Sara Havrlišan*, Katica Šimunović, Tomislav Šarić, Goran Šimunović, Danijela Pezer, Ilija Svalina, Ivan Majdančić
Mechanical Engineering Faculty in Slavonski Brod, Josip Juraj Strossmayer University of Osijek, Croatia
* Corresponding author e-mail: sara.havrlisan@sfsb.hr Abstract
With the main aim of selecting the optimal supplier of plastic joinery, in the present study two well-known multiple criteria decision making methods, namely Analytical Hierarchy Process (AHP) metho-dology and additive method, were applied. Four al-ternatives, i.e., four suppliers were evaluated accor-ding to the suggested criteria: price, delivery time and after-treatment following the installation of joinery. The results obtained by the AHP methodo-logy and additive method were compared, and con-clusions on the effect of each criterion weight were adopted.
Keywords: AHP methodology, additive method, supplier selection
1. Introduction
Supplier selection is a process of choosing the right supplier which can provide the right quality of products/services at the right price, in the right quantities and at the right time [1, 2]. The process is complex, primarily because of the involvement of many, sometimes conflicting qualitative and quantita-tive criteria. Due to the complexity of the process, different decision-making methods have been often used. On the basis of a detailed review of the literature in [3], it is concluded that 26 decision-making methods have been used in suppliers’ selection. These methods are divided into 3 groups: multi-criteria decision-making, mathematical programming and artificial intelligence methods. The selection of suppliers is primarily considered as a multi-criteria problem and the most commonly used methods of multiple criteria decision making have been applied as follows: AHP, ANP, ELECTRA, PROMETHEE, TOP-SIS, DEMATEL, VIKOR, and SMART [3]. For the pur-pose of systematic evaluation of suppliers, criteria and mul-tiple criteria AHP model for selecting the best supplier have been proposed in the paper [4]. The model is illustrated by the example of supplier selection to purchase parts for assembly of the agricultural machine. Fuzzy AHP method is used when selecting the most suitable suppliers in the aviation industry and is based on 6 criteria: cost /price, product quality, delivery, financial stability, cor-porate social responsibility and assortment [5].
In the paper [6], the selection of the best supplier was applied in the automotive industry, where the weight of each criterion is determined by fuzzy ANP method. The authors of the paper [7], investigating also the selection of the most appropriate supplier in
the automotive industry, have compared the two methods: Fuzzy AHP and Fuzzy TOPSIS. AHP method and the additive method (the last one also known as simple additive weights-SAW as well as weighted property method-in the field of optimal material selection) are applied and compared for the selection of optimal alternative of stock material [8].
In this paper, AHP methodology [9, 10] and addi-tive method [11] are applied and compared in the selection of supplier of plastic joinery based on the three defined criteria: price, delivery time and offer of after-treatment following the installation of joinery (further the term after-treatment will be used).
2. Description of the used methods Analytical hierarchy process
Analytical hierarchy process (AHP) methodology is developed by Thomas Saaty [9, 10]. This metho-dology is based on the decomposition of defined decision problem to the hierarchy structure. The hierarchy structure is a tree-like structure which con-sists of the main goal at the top of the hierarchy (the first level), followed by the criteria and sub-criteria (also sub-sub-criteria) and finally by the alternatives at the bottom of hierarchy (the last level).
The goal presents the optimum solution of the de-cision problem. It can be the selection of the best alternative among many feasible alternatives. Also, the ranking of all alternatives can be performed, by obtaining the priorities. Criteria (sometimes called objectives or attributes) are the quantitative or qualitative data (judgments) for evaluating the alternatives. The weights of the criteria present the relative importance of each criterion compared to the goal. Finally, alternatives present the group of feasible solutions of the decision problem. Alter-natives are evaluated against the set of criteria.
AHP methodology consists of the following basic steps [9, 10]:
- Decomposition of the defined decision problem to the hierarchic structure - building an AHP model with the overall goal at the top of the hierarchy (the first level), the evaluation criteria and finally the alternatives at the bottom of the hierarchy (the last level).
- Pair wise comparisons of the criteria and alterna-tives based on the Saaty’s scale of numbers from 1 to 9 (Table 1). The value 1 means equal impo-rtance of two criteria (or alternatives), while the value 9 stands for extreme importance of one
S. Havrlišan, K. Šimunović, T. Šarić, et al. 149
criterion (or alternative) to another. Pair wise com-parisons of the criteria are performed with respect to the goal or criteria at higher level. The weights of the criteria present the ratio of how much more important is one criterion than another, with respect to the goal or criterion at higher level. Pair wise comparisons of the alternatives are performed against each criterion and present the ratio of how much more important is one alternative than another, taking into account each criterion. The local priorities of alternatives are derived. Testing the consistency of subjective judgments is also performed (further explained).
