Supplier Selection for Construction Projects Through ‘TOPSIS’ and ‘VIKOR’ Multi-Criteria Decision Making Methods

Supplier Selection for Construction Projects Through ‘TOPSIS’ and ‘VIKOR’ Multi-Criteria Decision Making Methods

Dr. Bhatt Rajiv* & Dr. Bhatt Darshana**

*Associate Professor, Civil Engineering Department, A.D. Patel Institute of Technology, New Vallabh Vidyanagar, Gujarat, India

**Associate Professor, Structural Engineering Department, Birla Vishvakarma Mahavidyalaya, Vallabh Vidyanagar , Gujarat, India

Abstract- Materials constitute 60% in total cost of the project. Cement contributes for 10 to 15% of the total materials cost. Selecting a best supplier for supply of cement is very crucial for profit making and further achieving success of any construction project. In recent times, there has been a trend not to select a supplier who is having lowest bid offer. Multi-criteria approach is quite effective to select a best supplier. In this paper, seven criteria such as quality, cost, delivery time, technical capability, financial capability, commercial and managerial capability and trust are considered. Relative weights of criteria in the form of criteria weights are generated through Analytic Hierarchy Process (AHP). Then, Technique for order preference by similarity to ideal solution (TOPSIS) and Vlsekriterijumska Optimimizacija I Kompromisno Resenje (VIKOR) methods are applied for best supplier selection. The results show that one of the suppliers is ranked first by both the methods. Being the highest ranked supplier by the TOPSIS method, it shows that this supplier is the best in terms of the ranking index. As the same supplier is highest ranked by VIKOR method, it shows that it is the closest to the ideal solution. Such innovative approach can bring profit maximization and quality enhancement of construction projects.

Keywords–Supplier selection; Multi criteria methods; Analytic Hierarchy Process; TOPSIS; VIKOR

1. INTRODUCTION

   Material component is more than 60% of the total cost in any construction project. Construction companies have to follow strategies to get better quality material at most economical rate with shortest lead time. Hence, supplier plays a key role in achieving success of the project. Supplier selection is a crucial strategic decision which brings long term impact on companys efficiency and profitability. The main objective of supplier selection process is to reduce purchase risk, maximize overall value to the purchaser and develop closeness and long-term relationships between buyers and suppliers [15]. Supplier selection depends upon several conflicting factors such as: Quality, cost, delivery time, technical capability, financial capability etc. Hence, it is a multi criteria decision making problem. More research is needed to suggest best supplier due to increasing complexity of projects, increasing expectations of owners, more competition and higher performance expectations. Several methods, such as Analytic Hierarchy Process [1], Analytic Network Process (ANP) [14], linear weighting methods [18] and total cost approach [12] have helped decision makers to deal with supplier selection

   problem. While selecting the supplier, his information is not always precisely studied and hence decision making could prove to be wrong. Most of the construction companies are selecting the supplier based on few criteria and that too without use of any scientific technique. Cement is one of the most important of all construction materials. It contributes for 10 to 15% of total material cost in any construction project [3]. Quality of the structure largely depends on quality of cement. Hence, best supplier selection for purchase of cement is the most crucial decision in any construction project. This paper uses three multi criteria decision making techniques such as: Analytic Hierarchy Process (AHP), Technique for order preference by similarity to ideal solution (TOPSIS) and Vlsekriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method for best supplier selection for purchase of cement in construction project.

