This report shows you how to do selection by using analytical hierarchy planning. Management Science.

1. 1
SELECTION OF APARTMENT
USING
ANALYTICAL HIERARCHY PLANNING
DONE BY
ADARSH NJ
19DM015
SUBMITTED TO
PROF. KULDEEP LAMBA

2. 2
TABLE OF CONTENTS
S.NO. PARTICULARS PAGE NO.
1. Introduction 3
2. Advantages of AHP 3
3. Working of AHP 4
4. Index of Questionnaire 4
5. The Case – Selection of Apartment 5
6. Calculations 5
7. Conclusion 12

3. 3
INTRODUCTION
Analytical Hierarchy Planning also known as AHP is a tool to solve problem, and this tool was very
much popular in the late 1990’s and early 2000’s. The AHP method was created to understand the
structure of problem and the hindrances that managers face while solving a hard-decision-making
scenario.
It is an effective tool for dealing with complex decision making, and may aid the decision maker to
set priorities and make the best decision. By reducing complex decisions to a series of pairwise
comparisons, and then synthesizing the results, the AHP helps to capture both subjective and objective
aspects of a decision. In addition, the AHP incorporates a useful technique for checking the consistency of
the decision maker’s evaluations, thus reducing the bias in the decision-making process.
PROCESS OF SOLVING PROBLEMS THROUGH AHP METHOD:
The problem is looked at in three parts:
1. The issue that needs to resolved is the first part
2. The alternate solutions which are there to solve the problems are understood
3. The criteria used to evaluate the alternate solutions is understood
ADVANTAGES OF AHP
 AHP is advantageous as it understands the logical consistency of judgements used in determining
priorities.
 Both deductive and systematic approaches are integrated in solving complex problems.
 An overall estimate of the desirability of each alternative will be understood using AHP
 Deals with the interdependence of elements of a system
 It is a very convenient and straight forward method.

4. 4
WORKING OF AHP
The AHP considers a set of evaluation criteria, and a set of alternative options among which the
best decision is to be made. It is important to note that, since some of the criteria could be contrasting, it is
not true in general that the best option is the one which optimizes each single criterion, rather the one
which achieves the most suitable trade-off among the different criteria.
The AHP generates a weight for each evaluation criterion according to the decision maker’s
pairwise comparisons of the criteria. The higher the weight, the more important the corresponding
criterion. Next, for a fixed criterion, the AHP assigns a score to each option according to the decision
maker’s pairwise comparisons of the options based on that criterion. The higher the score, the better the
performance of the option with respect to the considered criterion. Finally, the AHP combines the criteria
weights and the options scores, thus determining a global score for each option, and a consequent ranking.
The global score for a given option is a weighted sum of the scores it obtained with respect to all the
criteria.
INDEX OF QUESTIONNAIRE
The index of questionnaire is as follows:
Intensity of
Importance
Definitions Explanation
1 Equal Importance Both elements contribute equally
to the objective
3, 4 Moderate Importance Experience and judgement
slightly favour one element over
the other
5, 6 Strong Importance Experience and judgement
strongly favour one element over
the other
7, 8 Very Strong Importance One element is favoured strongly
over the other
9 Extreme Importance The evidence favouring one
element over other is of the
highest possible affirmation

5. 5
THE CASE – SELECTION OF APARTMENT
The case involves the selection of apartment for a working person or for a student out of three
alternatives which are Skyline, Landmark and Confident Apartment in the Town of Kochi in Kerala. The
different criterions which are used in order to select the best apartment out of the three are its location,
Floor, Facilities and Rent.
Now we use Analytical Hierarchy Process to give weightage to each of these different apartments in
the context of becoming the best apartment to be choses based on the various criterions. We first need
numerical rating for pair wise comparison of the criteria followed by the pair wisecomparison of alternatives
with respect to each of the criteria considered. To record the ratings from multiple sources we need a
comparison matrix which is documented in the following section.
Skyline
Apartment
Landmark
Apartment
Confident
Apartment
Location Floor Facilities Rent

6. 6
CALCULATIONS
MATRICES OF QUESTIONNAIRE #1
PAIRWISE MATRIX OF CRITERIA
CRITERIA Location Floor Facilities Rent
Location 1 0.3333333 0.25 6
Floor 3 1 0.20 3
Facilities 4 5 1 6
Rent 0.166667 0.33 0.17 1
MATRIX OF ALTERNATIVES
LOCATION Skyline Landmark
Confident
Aps
Skyline 1 6 0.2
Landmark 0.166667 1 0.14285714
Confident
Aps 5 7 1
FLOOR Skyline Landmark
Confident
Aps
Skyline 1 0.25 0.2
Landmark 4 1 5
Confident
Aps 5 0.2 1
FACILITIES Skyline Landmark
Confident
Aps
Skyline 1 8 6
Landmark 0.125 1 0.16666667
Confident
Aps 0.166667 6 1
RENT Skyline Landmark
Confident
Aps
Skyline 1 0.1428571 7
Landmark 7 1 8
Confident
Aps 0.142857 0.125 1

