supplier selection using ahp and copras method

21th International Scientific Conference SM2016

Strategic Management and Decision Support Systems in Strategic Management Topic

Strategic management – determinants of development and business efficiency

Željko Stević

University of East Sarajevo, Faculty of Transport and Traffic Engineering, Doboj, Bosnia and Herzegovina [email protected]

658.7:519.8

SUPPLIER SELECTION USING AHP AND COPRAS METHOD Abstract: An efficient procurement necessary for production logistics subsystem, definitely affects the overall efficiency of a company’s business. The aim of the this research is evaluation and selection of suppliers. The selection is made among five companies based on five criteria applying the combined AHP-COPRAS model. A very important thing in solving this type of problems is the importance of certain criteria, which can greatly affect the final solution. The study applies the AHP method for the determination of criterion importance, and the use of COPRAS method provides a final solution. It is vital to make the right decision when selecting a supplier, because the optimal choice ensures lower cost and higher quality of the product itself, and therefore more competitiveness in the market. Keywords: Supplier, multi-criteria analysis, AHP, COPRAS

1. INTRODUCTION The application of multi-criteria analysis is very popular, especially recently when more attention has been paid to making the right decisions. It is used to solve different types of problems, and is widely used in management, where certain decisions are made on the basis of multi-criteria methods. The biggest challenge is making the right decisions that will enable efficient business, on the one hand, and fulfill more criteria, on the other. Today, procurement logistics plays a very important role in the supply chain, so its optimization enables a significant effect on the entire logistics system (Stević, Božičković and Mićić, 2015). Logistics gives an answer to question how to rationalize something, therefore, the aim of this paper is improvement of the supply process throughout ranking and selection of optimal supplier. To ensure the continuous manufacturing flow, it is necessary to timely obtain the required components and materials, taking into account the optimization of costs caused by this subsystem of logistics. The research object is a company engaged in the manufacture of pre-insulated pipes which requires the procurement of steel. For the purpose of suppliers’ evaluation, this paper uses the combination of methods of mulit-criteria analysis. Analitical hierarchy proccess (AHP) had been used for determination of significance of criteria, which compares criteria based on Saty’s scales for comparison, while COPRAS method was used for alternatives’ ranking.

2. LITERATURE REVIEW Multi-criteria analysis is rapidly expanding, especially during the past several years, and therefore, big number of problems is being solved nowadays using methods from that area. It is being used for solving problems of

diferent nature, it is also greatly accepted and used in the area of management and logistics, where certain decisions are being made exactly on the base of multi-criteria methods. Literature and various publications dealing with these or issues similar to ones from this paper, there can be found great number of criteria for supplier evaluation. However, one question arises: how to make right selection from certain group, which will assist in finding the best solution. Some authors (Weber, Current and Benton, 1991) tried to answer this question at the end of last century, so they examined criteria for selection of supplier in production and retail trade surrounding. Criteria’s were given in 74 documents published between 1966 and 1991. Group of authors came to conclusion that following criteria are dominant: quality, delivery and price; while geographic location, finacial status and production capacities belong to secondary group of factors. Then, (Verma and Pullman, 1998) commenced examination among big number of managers with the aim to examine in which way to make compromise during supplier selection. Their research pointed out that managers are paying the most attention to the quality as the most important suppliers’s attribute, before delivery and price. Research about influence of criteria in the supply chain is continuing on during the beginning of this century as well, so (Karpak, Kumcu and Kasuganti 2001) took reliability of delivery as a criteria for choice making while (Bhutta and Huq, 2002) used four criteria for evaluation of suppliers: price, quality, techniology and service. The AHP method was used even earlier to solve the problem of supplier selection (Nydick and Hill, 1992), (Barbarasoglu and Yazgac, 1997), (Handfield, Ragatz, Peterson and Monczka, 1999), (Narasimhan, 1983) and (Masella and Rangone 2000).

3. THE PROBLEM POSTULATE AND THE METHODOLOGY To select the most suitable solution, we use a combination of multi-criteria analysis methods. To determine the importance of criteria, we use Analytic Hierarchy Process that compares the criteria using the Saaty Scale (Saaty, 1980), while for the selection of the most acceptable solution of the set, we use the COPRAS method. Table 1 shows the characteristics of potential companies and the criteria by which it is necessary to make a decision: price per length meter, pipe length, delivery time, payment method and mode of transportation on the basis of which it should be decided on the most suitable company to obtain steel pipes in order to ensure the continuous manufacturing flow. The potential solutions are the companies presented in Table 1, of which three are located in the territory of Bosnia and Herzegovina, and the other two in the territory of Serbia. Table 1. The characteristics of potential suppliers Supplier 1 Supplier 2 Price per length 78.3 88.55 meter [BAM/m] Pipe length [m] 12 12 Delivery time [day] immediately immediately 100% in 100% in Payment method advance, 45 advance days delayed Mode of without without transportation