2. LITERATURE REVIEW

   Research on supplier selection has passed through three different phases: qualitative research, quantitative research and combination of qualitative and quantitative research [20]. Weber et al. [19] proposed analytic hierarchy process to evaluate suppliers. Ghodsypour & Obrien [6] combined AHP and linear programming method to select best suppliers and allocate the optimal order quantity. Kumar et al. [11] proposed fuzzy multi- objective programming model for supplier selection problem. Jadidi et al. [8] proposed a new approach based on TOPSIS concept to deal with problem of supplier selection. Kasirian & Hong [9] integrated AHP and ANP techniques to select the best supplier. At present, many techniques like AHP, ANP, ELECTRE III, multi attribute utility theory (MAUT), goal programming, fuzzy set theory, TOPSIS, VIKOR etc. are available for supplier selection. Bhutia & Phipon used integrated approach of AHP and TOPSIS for supplier selection and found is quite effective for optimized decision making [2]. Singh et. al. used TOPSIS technique for supplier selection in Auto Industry [17]. Wu & Liu

   [20] used fuzzy vague sets incorporating TOPSIS along with VIKOR for supplier selection. Cristobal [4] used TOPSIS and VIKOR for best contractor selection along with AHP technique for weight generation of criteria. Kilic, H.S. [10] used integrated approach of fuzzy technique for TOPSIS and linear programming for supplier selection. Shemshadi et al. [16] used fuzzy logic approach along with VIKOR method for supplier selection.

   In this paper AHP technique is integrated with TOPSIS and

   VIKOR methods for supplier selection in construction project for purchase of cement. In next section of Methodology, the TOPSIS and VIKOR methods are elaborately explained.

3. METHODOLOGY

   In recent past, many researchers have used TOPSIS and

   VIKOR methods for decision making of supplier selection problem [21]. Use of these two methods can help for best supplier selection on the basis of different criteria while considering their relative importance. The TOPSIS method determines the solution by giving the shortest distance from the ideal solution and with the greatest distance from the negative-ideal solution, while not considering the relative importance of these distances. The VIKOR method determines ranking of the criteria based on the particular measure of closeness to the ideal solution [13]. The compromise solution is a feasible solution that is the closest to

   where wij = weight of the ith criterion

   Step 4: Determine the positive ideal solution and negative ideal solution.

   A*= {v1*,.,vn *} = {(maxj vij | i I' ), (minj vij | i I'')} (3)

   A = {v1,.,vn }={(minj vij | i I' ), (maxj vij | i I'')} (4)

   where I' is associated with benefit criterion and I'' is associated with cost criterion.

   Step 5: Calculate the separation measure. The separation of each alternative from the positive ideal one is given by:

   S = (vij vi )

   n

   * 2

   j

   the ideal solution, and compromise means an agreement established by mutual concessions.

   1. TOPSIS Method

      i 1

      where i = 1,2,3.m

      (5)

      Technique for order preference by similarity to ideal solution (TOPSIS) was first introduced by Hwang and Yoon [7] with an idea to offer an alternative for elimination and choice expressing reality III (ELECTRE III) method. It is on the basis of principle

      Similarly, the separation of each alternative from the negative ideal one is given by

      n

      that the optimal point should have the shortest distance from the positive ideal solution and the farthest from the negative-ideal solution. So, it is most suitable for decision makers who want to

      Sj=

      i 1

      (vij

      v _ )2

      i

      (6)

      achieve maximum profit at minimum risk. The TOPSIS method consists of following steps:

      Step 1: Prepare a decision matrix as given below: X1 X2 Xj.. Xn

      A1 x11 x12 x1j x1n A2 x21 x22 x2j x2n

      D = Ai xi1 xi2 xij xin

      : : : : :

      Am xm1 xm2 xmjxmn

      Here,

      Ai = ithalternative supplier

      Xij = Numerical evaluation outcome for ithsupplier with respect to jthcriterion

      Step 2: Calculate the normalized decision matrix with following formula:

      x

      ij

      j

      where i = 1,2,3.m

      Step 6: Calculate the relative closeness with the ideal solution. The relative closeness of Ai with respect to A*is defined as:

      i j j j i

      C * = S / (S * + S ) , 0 C * 1 (7) where i = 1,2,3.m

      i

      i

      Larger the C * value better is the performance of the alternatives. Rank the alternatives by the value of C * in decreasing order. Propose the alternative that is the best ranked by the measure.

