IRJET-An Entropy-Weight Based TOPSIS Approach for Supplier Selection
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This document presents a methodology for supplier selection using the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method combined with entropy weight. It involves using a decision matrix to evaluate suppliers based on multiple quantitative and qualitative criteria. The weights of each criterion are determined using an entropy weight calculation. The TOPSIS method is then applied to rank suppliers based on their distance from the ideal positive and negative solutions. An illustrative example is provided to demonstrate the step-by-step calculations for applying this methodology to a supplier selection problem involving four suppliers and five evaluation criteria.
![International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 05 Issue: 06 | June 2018 www.irjet.net p-ISSN: 2395-0072
© 2018, IRJET | Impact Factor value: 7.211 | ISO 9001:2008 Certified Journal | Page 2831
Step 5 & 6: Compute dj value by using formula and calculate
wj value.
Table 7 Weight Calculation
ej
e1 e2 e3 e4 e5
0.99 0.99 0.97 0.97 0.89
dj = 1 – ej 0.10 0.10 0.30 0.30 0.11
0.11 0.11 0.33 0.33 0.12
Weight w1 w2 w3 w4 w5
Step 7: Construct the weighted normalized decision matrix.
Table 8: Weight Normalized Matrix
SC →
C1 C2 C3 C4 C5
A ↓
Supplier 1 0.06 0.05 0.19 0.17 0.08
Supplier 2 0.06 0.06 0.19 0.22 0.07
Supplier 3 0.05 0.05 0.15 0.12 0.02
Supplier 4 0.05 0.06 0.16 0.12 0.04
Step 8: Determine the positive ideal solution and negative
ideal solution.
Table 9 Positive and Negative Ideal Solution
A* 0.05 0.05 0.19 0.22 0.02
A- 0.06 0.06 0.15 0.12 0.08
Step 9: Calculate the separation measure for suppliers.
Table 10 Separation Measure for suppliers
Supplier
1
Supplier
2
Supplier
3
Supplier
4
S+ 0.079 0.052 0.108 0.107
S- 0.065 0.015 0.062 0.042
Step 10: Calculate the relative closeness to the ideal
Solution.
Table 11 Relative Closeness Coefficient
Alternatives
↓
S* S- S*+S- C*= S-/(S*+S-)
Supplier 1 0.079 0.065 0.144 0.45
Supplier 2 0.052 0.147 0.667 0.22
Supplier 3 0.180 0.062 0.170 0.36
Supplier 4 0.107 0.042 0.149 0.28
Step 10: Supplier ranking according to preferences.
Table 12 Alternatives Ranking
Alternatives TOPSIS Index Rank
Supplier 1 0.451 1
Supplier 2 0.220 4
Supplier 3 0.365 2
Supplier 4 0.282 3
5. RESULT AND CONCLUSIONS
In this study, Entropy weight based TOPSIS method for
decision making to tackle multi criteria decision making
problem affected by uncertainty and taking into account the
preferences of the decision maker is applied. This method
allows in finding the best alternative by given criteria and
characteristics. Entropy weight is used in TOPSIS analysis
which is used for making the right decision for the
organization. Results from Entropy and TOPSIS analysis are
objective and accurate. The ranking of the alternatives in
order are S1 > S3 > S4 > S2. Results indicate that S1 is the
best alternative with C* value of 0.451wherein S1 which is
the best alternative.
REFERENCES
[1] Omid Jadidi, F.F., and Enzo Bagliery TOPSIS Method for
Supplier Selection Problem World Academy of Science,
Engineering and Technology, International Journal of
Social, Behavioral, Educational, Economic, Businessand
Industrial Engineering, 4, 11 (2010).
[2]
[3] Athawale, V.M., A TOPSIS method-based Approach to
machine tool selection. The 2010 international](https://image.slidesharecdn.com/irjet-v5i6543-180818062802/85/IRJET-An-Entropy-Weight-Based-TOPSIS-Approach-for-Supplier-Selection-4-320.jpg)
![International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 05 Issue: 06 | June 2018 www.irjet.net p-ISSN: 2395-0072
© 2018, IRJET | Impact Factor value: 7.211 | ISO 9001:2008 Certified Journal | Page 2832
conference on industrial engineering and operations
management, (2010)
[4] Chuanyong Yin, “Supplier selection methods and their
comparison,” Legal System and Society, 2007, pp.306-
307.