Supplier 3

Supplier 4

Supplier 5

89.59

91

95.5

11.60-11.70 5-7 70% in advance, the rest to 30 days

5.8-6.2 3

10-12 30 50% in advance and 50% prior to delivery

with

100% in advance with

without Source: Author

Price per length meter is expressed in convertible marks (BAM), pipe length in meters and delivery time in days. The payment method for all alternatives is an advance payment, with certain differences depending on the alternatives. So, for the alternative one and four we have 100% advance payment without a possibility of different arrangements, while for the alternative two it can be 100% in advance or 45 days delayed providing a bank guarantee. The alternative three requests 70% in advance and the rest to 30 days, while the alternative five offers 50% in advance and 50% prior to delivery, i.e. the ability to pay in 30 days, because they need that much time to deliver the material. Referring to the mode of transportation, the alternatives three and four provide transportation that is not charged separately i.e. it is included in the price of materials, and in the procurement of materials for other alternatives, transportation must be provided by company which is object of research.

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4. DETERMINATION OF WEIGHT COEFFICIENTS USING THE AHP METHOD Analytic Hierarchy Process is a method which consists of the decomposition of problems into the hierarchy, where the target is located at the top, then criteria, sub-criteria and a set of potential solutions. It is used extensively for decision making in management, which is confirmed by (Konstantinos, 2014). The Analytic Hierarchy Process (AHP) developed by (Saaty, 1980) and, AHP is a theory of measurement by pairwise comparisons and relies on the opinion of experts to derive priority scales. Saaty in (Saaty, 1986), defined the axioms which the AHP is based on: the reciprocity axiom. If the element A is n times more significant than the element B, then element B is 1/n times more significant than the element A; Homogeneity axiom. The comparison makes sense only if the elements are comparable, e.g. weight of a mosquito and an elephant may not be compared; Dependency axiom. The comparison is granted among a group of elements of one level in relation to an element of a higher level, i.e. comparisons at a lower level depend on the elements of a higher level; Expectation axiom. Any change in the structure of the hierarchy requires re-computation of priorities in the new hierarchy. Some of the key and basic steps in the AHP methodology according to (Vaidya and Kumar, 2006) are as follows: to define the problem, expand the problem taking into account all the actors, the objective and the outcome, identification of criteria that influence the outcome, to structure the problem previously explained hierarchy, to compare each element among them at the appropriate level, where the total of nx(n-1)/2 comparisons is necessary, to calculate the maximum value of own vector, the consistency index and the degree of consistency. Let {A1, A2, ..., An} be n alternatives, and {w1, w2,...,wn} be their current weights. The pairwise comparison is conducted by usage the scale (1–9), (Saaty, 1980). A pairwise comparison matrix that is defined as follows:

(1)

This matrix A=[aij] represents the value of the expert's preference among individual pairs of alternatives (Ai versus Aj for all i, j = 1,2,...,n). After this, the decision-maker compares pairs of alternatives for all the possible pairs. Based on that, the comparison matrix A is obtained, where the element aij shows the preference weight of Ai obtained by comparison with Aj.

(2)

The aij elements estimate the ratios wi / wj, where w is the vector of current weights of the alternative. The matrix has reciprocal properties, which are aji=1/aij. The matrices are formed after all pairwise comparison and the vector of weights w=[w1,w2, . . . ,wn] is computed on the basis of Satty’s eigenvector procedure in two steps. First, the pair-wise comparison matrix, A = [aij]nxn, is normalized, and then the weights are computed. Normalization: (3) for all j = 1,2,..., n. Weight calculation: (4) for all j = 1,2,..., n.

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The consistency of the pairwise matrix (CI) is checked for a valid comparison. (5) where λmax is an important validating parameter in AHP and is used as a reference index to screen information by calculating the Consistency Ratio (CR) of the estimated vector. CR is calculated by using the following equation: (6) where RI is the random consistency index obtained from a randomly generated pairwise comparison matrix. This coefficient is recommended depending on the size of the matrix, so we may find in the papers (Lee, Chen and Chang, 2008; Anagnostopoulos, Gratziou and Vavatsikos, 2007) that the maximum allowed level of consistency for the matrices 3x3 is 0.05, 0.08 for matrices 4x4 and 0.1 for the larger matrices. If the calculated CR is not of the satisfactory value, it is necessary to repeat the comparison to have it within the target range (Saaty, 2003). In order to apply the COPRAS method for obtaining the most suitable solution, it is necessary to determine the significance of the criteria, i.e. their weight values. First, it is necessary to compare criteria in order to determine priorities. Table 2. The comparison of criteria K2 K3 K4 K5 K1 K1 K2 K3 K4 K5