   2. VIKOR Method

      Vlsekriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method works on the basis of the particular measure of closeness to the positive ideal solution. It gives a compromise solution that is the closest to the ideal solution, where compromise means an agreement established by mutual concessions [5]. VIKOR method has following four steps as given by Opricovic and Tzeng [13]: Step 1: Determine the best and worst values, which are known as positive ideal and negative ideal solutions:

      rij= xij /

      2 j = 1,2.j and i = 1,2n (1)

      * = max

      and = min

      j 1

      where j = number of alternatives ; i = number of criteria; and xij=

      j j ij

      th

      j j ij

      *

      value of the jth alternative for the ith criterion.

      and if i maxj ij

      function represents cost, then, j

      = minj ij and j =

      Step 3: Construct the weighted normalized decision matrix by multiplying the normalized decision matrix with its associated

      where ij

      = value of the jth alternative for the i criteria.

      weights which are derived by Analytic Hierarchy Process. The

      Step 2: Calculate the values of S and R by following equations:

      weighted normalized value vijis calculated as: j j

      vij = wij rij (2)

      n

      i i ij i i

      Sj = w ( f * f ) / ( f * f )

      i1

      (8)

      Kamal brand, Digvijay Cement Co. Ltd. (S1), Ambuja brand, Ambuja Cements Ltd. (S2), Ultratech brand, Ultratech Cement Ltd. Aditya Birla Group (S3), J K Laxmi brand, J K Laxmi Cement Ltd, J K Group (S4) and Hi-Bond brand, Hi Bond

      i i i ij i ij

      Rj = max w ( f * f ) / ( f * f ) (9)

      Here, Sj is the maximum group of utility of the majority of alternative j; Rj is a minimum of individual regret of the opponent of alternative j and wi is the weight of the criteria, which expresses the experts opinion regarding relative importance of the criteria.

      Step 3: Calculate the following values:

      j j

      S* = minj Sj ; S = maxj Sj; R* = minj Rj; R = maxj Rj

      Cement (India) Pvt. Ltd., Kishan Group of Companies (S5). To determine relative importance of criteria, AHP technique was used. Steps of AHP are explained below:

      1. Construct a pair wise comparison matrix for each criterion using a scale of 1 to 9 for their relative importance.

      2. Use Eigenvector approach of AHP: For each of the column, divide each entry in column i of A by the sum of the entries in column i. This will give new matrix called as normalized matrix in which the sum of the entries in each column is 1. Estimate Wi as the average of the entries in row i of the

         Qi = v(S

         S*) / ( S S*) (1 v)( R R*) / ( R R*)

         (10)

         matrix.

         v is introduced as a weight for the strategy of maximum group utility, whereas (1 – v) is weight of the individual regret. The solution obtained by min S is with a maximum group utility and

      3. Consistency check: Following steps are used to check the consistency of the decision makers opinion:

      4. Calculate AWT where A is the pair wise comparison matrix

         j j

         the solution obtained by minj Rj is with a minimum individual

         regret of the opponent. The value of v is taken as 0.5 however it

         and superscript T denotes transpose.

         1 n

         can be taken from 0 to 1.

         Step 4: Rank the alternatives, sorting by the values of S, R and Q in decreasing order. The results are three ranking lists. Propose as a

      5. Workout Eigen value max = in WT.

         ith

         n

         i1

         entry in AWT/ ith entry

         max n

         compromise solution the alternative A(1) which is the best ranked

      6. Calculate Consistency index (CI): CI =

         n 1

         . The

         by the measure Q (minimum), if the following two conditions are

         smaller the CI, lesser is the deviation from the consistency.

         satisfied:

         (2)

         (1)

      7. Compare CI with Random Consistency Index (RI). RI is

         1. Acceptable advantage: Q [A ] – Q [A ] DQ, where DQ = 1/ (J 1) and A(2) is the alternative with second position in the ranking list by Q.