7. 7
MATRICES OF QUESTIONNAIRE #2
PAIRWISE MATRIX OF CRITERIA
CRITERIA Location Floor Facilities Rent
Location 1 6 0.5 0.25
Floor 0.17 1 0.14 0.125
Facilities 2 7 1 6
Rent 4 8.00 0.17 1
MATRIX OF ALTERNATIVES
LOCATION Skyline Landmark
Confident
Aps
Skyline 1 8 0.14285714
Landmark 0.125 1 0.11111111
Confident
Aps 7 9 1
FLOOR Skyline Landmark
Confident
Aps
Skyline 1 0.125 0.2
Landmark 8 1 6
Confident
Aps 5 0.1666667 1
FACILITIES Skyline Landmark
Confident
Aps
Skyline 1 8 7
Landmark 0.125 1 0.14285714
Confident
Aps 0.142857 7 1
RENT Skyline Landmark
Confident
Aps
Skyline 1 0.125 0.125
Landmark 8 1 9
Confident
Aps 8 0.1111111 1

8. 8
MATRICES OF QUESTIONNAIRE #3
PAIRWISE MATRIX OF CRITERIA
CRITERIA Location Floor Facilities Rent
Location 1 7 0.33333333 4
Floor 0.14 1 0.20 0.166667
Facilities 3 5 1 5
Rent 0.25 6.00 0.20 1
MATRIX OF ALTERNATIVES
LOCATION Skyline Landmark
Confident
Aps
Skyline 1 4 0.16666667
Landmark 0.25 1 0.14285714
Confident
Aps 6 7 1
FLOOR Skyline Landmark
Confident
Aps
Skyline 1 0.1428571 0.2
Landmark 7 1 6
Confident
Aps 5 0.1666667 1
FACILITIES Skyline Landmark
Confident
Aps
Skyline 1 7 5
Landmark 0.142857 1 0.25
Confident
Aps 0.2 4 1
RENT Skyline Landmark
Confident
Aps
Skyline 1 0.2 5
Landmark 5 1 7
Confident
Aps 0.2 0.1428571 1

9. 9
CALCULATION OF CONSISTENCY RATIO
1) OF ALL THE CRITERIAS
Pairwise matrix of CRITERIA using Geometric Mean
CRITERIA Location Floor Facilities Rent
Location 1 2.41 0.35 1.82
Floor 0.41 1 0.18 0.40
Facilities 2.88 5.59 1 5.65
Rent 0.55 2.52 0.18 1
SUM 5 12 2 9
Normalised Matrix
CRITERIA Location Floor Facilities Rent
Criteria
Weights
Location 0.21 0.21 0.20 0.21 0.21
Floor 0.09 0.09 0.11 0.04 0.08
Facilities 0.59 0.49 0.59 0.64 0.58
Rent 0.11 0.22 0.10 0.11 0.14
Weighted Normalised Matrix
Criteria Weights 0.21 0.08 0.58 0.14
Criteria Location Floor Facilities Rent Sum
Sum/Weigh
t
Location 0.21 0.19 0.20 0.25 0.85 4.12
Floor 0.09 0.08 0.10 0.05 0.32 4.02
Facilities 0.59 0.45 0.58 0.77 2.40 4.16
Rent 0.11 0.20 0.10 0.14 0.56 4.05
ƛ max 4.09
Consistency Index (CI) 0.0288
Constant 0.58
Consistency Ratio (CR) 4.96% OK
2) OF LOCATION

10. 10
Pairwise Matrix of LOCATION by using Geometric
Mean
Location Skyline Landmark
Confident
Aps
Skyline 1 0.24 5.19
Landmark 4.16 1 7.56
Confident Aps 0.19 0.13 1
Sum 5.35 1.37 13.75
Normalised Matrix
Location Skyline Landmark
Confident
Aps
Criteria
Weights
Skyline 0.19 0.18 0.38 0.25
Landmark 0.78 0.73 0.55 0.69
Confident Aps 0.04 0.10 0.07 0.07
Weighted Normalised Matrix
Criteria Weights 0.25 0.69 0.07
Location Skyline Landmark
Confident
Aps Sum Sum/Weight
Skyline 0.25 0.16 0.35 0.77 3.11
Landmark 1.03 0.69 0.52 2.23 3.25
Confident Aps 0.05 0.09 0.07 0.21 3.02
ƛ max 3.13
Consistency Index (CI) 0.0632
Constant 0.90
Consistency Ratio (CR) 7.03% OK
3) OF FLOOR
Pairwise Matrix of FLOOR by using Geometric Mean
Floor Skyline Landmark
Confident
Aps
Skyline 1 3.30 0.23
Landmark 0.30 1 0.17
Confident Aps 4.35 5.77 1