[5] Jiang J., Chen Y.W., Tang D.W., Chen Y.W, (2010), "Topsis
with belief structure for group belief multiple criteria
decision making", international journal of Automation
and Computing, vol.7, no.3, pp 359-364
[6] Weber C.A., Current J.R., Benton W.C., (1991) "Vendor
selection criteria and methods", European Journal of
Operational Research 50, pp 2-18
[7] Hwang, C. L., & Yoon, K. “Multiple attribute decision
making methods and applications: A state of the art
survey”. New York: Springer-Verlag, 1981.
[8] Tahriri, F., Osman, M. R., Ali, A., & Mohd, R., (2008), "A
review of supplier selection methods in manufacturing
industries", Suranaree Journal of Science and
Technology, vol.15, no.3, pp 201-208.
[9] Weber C.A., Current J.R., Benton W.C., (1991) "Vendor
selection criteria and methods", European Journal of
Operational Research 50, pp 2-18.
[10] Zuyun CHEN, Shengqiang YANG and et al.. “Application
of uncertainty measurement model based on coefficient
of entropy to comprehensive evaluation of coal mine
safety”. Mining Safety & Environmental Protection,
2007(1) 34:75-77.
[11] Elsayed A Elsayed, Shaik Dawood A.K., Karthikeyan R.
"Evaluating Alternatives through the Application of
Topsis Method with Entropy Weight", International
Journal of Engineering Trends and Technology (IJETT)
Vol 46 (2), April, (2017).](https://image.slidesharecdn.com/irjet-v5i6543-180818062802/85/IRJET-An-Entropy-Weight-Based-TOPSIS-Approach-for-Supplier-Selection-5-320.jpg)
IRJET-An Entropy-Weight Based TOPSIS Approach for Supplier Selection
- 1. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 05 Issue: 06 | June 2018 www.irjet.net p-ISSN: 2395-0072 © 2018, IRJET | Impact Factor value: 7.211 | ISO 9001:2008 Certified Journal | Page 2828 An Entropy-Weight Based TOPSIS Approach for Supplier Selection Josy George1, Mukesh Sahu2, Haider Ali Naqvi3 1,2,3Assistant Professor, Department of Mechanical Engineering, Lakshmi Narain College of Technology Excellence, Bhopal (M.P), India ---------------------------------------------------------------------***--------------------------------------------------------------------- Abstract - Supplier selection is one of the most critical issues to be dealt by manufacturing firms in today’s competitive environment.It is a multi-criteria decision-making problem which involves both qualitative and quantitative factors. In ordertoselectthe best supplier, it is important to make a trade-offbetweenthese tangible and intangible factors which conflict witheachother. The objective of this paper is to develop a methodology to evaluate suppliers in supply chain cycle based on Technique for Order Preference by Similarity to Ideal Solution method (TOPSIS) by entropy weight concept. To understand this method a numerical example is proposed to illustrate the effectiveness of TOPSIS method. Key Words: TOPSIS Method, Entropy Weight, Supplier Selection, Multi-criteria decision making (MCDM) 1. INTRODUCTION Organizations must work with several suppliersto continue its activities. Selection of the suppliers in a group of candidate firms is a difficult decision problem. In these circumstances, supplier selection is vital for the firms. Determining the best supplier is the key for success to the companies with respect to strategic sense. The prime focus this paper is selection of supplier based on TOPSIS method, TOPSIS method was first developed by Hwang & Yoon and ranks the alternatives according to their distances from the positive ideal and the negative ideal solution, i.e. the best alternative has simultaneously the shortest distance from the ideal solution and the farthest distance from the negative ideal solution. The ideal solution is identified with a hypothetical alternative that hasthe best values for all considered criteria whereas the