternative from FPIS and FNIS

The Euclidean distances between each alternative and the FPIS and FNIS are computed.

Table 9: Distance to FPIS

C1-D is the distance from (C1-L, C1-M, C1-U) in Table 6 to (C1-L, C1-M, C1-U) in Table 7.

Table 10: Distance to FNIS

C1-D is the distance from (C1-L, C1-M, C1-U) in Table 6 to (C1-L, C1-M, C1-U) in Table 8.

Step 9: Calculate fuzzy distance

The fuzzy distance of each alternative from the FPIS and FNIS are calculated based on the Euclidean distances.

Table 11

Si+ is equal to the summation of C1-D, C2-D, C3-D and C4-D in Table 9.

Si- is equal to the summation of C1-D, C2-D, C3-D and C4-D in Table 10.

Step 10: Calculate the closeness coefficient

The closeness coefficient, which represents the relative closeness of each alternative to the ideal solution, is calculated.

Table 12

Here, closeness coefficient = Si_pos / (Si_pos + Si_neg)

According to these closeness coefficients, the ranking order of the candidates will be A5, A1, A2, A4 and A3, respectively.

Implementation of TOPSIS

Implementing the TOPSIS algorithm is straightforward, and you can find sample implementations in many Python packages and projects.

• TopsisPy: a Python Package implementing Topsis used for multi-criteria decision analysis method. https://pypi.org/project/topsispy/
• Topsis-navkiran: TOPSIS implementation in python for multi-criteria decision making. https://pypi.org/project/topsis-navkiran/
• TOPSIS-package: Python package for TOPSIS implementation using Vector Normalization. https://pypi.org/project/TOPSIS-Package/
• Github repositories:
  https://github.com/Glitchfix/TOPSIS-Python
  https://github.com/hamedbaziyad/TOPSIS
• Kaggle Notebook:
  https://www.kaggle.com/code/hungrybluedev/topsis-implementation

If you are dealing with big datasets, you could use Spark to implement the algorithm for better performance. This GitHub repo implements the TOPSIS algorithm using Java and Apache Spark.

References

• [1] Hwang, C. L., Yoon, K. (2012). Multiple attribute decision making: methods and applications a state-of-the-art survey (Vol. 186). Springer Science & Business Media
• [2] Yong,D.(2006). Plant location selection based on fuzzy TOPSIS. The International Journal of Advanced Manufacturing Technology, 28(7–8), 839–844
• [3] Chu,T.C., Lin,Y.C.(2003). A fuzzy TOPSIS method for robot selection.The International Journal of Advanced Manufacturing Technology, 21(4), 284–290.
• [4] Sałabun, W.(2013). The mean error estimation of TOPSIS method using a fuzzy reference models. Journal of Theoretical and Applied Computer Science, 7(3), 40–50.
• [5] https://scholar.harvard.edu/files/saghafian/files/pdf_52.pdf
• [6] https://pypi.org/project/topsispy/
• [7] https://pypi.org/project/topsis-navkiran/
• [8] https://pypi.org/project/TOPSIS-Package/
• [9] https://gist.github.com/HamzaouiDali/13a0a1b09037312eec942c64b028713d