11. 11
Sum 5.65 10.07 1.40
Normalised Matrix
Floor Skyline Landmark
Confident
Aps
Criteria
Weights
Skyline 0.18 0.33 0.16 0.22
Landmark 0.05 0.10 0.12 0.09
Confident Aps 0.77 0.57 0.71 0.69
Weighted Normalised Matrix
Criteria Weights 0.22 0.09 0.69
Floor Skyline Landmark
Confident
Aps Sum Sum/Weight
Skyline 0.22 0.30 0.16 0.68 3.06
Landmark 0.07 0.09 0.12 0.28 3.01
Confident Aps 0.97 0.53 0.69 2.18 3.18
ƛ max 3.09
Consistency Index (CI) 0.0431
Constant 0.58
Consistency Ratio (CR) 7.43% OK
4) OF FACILITIES
Pairwise Matrix of FACILITIES by using Geometric
Mean
Facilities Skyline Landmark Confident Aps
Skyline 1 2.71 6.46
Landmark 0.37 1 5.77
Confident Aps 0.15 0.17 1
SUM 1.52 3.89 13.23
Normalised Matrix
Facilities Skyline Landmark Confident Aps
Criteria
Weights
Skyline 0.66 0.70 0.49 0.61
Landmark 0.24 0.26 0.44 0.31
Confident Aps 0.10 0.04 0.08 0.07
Weighted Normalised Matrix
Criteria Weights 0.61 0.31 0.07

12. 12
Facilities Skyline Landmark Confident Aps Sum Sum/Weight
Skyline 0.61 0.85 0.48 1.94 3.15
Landmark 0.23 0.31 0.43 0.96 3.09
Confident Aps 0.10 0.05 0.07 0.22 3.02
ƛ max 3.09
Consistency Index (CI) 0.0443
Constant 0.58
Consistency Ratio (CR) 7.64% OK
5) OF RENT
Pairwise Matrix of RENT by using Geometric Mean
Rent Skyline Landmark
Confident
Aps
Skyline 1 0.14 2.62
Landmark 6.95 1 6.95
Confident Aps 0.38 0.14 1
Sum 8.33 1.29 10.57
Normalised Matrix
Rent Skyline Landmark
Confident
Aps
Criteria
Weights
Skyline 0.12 0.11 0.25 0.16
Landmark 0.83 0.78 0.66 0.76
Confident Aps 0.05 0.11 0.09 0.08
Weighted Normalised Matrix
Criteria Weights 0.16 0.76 0.08
Rent Skyline Landmark
Confident
Aps Sum Sum/Weight
Skyline 0.16 0.11 0.22 0.49 3.06
Landmark 1.11 0.76 0.58 2.45 3.24
Confident Aps 0.06 0.11 0.08 0.25 3.02
ƛ max 3.11
Consistency Index (CI) 0.0534
Constant 0.58
Consistency Ratio (CR) 9.21% OK

13. 13
FINDING THE BEST SCORE
ORIGINAL SCORE WEIGHTED SCORE
Criteria Weights Skyline Landmark
Confident
Aps Skyline Landmark
Confident
Aps
Location 0.21 0.25 0.69 0.07 0.05 0.14 0.01
Floor 0.08 0.22 0.09 0.69 0.02 0.01 0.06
Facilities 0.58 0.61 0.31 0.07 0.35 0.18 0.04
Rent 0.14 0.16 0.76 0.08 0.02 0.10 0.01
SUM 0.44 0.43 0.12
CONCLUSION
According to the result of AHP which was carried out to ascertain the best apartment for someone
to move in to the town of Kochi in Kerala, out of the various alternatives with the criterions provided, the
result is as follows:
Skyline Apartment scored the highest with the score of 0.44, barely higher than Landmark
Apartment with a score of 0.43 and Confident Apartment being the lowest with a core of 0.12. Hence, it
can be said that a person who wants to move in to an apartment in the town of Kochi in Kerala, he/she
should be choosing Skyline Apartment, since it is the best out of the alternatives.