negative ideal solution is identified with a hypothetical alternative thathas the worst criteria values. In practice, TOPSIS has been successfully applied to solve selection/evaluation problems with a finite number of alternatives because it is intuitive and easy to understand and implement. The acronym TOPSIS stands for Technique for Order Preference by Similarity to the Ideal Solution. In general,the process for the TOPSIS algorithm starts with forming the decision matrix representing the satisfaction value of each criterion with each alternative. Next, the matrix is normalized with a desired normalizing scheme, and the values are multiplied by the criteria weights. Subsequently, the positive-ideal and negative-idealsolutionsarecalculated, and the distance of each alternative to these solutions is calculated with a distance measure. Finally, the alternatives are ranked based on their relative closeness to the ideal solution. The TOPSIS technique is helpful for decision makers to structure the problems to be solved, conduct analyses, comparisons and ranking of the alternatives. 2. LITERATURE REVIEW Selection supplier is a strategic decision in the course of supply chain management. The selection of suppliers depends on the sourcing strategy of the buyer/manufacturer. It helpsin optimizing the supplychain and thus increasing the efficiency of the supply chain. An incorrect supplier selection can drivethe entiresupplychain into confusion. Selecting suppliers and service providers through competitive bid ding processes is a vital activity for most operating organizations and manufacturers. In today’s competitive markets, companies have understood the importance of selecting proper suppliers who can supply their requirement with their desired quality and in a scheduled time. Therefore, businesses try to measure the performance of their suppliers to select the best supplier to gain supply chain surplus. Consequently,supplierselectionis a key factor of the procurement process. Basically, selecting a proper supplier is considered as a non-trivial task. To achieve this goal, the majority of the decision makers empirically evaluate and select suppliers. The Entropy method can be used not only to quantitatively estimate data quantity, but also to calculate objectively the relative weight of information. Entropy was originally intended to imply a physical phenomenon of numerator turbulence degree or the probability scale under a specified condition. If entropy values are lower, the numerator degrees are more proportional, implying as close to perfect entropy aspossible. Conversely, if entropy valuesarehigher, the numerator degrees have a more irregular inflection. Therefore, entropy weight method was introduced toobtain the relative weight of each attribute. Additionally, in information theory, entropy can be used to measure expected information content of a certain message.
- 2. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 05 Issue: 06 | June 2018 www.irjet.net p-ISSN: 2395-0072 © 2018, IRJET | Impact Factor value: 7.211 | ISO 9001:2008 Certified Journal | Page 2829 3. ENTROPY WEIGHT BASED TOPSIS MODEL A Multi-Criteria Decision Making (MCDM) technique helps the decision makers (DMs) to evaluate the best alternatives.TOPSIS method is a most common technique of multi-Attribution Decision Making (MADM) models. “Technique for Order Preference by Similarityto IdealSolution (TOPSIS)” isa method of multi-criteria decision analysis andthis methodwas introduced by Hwang and Yoon in 1981. TOPSIS logic is rational and understandable. It chooses the alternative which has the shortest geometric distance fromthe positive ideal solution and compares a set of alternatives by identifying weights for each criterion, normalizes the scores for each criterion