Application of the AHP in Selection of Head in Educational Institute

Analytical Hierarchy Process (AHP)

This paper presents the Analytical Hierarchy Process (AHP) as a potential decision making tool for an important decision to select a suitable candidate to Head an educational Institute. The pre requisition problem is used as an example. A hierarchical structure is constructed for the selection criteria and the professors wishing to apply for the required position. By applying the AHP, the prequalification criteria can be prioritized and a descending-order list of potential candidates can be made in order to select the best person to perform the requisite task. A sensitivity analysis has been performed to check the sensitivity of the final decisions subjected to minor changes in judgments. The paper presents group decision-making using the AHP.

The AHP allows group decision making, where group members can use their experience, values and knowledge to break down a problem into a hierarchy and solve it by the AHP steps.

Steps for applying the AHP

1. Define the problem and determine its goal.2. Structure the hierarchy from the top (the objectives from a

decision-makers viewpoint) through the intermediate levels (criteria on which subsequent levels depend) to the lowest level which usually contains the list of alternatives.

3. Construct a set of pair-wise comparison matrices (size nx n) for each of the lower levels with one matrix for each element in the level immediately above by using the relative scale measurement shown in Table 1. The pair-wise comparisons are done in terms of which element dominates the other.

4. There are n(n-1)/ judgments required to develop the set of matrices in step 3. Reciprocals are automatically assigned in each pair-wise comparison.

Steps for applying the AHP

5. Hierarchical synthesis is now used to weight the eigenvectors by the weights of the criteria and the sum is taken over all weighted eigenvector entries corresponding to those in the next lower level of the hierarchy.

6. Having made all the pair-wise comparisons, the consistency is determined by using the eigen value, λmax, to calculate the consistency index, CI as follows: CI = (λmax – n)/( n- 1), where n is the matrix size. Judgment consistency can be checked by taking the consistency ratio (CR) of CI with the appropriate value in Table 2. The CR is acceptable, if it does not exceed 0.10. If it is more, the judgment matrix is inconsistent. To obtain a consistent matrix, judgments should be reviewed and improved.

7. Steps 3±6 are performed for all levels in the hierarchy.

Details of ProfessorsTable 3 Criterion Professor -> A B C D E F

1 Total Exp. 13 Years 15 Years 17Years 20 Years 12 Years 11 Years

2 Exp as Departmental Head 3 Years 5 Years 7 Years 10 Years 2 Years 1 Year This is Essential with Ph. D.

3 Administration Average Average Good Good Below Poor

Like Students discipline, Students Average Result, Relation with AICTE and university

4 Research Activity Average Good Good ExcellentBelow Avg. Below Avg.

Ph. D. 3 7 10 15 2 2 M. Tech Guided 15 17 22 27 13 12 Patent 3 9 10 12 1 0 Books 2 4 6 8 2 0 Papers in Journals 36 47 55 65 15 10

5 Expected Salary (in Lacks) 2.5 2.75 3.12 2.5 2.25 2.25

6 Current Working as Deptt In charge

Deptt. Head

Deptt. Head

Institute Head

Deptt. In charge

Deptt. In charge

Pair-wise comparison scale for AHP preferences

Numerical rating Verbal judgments of preferences9 Extremely preferred8 Very strongly to extremely7 Very strongly preferred6 Strongly to very strongly5 Strongly preferred4 Moderately to strongly3 Moderately preferred2 Equally to moderately1 Equally preferred

Pair-wise comparison matrix for total experience (TE) Table 4

Exp. A B C D E FA 1 2 6 1/3 2 2B 1/2 1 5 1/2 3 3C 1/6 1/5 1 1/5 1/2 1/4D 3 2 5 1 4 2E 1/2 1/3 2 1/4 1 3F 1/2 1/3 4 1/2 1/3 1

Calculation

1. Synthesizing the pair-wise comparison matrix (example: Table 5);

2. Calculating the priority vector for a criterion such as experience (example: Table 5);

3. Calculating the consistency ratio;4. Calculating λmax;5. Calculating the consistency index, CI;6. Selecting appropriate value of the random consistency ratio

from Table 27. Checking the consistency of the pair-wise comparison matrix

to check whether the decision-maker's comparisons were consistent or not.