- Synthesizing the results by the calculation of the total priorities of alternatives. The total priority of each alternative is calculated by the multiplication of the local priority of alternative by the weight of corresponding criterion and then summing all the products for each criterion. Example of calculation of total priority of alternative (considering three criteria) is shown by Equation (1).
p=a∙x+b∙y+c∙z (1)
where:
p – total priority of the alternative
a, b, c – local priorities of the alternative for the first, second and third criterion, respectively x, y, z, – weights of the first, second and third
criterion, respectively.
Sensitivity analysis can be also performed and it gives the response of the alternative priorities to the change of the input data. Furthermore, AHP methodology allows monitoring the consistency of assessments at any time of the pair wise compari-son, by the use of consistency index and consis-tency ratio [9, 10].
Table 1. Saaty’s scale for pair wise comparisons Scale Description of the importance
1 equal
3 moderate
5 strong
7 very strong
9 extreme
2, 4, 6, 8 intermediate values Additive method
Additive method [11], also known as simple addi-tive weights - SAW, uses normalized weights (weig-hting factors) of criteria multiplied by the normalized (or transformed) values of criteria. The alternative with the maximal value of the score will be the best alternative. A term or a version of additive method, called weighted properties (property) method, or weighted properties index method has been often used in the field of optimal material selection.
If we compare the terminology of weighted pro-perties method and AHP methodology and other decision making methods, the term properties is equivalent to the term criteria.
This method is very useful when there are a lot of important criteria (properties) to compare and evaluate. Scaled (normalized, transformed) value of the ith criterion (SVi) is multiplied by the weighting factor (Bi) (see Equation 2). The sum of multiplied scaled values of criteria and weighting factors represents the performance index of the jth alternative (Vrj), see Equation (2).
Vrj=�Bi k i=1
∙Svi→max. (2)
where:
Vrj – performance index or overall score Bi – weighting factor, weight of criterion SVi – scaled criterion value
k – number of criteria.
Weighting factor Bi or weight of criterion represents the relative importance of the criteria according to the defined objective. This factor is determined by using the experience, the digital-logic method or some other methods (for instance Fuller triangle or decision makers can introduce arbitrary numbers for the weighting factors). Digital-logic method, which will be applied in the present study, is based on the comparison of criteria, where more important criterion has mark 1, and less important one has mark 0. After that, for every criterion the number of positive decisions is determined.
Weighting factor for the criterion is the ratio of the number of positive decisions and the total number of decisions, which is presented by Equation (3).
The total number of decisions=k(k-1)
2 (3) Scaled values of the criteria are applied because of more reliable comparison of the criteria with different units of measurements. Equation (4) represents the dimensionless scaled criterion value for the criteria where a lower value is desirable (for example costs, mass loss, etc.).
Sv= minimum value in the list
numerical value of the criterion (4) Equation (5) represents the dimensionless scaled criterion value for the criteria where a higher value is desirable (for example hardness, tensile strength, etc.).
Sv=numerical value of the criterion
maximum value in the list (5) All the criteria data are transformed to the 0 - 1 scale (or 0 – 100, with multiplying by 100). The criterion with the value 1 (or 100) is the best criterion for the particular alternative.
3. Supplier selection
According to the given suppliers’ offers, the selection of the best supplier of plastic joinery is performed in this section. The two above-mentioned Application of AHP and Additive Method in Supplier Selection
150
multi-criteria decision making methods will be applied considering the three criteria shown in Table 2. Referring to Table 2, it is evident that:
- Suppliers 1 and 2 have offered the after-treatment included in the offered price
- Supplier 3 has the shortest delivery - Supplier 4 has offered the lowest price.
To make decision about the best supplier, AHP and additive methods will be used to assist in objective decision making.
Supplier selection by the use of AHP methodology The hierarchy model of the supplier selection problem consisting of the main goal at the top of the hierarchy, followed by the three criteria and finally by the four alternatives at the bottom of the hierarchy (the last level) is presented in Figure 1.