and calculates the geometric distance between each alternative and the ideal alternative in order to give the best score for each criterion. TOPSIS method helps to choose the right suppliers with a various finite number of criteria. Step - I: The structure of matrix X1 X2 … Xj A1 X11 X12 … X1j A2 X21 X22 … X2j D = . . . … . . . . … . Ai Xi1 Xi2 … Xij Step - II: Calculate the Normalized the matrix D by using the following formula: Step - III: Normalize the decision matrix by using formula. Step - IV: Compute ej value by using formula Where Step - V: Compute dj value by using formula Step - VI: Calculate wj value, which shows the weight of jth criteria, by using formula below. The sum of the weights of all criteria must be equal to 1. Step - VII: Construct the weighted normalized decision matrix by multiplying: Step - VIII: Determine the positive ideal solution and negative ideal solution Step - IX: Calculate the separation measure Step - X: Calculate the relative closeness to the ideal Solution , 0 ≤ ≤ 1 Step - XI: Calculate the total score and select the alternative closest to 1. 4. ILLUSTRATIVE EXAMPLE For a company that wants select its supplier, suppose the following criteria and characteristics as the most important items to focus: Price (C1), Project Completion Time (C2), Work Quality (C3), Amountof equipment (C4),Distance(C5). After consideration following decision matrix is obtained:
- 3. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 05 Issue: 06 | June 2018 www.irjet.net p-ISSN: 2395-0072 © 2018, IRJET | Impact Factor value: 7.211 | ISO 9001:2008 Certified Journal | Page 2830 Table 1: Quantitative information Selection Criteria → C1 C2 C3 C4 C5 Alternatives ↓ Supplier 1 80 12 Very Good Good 260 Supplier 2 75 14 Very Good Very Good 230 Supplier 3 72 13 Good Sufficient 50 Supplier 4 65 15 Sufficient Sufficient 140 Table 2: Decision matrix Selection Criteria → C1 C2 C3 C4 C5 Alternatives ↓ Supplier 1 80 12 9 7 260 Supplier 2 75 14 9 9 230 Supplier 3 72 13 7 5 50 Supplier 4 65 15 5 5 140 4.1 CALCULATIONS Step 1: The structure of matrix Table 3 Criterion Parametric values Selection Criteria → C1 C2 C3 C4 C5 Alternatives ↓ Supplier 1 80 12 9 7 260 Supplier 2 75 14 9 9 230 Supplier 3 72 13 7 5 50 Supplier 4 65 15 5 5 140 292 54 30 26 680 146. 4 27.0 9 15.3 6 13.4 1 377.6 2 Step 2: Calculate the Normalized the matrix by using the mentioned formula in methodology section. Table 4: Normalized Matrix SC → C1 C2 C3 C4 C5 A ↓ Supplier 1 0.55 0.44 0.58 0.52 0.68 Supplier 2 0.51 0.51 0.58 0.67 0.60 Supplier 3 0.49 0.47 0.45 0.37 0.13 Supplier 4 0.44 0.55 0.32 0.37 0.37 Step 3: Normalize the decision matrix by using the mentioned formula in methodology section. Table 5 Proportional Matrix 1 SC → C1 C2 C3 C4 C5 A ↓ Supplier 1 0.28 0.22 0.30 0.26 0.38 Supplier 2 0.26 0.25 0.30 0.34 0.33 Supplier 3 0.25 0.24 0.23 0.19 0.07 Supplier 4 0.22 0.27 0.16 0.19 0.20 Step 4: Compute ej value by using formula by using the mentioned formula in methodology section. Table 6 Proportional Matrix 2 SC → C1 C2 C3 C4 C5 A ↓ Supplier 1 0.28 0.22 0.30 0.26 0.38 Supplier 2 0.26 0.25 0.30 0.34 0.33 Supplier 3 0.25 0.24 0.23 0.19 0.07 Supplier 4 0.22 0.27 0.16 0.19 0.20 - 1.38 - 1.38 - 1.35 - 1.35 - 1.24 -k - 0.72 - 0.72 - 0.72 - 0.72 - 0.72 ej 0.99 0.99 0.97 0.97 0.89