         2. Acceptable stability in decision making: The alternative A(1) must also be the best ranked by S or/and R. This compromise solution is stable within a decision making process, which could be the strategy of maximum group utility (when v > 0.5 is needed), or by consensus (v is approximately 0.5) or with veto (v < 0.5).

            If one of the above conditions is not satisfied, then a set of compromise solutions is proposed which is given as below:

         3. Alternative A(1) and A(2) if only condition 2 is not satisfied, or

      Alternatives A(1), A(2),.. A(M) if the condition 1 is not satisfied. A(M) is determined by the relation Q [A(M) ] – Q [A(1) ] < DQ for maximum n; the positions of these alternatives are in closeness.

4. CASE STUDY

   Cement is the major building material which is required for every construction project. It consists almost 20% of total material cost of the project. There are various companies in the market which manufactures good quality cement. In this study, cement supplier selection problem is solved through TOPSIS and VIKOR method. TOPSIS and VIKOR methods were used along with Analytic Hierarchy Process (AHP) technique. AHP helps the evaluator to decide how well each supplier satisfies or scores for each criterion, while assigning weights on the basis of experts opinion.

   This study has decided 7 different criteria for best supplier evaluation: Quality (CR 1), Cost (CR 2), Delivery time (CR 3), Technical capability (CR 4), Financial capability (CR 5), Managerial & Commercial capability (CR 6) and Trust (CR 7). Various alternative suppliers for selection as the best one were:

   taken as per value given following Table. If (CI/RI) < 0.10, the degree of consistency is acceptable. If (CI/RI) > 0.10, expert is inconsistent and results may not be correct. Table 1 shows Random Consistency Index (RI) for different values of n.

   Table 1: Values of Random Index (RI)

   n	2	3	4	5	6	7	8	9	10
   RI	0	0.58	0.90	1.12	1.24	1.32	1.41	1.45	1.51

   In this study responses of 12 purchase managers were taken. They were actively involved in purchase of construction materials in varios construction organizations. Their responses were handled through AHP technique and weights were generated for each respondent. Weights of all respondents were aggregated through Geometric Mean Method (GMM) to get final aggregated weight for each criterion. Table 2 gives weights of each respondent and final aggregated weight with their Consistency Ratio (CR). It is to be noted that each respondents CR value is below 0.10.

   After deriving criteria weights with AHP process, next step is to evaluate different suppliers based on above criteria. An experienced purchase manager was asked to evaluate them on 1 to 9 scales. 9 point scale for various criterions is as given below:

   • For Quality (CR 1), Technical capability (CR 4), Financial capability (CR 5), Managerial & Commercial capability (CR

     6) and Trust (CR 7): Very poor 1, Between very poor and poor 2, Poor 3, Between poor & good 4, Good 5, Between good and very good 6, Very good 7, Between very good & extremely good 8 and Extremely good 9.

   • For Cost (CR 2): Very low 1, Between very low and low 2, Low 3, Between low & high 4, High 5, Between high

     and very high 6, Very high 7, Between very high & extremely high 8 and Extremely high 9.

   • For Delivery Time (CR 3): Very Slow 1, Between very slow and slow 2, Slow 3, Between slow & fast 4, Fast 5, Between fast and very fast 6, Very fast 7, Between very fast & extremely fast 8 and Extremely fast 9.

   Based on feedbacks of an experienced purchase manager of a construction firm, each supplier was evaluated on 1 to 9 scales for performance under seven different criteria. Table 3 gives evaluation attributes for various suppliers of cement.

   Next, the TOPSIS and the VIKOR methods are applied. From available criteria, Quality, Delivery time, Technical capability, Financial capability, Managerial & Commercial capability and Trust are beneficial attributes, so, higher values are desirable. Cost is non beneficial attribute and so lower value is desirable. Applying TOPSIS method, the normalized matrix and weighted normalized matrix as per Eqs. (1) and (2) are calculated.