Average Random Consistency (RI)

Size of matrix 1 2 3 4 5 6 7 8 9 10

Random consistenc

y 0 0 0.6 0.9 1.1 1.2 1.3 1.4 1.5 1.5

Synthesized Matrix for Total Experience Table 5

Exp. A B C D E F Priority vector

A 0.1765 0.3409 0.2609 0.1198 0.1846 0.1778 0.2101

B 0.0882 0.1705 0.2174 0.1796 0.2769 0.2667 0.1999

C 0.0294 0.0341 0.0435 0.0719 0.0462 0.0222 0.0412

D 0.5294 0.3409 0.2174 0.3593 0.3692 0.1778 0.3323

E 0.0882 0.0568 0.0870 0.0898 0.0923 0.2667 0.1135

F 0.0882 0.0568 0.1739 0.1796 0.0308 0.0889 0.1030

∑=1

λ max=6.5644, CI=0.1129, RI =1.24, CR=0.0910 < 0.1 OK

Pair-Wise Comparison Matrix for the six criteria Table 6

TE Exp Ad Re Sa CW Priority Vector

A 1 3 6 4 3 2 0.3644B 1/3 1 5 2 2 3 0.2057

C 1/6 1/5 1 1/3 1/5 1/3 0.0390

D 1/4 1/2 3 1 2 4 0.1626

E 1/3 1/2 5 1/2 1 3 0.1401

F 1/2 1/3 3 1/4 1/3 1 0.0882

∑ =1

λmax =6.5713, CI =0.1143, RI = 1.24, CR =0.0922 < 0.1 OK.

Overall Priority

• The calculations for finding the overall priority of Professor are given below :

• Overall priority of Professor A = 0.2101(0.3644) +0.1201(0.2057)

+0.1785(0.0390) +0.1489(0.1626) +0.1120(0.1401) +0.3321(0.0882)

= 0.1774• Similarly Overall Priorities are calculated for

other 5.

Result and Discussion

T.Exp (0.3644)

Exp. (0.2057)

Administration (0.0390)

Research (0.1626)

Salary (0.1401)

CW (0.0882)

Priority Vector

Rank

A 0.3128 0.3186 0.3695 0.3492 0.3695 0.3416 0.1774 4B 0.2474 0.2383 0.2230 0.2131 0.2129 0.2109 0.1864 3C 0.0448 0.0515 0.0600 0.0491 0.0473 0.0483 0.1927 C-2D 0.1651 0.1721 0.1576 0.1970 0.1756 0.1903 0.2513 D-1E 0.1255 0.1319 0.1059 0.0984 0.0959 0.1103 0.1089 5F 0.1043 0.0877 0.0842 0.0931 0.0987 0.0986 0.0830 6

• Priority matrix for Professor Pre requisition involves criteria, priorities, requirements and preferences that are determined by management, as well as the characteristics of the individual professor. AHP allows group decision-making.

• AHP is based upon a firm theoretical foundation and, as examples in the literature and the day-to-day operations of various governmental agencies, corporations and consulting firms illustrate, the AHP is a viable, usable decision-making tool.

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system in government projects. Master thesis, King Fahd University of Petroleum and Minerals, KFUPM, Dhahran, Saudi Arabia, 1988

[2] Al-Alawi MA. Contractor prequalification: a computerized model for public projects in Bahrain. Master thesis, King Fahd University of Petroleum and Minerals, KFUPM, Dhahran, Saudi Arabia, 1991

[3] Al-Ghobali KHR. Factors considered in contractors prequalification process in Saudi Arabia. M.S. thesis, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia, 1994

[4] Belton V. A comparison of the analytic hierarchy process and a simple multi-attribute value function. European Journal of Operational Research 1986;26:7±21.

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