Question

Suppose that there are three Suppliers (Supplier A, Supplier B, Supplier C) and we are interested to evaluate the performance of the suppliers by using AHP method. Some of the criteria for supplier selection process can be defined as follows:

Cost, Quality, and Timeliness.

1. We would like to add more factors as criteria to the three above mentioned criteria. What else factor can be defined as criteria? Define at least two more criteria.
2. By considering only the above three criteria (Cost, Quality, and Timeliness), you first introduce three different suppliers that you may know and further rank these three alternative suppliers and select the best one using AHP method. The pairwise comparison matrix for each of the three suppliers for each criterion and the comparison matrix for the three criteria can be given by you based on your judgment and experiences.   

Answer 1

The first step in any supplier rating procedure is to find the appropriate criteria to be used for assessing the supplier. To comply with the criteria for supplier selection and their importance, required data were collected based on the consideration of literature. Based on considering the studies of Dickson (1966); Weber, Current, and Benton (1991); Krishnan (2008); and Tahriri, Osman, Yusuff and Esfandiary, (2008), five important criteria were selected.

The criteria were selected are the most criteria used in many different industries. Many studies, mentioned in the literature review, rate each factor by using the four-category scale of "Not important (1 to 3)", "Some-what important (4 to 5)", "Important (6 to 7)" and "Very important (8 to 9)" (Tam and Tummala, 2001). The selected criteria were found cover ABC Company’s needs. In addition, the presence of too many criteria makes the pair-wise comparisons in evaluating suppliers a difficult and time consuming process. To overcome these problems, the cut-off value to reduce the number of criteria to a few is desirable

In this step, the definition of the sub-criteria and sub sub-criteria has been done for supplier selection based on the five important criteria selected as the results of the previous step with the consideration of literature. Also, the sub and sub-criteria selected have been done by using the same rule that was used to select the criteria mentioned in the first step.

After gathering the needed sub and sub-criteria, they were identified and averaged. Fourteen sub-criteria and thirty-two sub sub-criteria were selected for levels (3) and (4) in supplier selection model as shown in (Figure 1)

Step 3: Structure the hierarchical model

This phase involves building the AHP hierarchy model and calculating the weights of each levels of supplier selection model. The developed AHP model, based on the identified criteria, sub-criteria and sub sub-criteria, contains five levels: the goal, the criteria, sub-criteria, sub-sub criteria, and alternatives.

(Figure 1) shows an illustrative five-level hierarchy for the supplier selection problem. The first level of the hierarchy is identified to select the supplier for ABC Company. The second level (criteria) contains cost, quality, delivery, management and organization, and financial. The third and fourth level of the hierarchy consist fourteen sub-criteria and thirty-two sub sub-criteria. The lowest level of the hierarchy contains of the alternatives, namely the different supplier to be evaluated in order to select the best supplier. The AHP model shown in (figure 1) is generally applicable to any supplier selection process of ABC Company. Based on the consideration of literature, the priority weight of each criterion in each level was determined. The pair-wise comparison judgments were used to find the important criteria in level two. This approach is found to be very useful in collecting data. The function of the pair-wise comparisons is by finding the relative importance of the criteria and sub-criteria, which is rated by the nine-point scale proposed by Saaty (1980), as shown in Table 1, indicating the level of relative importance from equal, moderate, strong, very strong, to extreme level by 1, 3, 5, 7, and 9, respectively. The intermediate values between two adjacent arguments were represented by 2, 4, 6, and 8.

As mentioned, the priority weight was determined. Here is a sample of pair-wise comparison matrix that shows how to calculate criteria, in level two, which were judged by other studies mentioned in the literature. The entry for the five row and the five column gives the importance of that row's criterion relative to the column's criterion as shown in Table 2.

It is obvious that the cost criterion is the heaviest among other criteria. The first row illustrates how the cost weight strongly compares to the others. For example, the cost criterion is preferred to the quality by the value of 2, preferred to the delivery by the value of 4 and preferred to the management and organization and financial by the value of 5 for each of them. A good performance on quality, the criterion for the second row and column, is moderately more important than having good delivery, the management and organization and financial, (shown by the value of 2,4 and 4 Sequentially). A value of 1 is assigned to the diagonal elements since delivery (row) is equally preferred to delivery (column).

After obtaining the pair-wise judgments as in Table 3, the next step is the computation of weighting of elements in the matrix. After calculating each column to find the total, divided the elements of that column by the total of the column. Finally, add the elements in each resulting row and divide this sum by the number of elements in the row to get the average. (Appendix 2) illustrates the calculations of the matrix. The results of priority weights are cost (0.444), quality (0.268), delivery (0.134), the management and organization (0.088) and financial (0.066)

The consistency ratio (C.R.) for the comparison above is calculated to determine the acceptance of the priority weighting. The consistency test is one of the essential features of the AHP method, which aims to eliminate the possible inconsistency revealed in the criteria weights through the computation of consistency level of each matrix. The consistency ratio (CR) was used to determine and justify the inconsistency in the pair-wise comparison made by the respondents. Based on Saaty's (1980) empirical suggestion that a C.R. = 0.10 is acceptable, it is concluded that the foregoing pair-wise comparisons to obtain attribute weights are reasonably consistent. If the CR value is lower than the

acceptable value, the weight results are valid and consistent. In contrast, if the CR value is larger than the acceptable value, the matrix results are inconsistent and are exempted for the further analysis. Estimating the consistency ratio is as follows: The following can be done manually or automatically by the AHP software,

Selecting appropriate value of random consistency ratio, RI, for a matrix size of five using Table 4, we find RI = 1.12. We then calculate the consistency ratio, CR, as follows:

cr=ci/ri=0.0238/1.12=0.02128

As the value of CR is less than 0.1, the judgments are acceptable (Al-Harbi, 2001).

The prioritized of sub-criteria in the third level and sub sub-criteria in the fourth level also depend on the local weights. The global weights are calculated by multiplying the local weights with criteria, sub-criteria and sub sub-criteria. As an example the calculations of the global weights of cost criteria are shown as follows. The result of priority criteria's with local weights of each level is shown in Table 5a.

Table 5b exhibits the local weights for each criterion in each level. The results show that in the second level of criteria, cost with local weight of (0.444) had been prioritized as the first criteria followed by quality (0.268), delivery (0.134), management and organization (0.088), and financial (0.066).

Conclusion

The issues of supplier selection have attracted the interest of researchers since the 1960s, and research in this area has evolved. Continuing the previous works in supplier selection area, the work has successfully achieved its objectives.

The main contribution of the work was the identification of the important criteria for the supplier selection process. Then a multi-criteria decision model for evaluating and selecting a supplier was developed. The model for supplier evaluation and selection was developed using the AHP method. The AHP model is assessing decision-makers to identify and evaluate the supplier selection.

Finally, the developed model is tested on four supplier selection problems. The results show the models are able to assist decision-makers to examine the strengths and weaknesses of supplier selection by comparing them with appropriate criteria, sub-criteria and sub sub-criteria.

• The developed model has not been implemented yet. It is just tested on four supplier selection problems as mentioned, but the outcome implies that the price criterion has the majority weight among other criteria. That’s suitable for using in ABC Company who uses the only price criterion to select and evaluate suppliers. Even though it was given the highest weight to the price the other criteria were given unbiased weights. In other words, every criterion had been given what was deserved weight in order to achieve the best method to select the right supplier. In addition, ABC Company could be satisfied when using the developed model that gives the price criterion unbiased ability to evaluatesuppliers. Choosing the right supplier could give the right quantity and the right cost on the right timeline.