1 5 5 1/3 1/7

1/5 1 1 1/5 1/9

1/5 1 1 1/5 1/7

3 5 5 1 1/5

7 9 7 5 1

Source: Author

The comparison of the pairs of criteria was completed in relation to current needs and demands of the market. The workers from the commercial service of company, which was the subject of the research, were included in a criterion comparison process. After the comparison of criteria, we obtained results shown in Figure 1 where we can see that the most important are two criteria, the length of the pipe with the level of significance of 0.385, and the second most important criterion is the time of delivery, which has slightly lower priority with the level of significance of 0.374. The other three criteria have much lower priority than the previous two mentioned. It is important to note that the sum of all values of the criteria must be equal to one.

Picture 1. The significance of criteria Source: Author

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AHP is one of popular methods and it has the ability to identify and analyze the subjectivity of decision-makers in the estimation and evaluation process of hierarchy elements. A man is rarely consistent in assessing the value or relation of the quality elements in the hierarchy. AHP in a specific way solves this problem by measuring the degree of consistency and inform decision-makers about that. The degree of consistency regarding the comparison of criteria is 0.09, which means that the results are valid because it is lower than 0.10 (if the results are in the range of up to 0.10, they are considered to be valid).

5. RANKING ALTERNATIVES USING COPRAS METHOD The COPRAS (COmplex PRoportional ASsessment) method is presented by (Zavadskas, Kaklauskas and Sarka, 1994). Description of COPRAS methods and possibilities of its application are published in a large number of papers (Zavadskas, Kaklauskas and Kvederytė 2001), (Vilutiene and Zavadskas, 2003), (Kaklauskas, Zavadskas, Raslanas, Ginevicius, Komka and Malinauskas, 2006). Ranking alternatives by the COPRAS method assumes direct and proportional dependence of significance and priority of investigated alternatives on a system of criteria (Ustinovichius, Zavadkas and Podvezko, 2007). The determination of significance and priority of alternatives, by using COPRAS method, can be expressed concisely using next steps: Step 1. Set the initial decision matrix, X.

(7) where xij is the assessment value of i-th alternative in respect to j-th criterion, m is the number of alternatives and n is the number of criteria.

Step 2: Normalize the decision matrix using linear normalization procedure. In MCDM process, criteria usually have different units of measure. In order to transform performances of considered alternatives into comparable dimensionless values, normalization procedure is used. An overview of some of the most important multi-criteria methods, and their normalization procedures, is shown in (Ginevicius, 2007). For normalization in COPRAS method the following formula is used: (8) Normalized decision matrix is:

Step 3. Determine the weighted normalized decision matrix D, by using the following equation: (9)

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where rij is the normalized performance value of i-th alternative on j-th criterion and wj is the weight of j-th criterion. The weighted normalized decision matrix is:

The sum of weighted normalized values of each criterion is always equal to the weight for that criterion:

(10) Step 4: In this step the sums of weighted normalized values are calculated for both the beneficial and nonbeneficial criteria by using the following equations:

(11)

(12)

where y+ij and y-ij are the weighted normalized values for the beneficial and non-beneficial criteria, respectively. Step 5. Calculation of the relative weight of each alternative. The relative weight Qi of i-th alternative is calculated as follows:

.

(13)

Formula (13) can also be written in simplified form as follows:

(14)

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Step 6. Determine the priority order of alternatives. The priority order of compared alternatives is determined on the basis of their relative weight. The alternative with higher relative weight has higher priority (rank), and the alternative with the highest relative weight is the most acceptable alternative.

  A* =  Ai max Qi  . i  

(15)

In decision making like this it is necessary to consider the impact of multiple-criteria, which usually have different significance. According (Popovic, Stanujkic and Stojanovic, 2012) COPRAS method provides an effective and understandable procedure for such purposes. By applying previously methodology result presented by previous matrix and supplier two is optimal solution, because has the largest value. Same results is obtained in (Stević, Alihodžić, Božičković, Vasiljević and Vasiljević, 2015), where author's AHP used for assessing the weight criteria, and Topsis method for obtaining the final ranking of alternatives.

6. CONCLUSION Procurement's logistics in today's modern age is a very important factor in the complete supply chain, so its optimization can ascertain certain effect on the entire logistics system. Today, making decisions which will, on one side lessen the expenses, and on the other side fulfill user’s needs, certainly represents a challenge. Accordingly, decision makers are bearing great responsibility when modeling supply chain which includes the above mentioned. Company must strive to enlarge the quality of product itself, so the end user is satisfied with provides services, what would make him a loyal user. Due to above mentioned, it is necessary, during the first phase of logistics, ie. purchasing logistics, to commit good evaluation and choice of supplier, what can largely influence the forming of product’s final price and in that way accomplish significant effect in complete supply chain Therefore, evaluation of suppliers using the combination of multi-criteria methods, can bring clearer picture about all potential suppliers, their advantages and weaknesses.