   The ideal (A*) and negative-ideal (A ) solutions are calculated

   using Eqs. (3) and (4) and they are shown in Table 5. Table 6 shows the values of the separation measures (S * and S ) and the

   supplier as the lowest one, whereas VIKOR has ranked 5th supplier as the lowest one.

5. CONCLUSION

Cement plays very crucial role in success of construction projects. It contributes around 15% of total material cost. Hence, proper supplier selection for Cement is vital for performance of projects. Most of the construction companies select the supplier which offers lowest rates of materials. This may affect the project performance in longer run. In this paper, multi-criteria decision making methods like AHP, TOPSIS and VIKOR are used for the selection of best supplier for supply of cement to construction companies. The novel approach adopted in this paper considers multi-criteria in supplier selection along with their relative importance. Results show that one of the suppliers is best by TOPSIS as well as VIKOR method. TOPSIS suggests best supplier according to ranking index and VIKOR method suggests best supplier who is closest to the ideal solution. Such innovative approach can bring profit maximization and quality enhancement of construction projects.

j j

i

relative closeness to the ideal solution (C *) with reference to the

five suppliers calculated using Eqs. (5) to (7).

As Supplier 3 is having maximum value of Ci* (0.5498), he is the best supplier out of the available ones. With reference to VIKOR method, Table 7 shows the best * and the worst values

ACKNOWLEDGMENT

Authors are thankful to the participating purchase managers in giving their valuable feedbacks.

j j

of all criterion functions. The values of Sj, Rj and Qi are obtained using Eqs. (8) to (10) respectively. Sample calculations of them are as given below.

The results obtained by TOPSIS and VIKOR methods are given in Table 8. Ranking of Suppliers by the TOPSIS method gives Supplier 3 as the best one. VIKOR method finds that Supplier 3 is closest to the ideal solution. By VIKOR method, Supplier 3 is found as best one as a compromise solution as its Q is the minimum (0). In addition to this, conditions given in step 4(1) and 4(2) are satisfied as Q [A(2) ] – Q [A(1) ] > DQ (0.3135 0.25), and Supplier 3 is also best ranked by S and R value (S = 0.0584 and R = 0.0585 both are minimum). There is a difference in ranking for lowest ranked supplier. TOPSIS has ranked 2nd

Table 2: Weights of different criteria by Respondents with Consistency Ratio (CR)

Table 3: Structure of decision matrix Supplier with evaluation attributes

Table 4: Weighted normalized matrix by TOPSIS method

Table 5: Ideal (A*) and Negative-ideal (A) solutions TOPSIS method

Table 6: Separation measures (S *and S ) and Relative closeness to Ideal Solution (C *)

j j i

S1 = 0.2623( 9 7 8 6 9 9 9 9 7 7 8 8 8 7

= 0.3136

) 0.2083( ) 0.085( ) 0.1170( ) 0.0904( ) 0 .0644( ) 0.1990( )

0.1312

9 5 8 3 9 7 9 7 7 5 8 7 8 6

R1 = Max {0.2623(9 7), 0.2083(8 6), 0.0585(9 9), 0.1170(9 9), 0.0904(7 7), 0.0644(8 8), 0.1990(8 7)} =

9 5 8 3 9 7 9 7 7 5 8 7 8 6

0.3136 0.0585 0.13115 0.0585

Q1 = 0.50 0.9999 0.0585

(1 0.5)

0.2623

0.0585

= 0.3135 (v is assumed as 0.50)

The values of Si, Ri and Qiare given in Table 7. Table 7: Values of Si, Ri and Qi by VIKOR method

Table 8: Results of TOPSIS and VIKOR methods

REFERENCES

1. Barbarosoglu, G. and Yazgac, T. (1997). An application of the analytic hierarchy process to the supplier selection problem. Production and Inventory management Journal 1st Quarter. Pp. 14-21.