Table 2. Suggested criteria and corresponding values for different suppliers
Supplier 1 Supplier 2 Supplier 3 Supplier 4
Price, € 1957 1433 1230 1140
Delivery term, days 28 30 25 35
After-treatment/grade* YES/5 YES/5 NO/1 YES, but not included in the price/3
*1 – the worst grade; 5 – the best grade
Figure 1. AHP model for supplier selection After AHP model is defined, the weights of each
proposed criterion by the pair wise comparison (Table 3) using Saaty’s scale (Table 1) have to be obtained as well as local and total priorities of alternatives (suppliers). Local priorities of suppliers are calculated by pair wise comparisons of alternatives with respect to each criterion, using Saaty’s scale. Total priority for every alternative is calculated by Equation (1).
Table 3. Pair wise comparisons of criteria Price Delivery
term After-treatment
Price 1 3 2
Delivery term 1/3 1 1/3
After-treatment 1/2 3 1
∑ 11/6 7 10/3
Normalised matrix presented in Table 4 is used for the calculation of the criteria weights according to the methodology described in the previous section. This matrix is obtained by dividing each value from the Table 3 by the sum of the appropriate column. The criterion weight is the average value of the related row in Table 4. It can be seen from Table 4 that the criterion price has the highest weight, while the criterion delivery term has lower weight than the criterion after-treatment.
Table 4. Normalised matrix and criteria weights Price Delivery
term
After-treatment Weight
Price 6/11 3/7 3/5 0.525
Delivery term 6/33 1/7 1/10 0.142 After-treatment 3/11 3/7 3/10 0.333 According to the AHP methodology, the next step is the comparison of the alternatives related to each criterion and the calculation of local priorities, which is shown in Tables 5, 6 and 7. Total priority of each alternative which is shown in Table 8 is calculated on the basis of the Equation 1.
The highest total priority has supplier 2 as well as supplier 3. These suppliers offer the prices which are not the highest and there is a moderate difference between them; delivery terms are not the longest and there is a moderate difference between them. But, there is a strong difference between the grades for the criterion after-treatment. Supplier 2 offers after-treatment, as well as the supplier 1 (but this supplier offers the highest price). Contrary, supplier 3 doesn’t offer after-treatment (but this supplier offers low price and the shortest delivery time). On the basis of the results of the digital-logic method the criteria weights are calculated (Table 9).
Supplier selection
Price Delivery term After-treatment
Supplier 1 Supplier 2 Supplier 3 Supplier 4
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Table 5. Pair wise comparison of alternatives with respect to the criterion “price”
Supplier 1 Supplier 2 Supplier 3 Supplier 4 Local priority
Supplier 1 1 1/2 1/3 1/4 0.100
Supplier 2 2 1 1/2 1/2 0.185
Supplier 3 3 2 1 1 0.345
Supplier 4 4 2 1 1 0.370
Table 6. Pair wise comparison of alternatives with respect to the criterion “delivery term”
Supplier 1 Supplier 2 Supplier 3 Supplier 4 Local priority
Supplier 1 1 1 1 3 0.297
Supplier 2 1 1 1/2 2 0.225
Supplier 3 1 2 1 4 0.377
Supplier 4 1/3 1/2 1/4 1 0.100
Table 7. Pair wise comparison of alternatives with respect to the criterion “after-treatment”
Supplier 1 Supplier 2 Supplier 3 Supplier 4 Local priority
Supplier 1 1 1 5 3 0.394
Supplier 2 1 1 5 3 0.394
Supplier 3 1/5 1/5 1 1/2 0.075
Supplier 4 1/3 1/3 2 1 0.137
Table 8. Criteria weights, local and total priorities of alternatives Alternative Criteria and criteria weights
Total priority Price Delivery term After-treatment
0.525 0.142 0.333
Supplier 1 0.100 0.297 0.394 0.225
Supplier 2 0.185 0.225 0.394 0.260
Supplier 3 0.345 0.377 0.075 0.260
Supplier 4 0.370 0.100 0.137 0.255
Table 9. Pair wise comparisons of criteria by the use of digital-logic method
Criterion Comparison of criteria Total
grade Weight
Price 1 1 2 2/3=0.667
Delivery term 0 0 0 0/3=0
After-treatment 0 1 1 1/3=0.333
Supplier selection by the use of additive method Criteria scaled values (obtained by Equations (4) and (5)), weights and overall scores calculated by the Equation (2), are presented in Table 10. The highest overall score has supplier 4 as well as supplier 2 (the difference is negligible).