REFERENCES Anagnostopoulos, K. P., Gratziou, M., & Vavatsikos, A. P. (2007). Using the fuzzy analytic hierarchy process for selecting wastewater facilities at prefecture level. European Water, 19(20), 15-24. Barbarosoglu, G., & Yazgac, T. (1997). An application of the analytic hierarchy process to the supplier selection problem. Production and inventory management journal, 38(1), 14. Bhutta, K. S., & Huq, F. (2002). Supplier selection problem: a comparison of the total cost of ownership and analytic hierarchy process approaches. Supply Chain Management: An International Journal, 7(3), 126-135. Ginevičius, R. (2008). Normalization of quantities of various dimensions. Journal of business economics and management, 9(1), 79-86. Handfield, R. B., Ragatz, G. L., Peterson, K., & Monczka, R. M. (1999). Involving suppliers in new product development?. California management review,42, 59-82.

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Kaklauskas, A., Zavadskas, E. K., Raslanas, S., Ginevicius, R., Komka, A., & Malinauskas, P. (2006). Selection of low-e windows in retrofit of public buildings by applying multiple criteria method COPRAS: A Lithuanian case. Energy and Buildings, 38(5), 454-462. Karpak, B., Kumcu, E., & Kasuganti, R. R. (2001). Purchasing materials in the supply chain: managing a multiobjective task. European Journal of Purchasing & Supply Management, 7(3), 209-216. Konstantinos, P. (2014). The Analytical Hierarchical Process. International Hellenic University. Lee, A. H., Chen, W. C., & Chang, C. J. (2008). A fuzzy AHP and BSC approach for evaluating performance of IT department in the manufacturing industry in Taiwan. Expert systems with applications, 34(1), 96-107. Masella, C., & Rangone, A. (2000). A contingent approach to the design of vendor selection systems for different types of co-operative customer/supplier relationships. International Journal of Operations & Production Management, 20(1), 70-84. Narasimhan, R., (1983). An analytic approach to supplier selection. Journal of Purchasing and Supply Management 1, 27-32. Nydick, R. L., & Hill, R. P. (1992). TJsing the Analytic Hierarchy Process to Structure the Supplier Selection Procedure. Popovic, G., Stanujkic, D., & Stojanovic, S. (2012). Investment project selection by applying copras method and imprecise data. Serbian Journal of Management, 7(2), 257-269. Saaty, T. L. (1980).„The Analytic Hierarchy Process”, Mc Graw‐Hill, NewYork Saaty, T. L. (1986). Axiomatic foundation of the analytic hierarchy process. Management science, 32(7), 841-855. Saaty, T. L. (2003). Decision-making with the AHP: Why is the principal eigenvector necessary. European journal of operational research, 145(1), 85-91. Stević Ž., Alihodžić A., Božičković Z., Vasiljević M., Vasiljević Đ. (2015). Application of combined AHP-TOPSIS model for decision making in management. 5th International conference „Economics and Management -based On New Technologies“, Serbia 33-40 Stević Ž.; Božičković Z.; Mićić B. (2015). Optimization of the import of Chipboard - a case study, International Journal of Engineering, Business and Enterprise Applications, 14(1), September-November, pp. 19-23 Ustinovichius, L., Zavadkas, E. K., & Podvezko, V. (2007). Application of a quantitative multiple criteria decision making (MCDM-1) approach to the analysis of investments in construction. Control and cybernetics, 36(1), 251. Vaidya, O. S., & Kumar, S. (2006). Analytic hierarchy process: An overview of applications. European Journal of operational research, 169(1), 1-29. Verma, R., & Pullman, M. E. (1998). An analysis of the supplier selection process. Omega, 26(6), 739-750. Vilutienė, T., & Zavadskas, E. K. (2003). The application of multi-criteria analysis to decision support for the facility management of a residential district. Journal of Civil Engineering and Management, 9(4), 241-252. Weber, C. A., Current, J. R., & Benton, W. C. (1991). Vendor selection criteria and methods. European journal of operational research, 50(1), 2-18. Zavadskas, E. K., Kaklauskas, A., & Kvederytė, N. (2001). Multivariant design and multiple criteria analysis of a building life cycle. Informatica, 12(1), 169-188. Zavadskas, E. K., Kaklauskas, A., & Sarka, V. (1994). The new method of multicriteria complex proportional assessment of projects. Technological and Economic Development of Economy, 1(3), 131-139.

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