- 4. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 05 Issue: 06 | June 2018 www.irjet.net p-ISSN: 2395-0072 © 2018, IRJET | Impact Factor value: 7.211 | ISO 9001:2008 Certified Journal | Page 2831 Step 5 & 6: Compute dj value by using formula and calculate wj value. Table 7 Weight Calculation ej e1 e2 e3 e4 e5 0.99 0.99 0.97 0.97 0.89 dj = 1 – ej 0.10 0.10 0.30 0.30 0.11 0.11 0.11 0.33 0.33 0.12 Weight w1 w2 w3 w4 w5 Step 7: Construct the weighted normalized decision matrix. Table 8: Weight Normalized Matrix SC → C1 C2 C3 C4 C5 A ↓ Supplier 1 0.06 0.05 0.19 0.17 0.08 Supplier 2 0.06 0.06 0.19 0.22 0.07 Supplier 3 0.05 0.05 0.15 0.12 0.02 Supplier 4 0.05 0.06 0.16 0.12 0.04 Step 8: Determine the positive ideal solution and negative ideal solution. Table 9 Positive and Negative Ideal Solution A* 0.05 0.05 0.19 0.22 0.02 A- 0.06 0.06 0.15 0.12 0.08 Step 9: Calculate the separation measure for suppliers. Table 10 Separation Measure for suppliers Supplier 1 Supplier 2 Supplier 3 Supplier 4 S+ 0.079 0.052 0.108 0.107 S- 0.065 0.015 0.062 0.042 Step 10: Calculate the relative closeness to the ideal Solution. Table 11 Relative Closeness Coefficient Alternatives ↓ S* S- S*+S- C*= S-/(S*+S-) Supplier 1 0.079 0.065 0.144 0.45 Supplier 2 0.052 0.147 0.667 0.22 Supplier 3 0.180 0.062 0.170 0.36 Supplier 4 0.107 0.042 0.149 0.28 Step 10: Supplier ranking according to preferences. Table 12 Alternatives Ranking Alternatives TOPSIS Index Rank Supplier 1 0.451 1 Supplier 2 0.220 4 Supplier 3 0.365 2 Supplier 4 0.282 3 5. RESULT AND CONCLUSIONS In this study, Entropy weight based TOPSIS method for decision making to tackle multi criteria decision making problem affected by uncertainty and taking into account the preferences of the decision maker is applied. This method allows in finding the best alternative by given criteria and characteristics. Entropy weight is used in TOPSIS analysis which is used for making the right decision for the organization. Results from Entropy and TOPSIS analysis are objective and accurate. The ranking of the alternatives in order are S1 > S3 > S4 > S2. Results indicate that S1 is the best alternative with C* value of 0.451wherein S1 which is the best alternative. REFERENCES [1] Omid Jadidi, F.F., and Enzo Bagliery TOPSIS Method for Supplier Selection Problem World Academy of Science, Engineering and Technology, International Journal of Social, Behavioral, Educational, Economic, Businessand Industrial Engineering, 4, 11 (2010). [2] [3] Athawale, V.M., A TOPSIS method-based Approach to machine tool selection. The 2010 international
- 5. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 05 Issue: 06 | June 2018 www.irjet.net p-ISSN: 2395-0072 © 2018, IRJET | Impact Factor value: 7.211 | ISO 9001:2008 Certified Journal | Page 2832 conference on industrial engineering and operations management, (2010) [4] Chuanyong Yin, “Supplier selection methods and their comparison,” Legal System and Society, 2007, pp.306- 307. [5] Jiang J., Chen Y.W., Tang D.W., Chen Y.W, (2010), "Topsis with belief structure for group belief multiple criteria decision making", international journal of Automation and Computing, vol.7, no.3, pp 359-364 [6] Weber C.A., Current J.R., Benton W.C., (1991) "Vendor selection criteria and methods", European Journal of Operational Research 50, pp 2-18 [7] Hwang, C. L., & Yoon, K. “Multiple attribute decision making methods and applications: A state of the art survey”. New York: Springer-Verlag, 1981. [8] Tahriri, F., Osman, M. R., Ali, A., & Mohd, R., (2008), "A review of supplier selection methods in manufacturing industries", Suranaree Journal of Science and Technology, vol.15, no.3, pp 201-208. [9] Weber C.A., Current J.R., Benton W.C., (1991) "Vendor selection criteria and methods", European Journal of Operational Research 50, pp 2-18. [10] Zuyun CHEN, Shengqiang YANG and et al.. “Application of uncertainty measurement model based on coefficient of entropy to comprehensive evaluation of coal mine safety”. Mining Safety & Environmental Protection, 2007(1) 34:75-77. [11] Elsayed A Elsayed, Shaik Dawood A.K., Karthikeyan R. "Evaluating Alternatives through the Application of Topsis Method with Entropy Weight", International Journal of Engineering Trends and Technology (IJETT) Vol 46 (2), April, (2017).