Table 10. Criteria scaled values, weights and overall scores
Supplier 1 Supplier 2 Supplier 3 Supplier 4 Criterion weight
Price 0.58 0.79 0.93 1 0.667
Delivery term 0.89 0.83 1 0.71 0
After-treatment 1 1 0.20 0.60 0.333
Overall score (Vr) 0.71986 0.85993 0.68691 0.8668
4. Discussion
When comparing the selection of the best supplier by the use of these two methods, it is remarkable that they give the same ranking of the criteria weights. The criterion price has the highest weight, while the criterion delivery term has lower weight than the criterion after-treatment. But the values of criteria weights are not the same influencing the final result (ranking of alternatives, i.e. suppliers). Saaty’s scale containing 9 numbers for pair wise comparisons has given the following weights for the criteria price, delivery term and after-treatment: 0.525, 0.142 and 0.333, respectively. By the use of digital-logic method containing only 2 numbers (1 and 0), which is actually black and white approach, the weights for the criteria price, delivery term and after-treatment are as follows:
0.667, 0 and 0.333, respectively. In that case, the cri-terion delivery term had never been more important when comparing with other two criteria (price and after-treatment) and the corresponding weight was zero. As a result, the ranking of suppliers by the use of two applied methods is different. When considering the AHP methodology, suppliers 2 and 3 are the best.
However, when applying the additive method supplier 4 was the best. But, here the overall score for supplier 2 (the best alternative obtained by the AHP methodo-logy too) is very close to the overall score of supplier 4.
From that reason, the black and white approach of digital logic method is further overcome by the use of the arbitrary numbers for the weighting factors (five point scale assigned to criteria, where 5 is the best grade, and contrary, 1 is the worst grade). The weight of a particular criterion is obtained by dividing the
Application of AHP and Additive Method in Supplier Selection 152
grade by the sum of the grades for all the criteria, which is shown in Table 11.
Table 11. Using of arbitrary numbers for weights Price Delivery term After-treatment
Grade 5 2 4
Weight 5/11=0.46 2/11=0.18 4/11=0.36 In this way, by combining these weights with the scaled values from the Table 10, the ranking of alternatives is as follows: supplier 2 (overall score 0.87), supplier 4 (overall score 0.8), supplier 1 (overall score 0.78) and supplier 3 (overall score 0.68). The second approach can be the integration of the criteria weights obtained by the use of AHP methodology and scaled or transformed values of the criteria. The used approaches are shown in
Table 12, where overall scores 1, 2 and 3 are obtained by the use of Equation (2).
The weights obtained by the digital-logic method (weight 1), use of arbitrary numbers (weight 2) and by Saaty’s scale (weight 3) are multiplied by the scaled values of criteria. The total priorities of the alternatives obtained by the original AHP met-hodology are presented in the last row of Table 12.
Since the supplier 2 has obtained the highest scores for four times (of four available), the decision can be made that this supplier will be chosen for the cooperation. This supplier offers after-treatment included in the price and the acceptable delivery time. The price is not the lowest, but is considerable lower than the offered price of the supplier 1 and not very different from the suppliers 3 and 4.
Table 12. Comparison of the different approaches
Supplier 1 Supplier 2 Supplier 3 Supplier 4 Weight 1 Digital-logic Weight 2
Arbitrary numbers Weight 3 Saaty’s scale
Price 0.58 0.79 0.93 1 0.667 0.46 0.525
Delivery term 0.89 0.83 1 0.71 0 0.18 0.142
After-treatment 1 1 0.2 0.6 0.333 0.36 0.333
Overall score 1 0.71986 0.85993 0.68691 0.8668 Overall score 2 0.787 0.8728 0.6798 0.8038 Overall score 3 0.76388 0.86561 0.69685 0.82562 Original AHP method 0.225 0.260 0.260 0.255 5. Conclusion
At the present, there are a lot of multiple criteria decision making methods widely applicable over many fields and areas of human endeavour. How-ever, two very important problems can exist: how to determine criteria weights and which criteria have to be taken into account for a particular problem. When considering the problem of the selection of best supplier, many investigations have been done and conclusion can be made that this is a very specific problem depending on the industry or field related to the supplier selection.
In the present paper, the selection of best supplier of plastic joinery based on the three defined criteria, namely price, delivery time and after-treatment is per-formed. Some additional criteria related to the thermal properties of the used glass or even ecological ones could be included. Furthermore, the sub-criteria associated with the price could be added (e.g.
delayed payment, which is very common in Croatia and instalment payments). Regarding criteria weights, it is evident that the application of different methods can give different results. It is obvious that a great experience of decision maker(s) in making judgements is needed. Consequently, many investi-gators have been applying different methods and integrated approaches to avoid subjectivity and to confirm the best solution as it is done here.
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