2. Bhutia P W & Phipon R (2012). Application of AHP and TOPSIS method for supplier selection problem, IOSR Journal of Engineering (IOSRJEN), Volo.2, Issue 10, pp.43-50, October 2012.

3. Chakraborti, M. (2001). Estimating, costing, specification & valuation in civil engineering: Principles and applications. ISBN 81-85304-36-X.

4. Cristobal, J.R.S (2012). Contractor selection using multi criteria decision making methods. Journal of Construction Engineering & Management, ASCE. June 2012. pp. 751-758.

5. Cristobal, J.R.S., Biezma, M.V., Martinez, R. Somoza, R. (2009). Selection of materials under aggressive environments : The VIKOR method. 3rd International Conference on Integrity, Reliability and Failure, Porto/Portugal, 20-24 July 2009

6. Ghodsypour, S. & Obrien, C. (1998). A decision support system for supplier selection using an integrated analytic hierarchy process and linear programming. International Journal of Poduction Economics. 56(57). pp. 199-212.

7. Hwang, C.L. and Yoon, K. (1981). Multi-attribute decision making. Lecture notes in economics and mathematical systems 186. Springer- Verlag, Berlin.

8. Jadidi, O. and Hong, T. (2008). An optimal grey based approach based on TOPSIS concepts for supplier selection problem. International Journal of Management Science and Engineering Management. 4(2). pp. 104-117.

9. Kasirian, M. Mohd, R., and et al (2010). Application of AHP and ANP in supplier selection process-a case in an automotive company. International Journal of Management Science and Engineering Management. 5(2). pp. 125-135.

10. Kilic, H.S. (2013). An integrated approach for supplier selection in multi-item/multi-supplier environment. Appl. Math. Modelling. doi. http://dx.doi.org/10.1016.j.apm.2013.03.010

11. Kumar, M., Vrat, P. and Shankar, R. (2004). Fuzzy programming approach for vendor selection problem in supply chain. Computer & Industrial Engineering. 46(1). pp. 69-85.

12. Mozenka, R.M. & Trecha, S.J. (1998). Cost-based supplier performance evaluation. Journal of purchasing and materials management. 24(2). pp. 2-7.

13. Opricovic, S. and Tzeng, G.H. (2004). Compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS. European Journal of Operations Research. 156(2). pp. 445-455.

14. Sarkis, J. & Taluri, S. (2000). A model for strategic supplier selection,

    Proceedings of ninth International Conference on IPSERA. Pp. 652-661.

15. Shahroudi, K. & Tonekaboni, S.M. (2012). Application of TOPSIS method to supplier selection to Iran auto supply chain. Journal of Global Strategic Management. Dec. 12, pp. 123-131.

16. Shemshadi, A., Shirazi, H., Toreihi, M., Tarokh, M.J. (2011). A fuzzy VIKOR method for supplier selection based on entropy measure for objective weighting. Expert Systems with Applications. 38(2011). pp. 12160-12167.

17. Singh R, Rajput H & Chaturvedi V (2012). Supplier selection by Technique of Order Preference By Similarity to Ideal Solution (TOPSIS) method for Automotive Industry, International Journal of Advanced Technology & Engineering Research (IJATER), Vol.2, Issue 2, March 2012.

18. Thompson, K.N. (2000). Vendor profile analysis. Journal of purchasing and material management. 26(1). pp. 11-18.

19. Weber, C., Current, J. and Benton, W. (1991). Vendor selection criteria and methods. European Journal of Operational Research. 50(1). pp. 2- 18.

20. Wu, M. & Liu, Z. (2011). The supplier selection application based on two methods: VIKOR algorithm with entropy method and Fuzzy TOPSIS with vague sets method. International Journal of Management Science and Engineering Management. 6(2), pp. 110-116.

21. Zammori, F.A., Braglia, M., and Frosolini, M. (2009). A fuzzy multi- criteria approach for critical path definition. International Journal of Project Management. 27(3). pp. 278-291.