India is the world’s largest two-wheeler market and despite the losses suffered by bike makers in India during the shift to BS-IV, the industry recovered well with a massive growth of 14.80 percent. Overall the two-wheeler industry saw a total sales of over 2.01 cr. units sold in the Indian domestic market and exports from the country also shot up by over 20 percent. Within the Two Wheelers segment, Motorcycles grew by 13.69 percent respectively.(Financial Express). From that report we can conclude that every 5th person owns a 2-wheeler and it is a vast market. So we try to understand the decision making part which done before buy a bike. We took five criteria to which helps customers to take decision and five alternative choice from which customer can choose their final product.

1. BIRLA INSTITUTE OF MANAGEMENT
TECHNOLOGY
MANAGMENT SCIENCE ASSIGNMENT
ANALYTICAL HIERARCHICAL PROCESS
Submitted by: Akshit Gupta Submitted to :
19DM024 Kuldeep Lamba

2. Contents
Problem Statement...................................................................................................................... 3
Introduction.................................................................................................................................3
AHP……………………………………………………………………………….......................................................................4
How AHP Works.......................................................................................................................4
Questionnare............................................................................................................................... 5
Questions: ...............................................................................................................................6
Criteria.................................................................................................................................6
Analysis.......................................................................................................................................8
Consistency Analysis.................................................................................................................8
Summary................................................................................................................................... 14
References............................................................................................................................. 14

3. Problem Statement
India is the world’s largesttwo-wheeler market and despite the losses suffered
by bikemakersin Indiaduringthe shiftto BS-IV,theindustryrecoveredwellwith
a massivegrowthof 14.80percent.Overallthe two-wheeler industrysaw a total
sales of over 2.01 cr. units sold in the Indian domestic market and exports from
the country also shotup by over 20 percent. Within the Two Wheelers segment,
Motorcycles grew by 13.69 percent respectively.(Financial Express). From that
report we can conclude that every 5th person owns a 2-wheeler and it is a vast
market. So we try to understand the decision making part which done before
buy a bike. We took five criteria to which helps customers to take decision and
five alternative choice from which customer can choose their final product.
Introduction
AHP
AHP is a decision-making method developed by Prof. Thomas L. Saaty in 1970s
that is used to solvecomplex MCDMproblems. Itrequires a decision maker to
offer judgments about each criterion’s relative importance and specify a
predilection for each decision alternative using each criterion. It is highly

4. efficient in identifying the selected criteria, their weighting, and analysis, and it
allows a logical data combination, which could be quantitative, qualitative,
experience, insight, and intuition in its algorithmic framework. AHP enables
decision makers to determine each criterion’s weight.
Features of AHP
AHP isa very flexibleand powerfultoolbecausethescores, andthereforethe final
ranking,areobtained on thebasisof thepairwiserelative evaluationsof both the
criteriaandtheoptionsprovided bytheuser.ThecomputationsmadebytheAHP
are always guided by the decision maker’s experience, and the AHP can thus be
consideredas a toolthatis ableto translatetheevaluations(both qualitativeand
quantitative) madebythedecisionmakerinto a multicriteria ranking. In addition,
the AHP is simple because there is no need of building a complex expert system
with the decision maker’s knowledge embedded in it
How AHP Works
AHPconsiders a setof evaluation criteria, and a setof 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.
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 performanceof the option with respect to the considered criterion.
Finally, the AHP combines the criteria weights and the options scores, thus
determining a global scoreforeach option, and a consequentranking.Theglobal
scorefor a given option is a weighted sum of the scores itobtained with respect
to all the criteria.

5. Questionnare
After the completion of the structure, the second step of the AHP process is to
make a questionnaire to determine the preference of the respondents. The
questionnaire for a 4 criteria, 3 alternative process would require at least some
questions to be answered in order to make the right decision so as to choose a
preference of car
The questionnaireis madeon the basisof pairwisescaling method, Theselection
criteria is shown the table for reference.
Criteria 9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9 Criteria
Price 9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9
Price 9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9
Price 9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9
Mileage 9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9
Mileage 9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9
Mileage 9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9
Looks 9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9
9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9
Weightage Scale Value
Extremely Important 8, 9
Very Important 6, 7
Moderately Important 4, 5
Important 2, 3
Equally Important 1
Explanation:

6. i. If you choose 1,when comparing Appearance over comfort that means
you give equal importance to both the criteria
ii. If you choose 9 towards the left, It means that Appearance on the left
hand side is 9 times more important than criteria n the right which is
comfort
iii. If you choose 6 towards the right, it means that you give very strong
importance to cost over Appearance
Questions:
Criteria
Questions 1 to 3: what is the relative importance of “PRICE” with respect to
others?
Questions 4 to 5 : whatis the relative importance of “MILEAGE” with respect to
others?
Questions6 : whatis therelative importanceof “LOOKS”with respectto others?
9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9
9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9
9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9
PRICE LOOKS
PRICE COLOR
PRICE MILEAGE
9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9
9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9
MILEAGE COLOR
MILEAGE LOOKS
9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9
LOOKS COLOR

7. Questions 7 to 9 (PRICE): Relative importance of brands APACHE, ENFIELD, R15
with respect to PRICE?
Questions10to 12(MILEAGE):Relative importanceof brandsAPACHE,ENFIELD,
R15 with respect to MILEAGE?
9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9
9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9
9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9
APACHE R15
ENFIELD R15
ALTERNATIVESCOMPAREDWITHRESPECTTOPRICE
APACHE ENFIELD
9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9
9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9
9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9
APACHE R15
ENFIELD R15
APACHE ENFIELD
ALTERNATIVESCOMPAREDWITHRESPECTTOMILEAGE

8. Questions 13 to 15 (LOOKS): Relative importance of brands APACHE, ENFIELD,
R15 with respect to LOOKS?
Questions 13 to 15 (COLOR): Relative importance of brands APACHE, ENFIELD,
R15 with respect to COLOR?
Analysis
Consistency Analysis
STEP 1:
The first step of the process is to check for the consistency of the criteria. The
consistency of the data is expected to be within the range of 1% to 10%. Before
this the important step is to answer the questionnaire with utmost sincerity in
9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9
9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9
9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9
ENFIELD R15
APACHE R15
ALTERNATIVESCOMPAREDWITHRESPECTTOLOOKS
APACHE ENFIELD
9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9
9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9
9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9
ENFIELD R15
APACHE R15
APACHE ENFIELD

9. order to get a consistent output. The data from the respondent is as shown
below.
STEP 2:
After finding out the summation of all criteria, we normalize the entire matrix
my dividing each value of the column with its sum. Then the weighted average
of each row is also taken. The Sum of each column shall be 1.
STEP 3: The Vales of Lambdamax, Consistency Index(CI), Random Consistency
Index(RI) and the ratio of CI/RI are calculated to find out the consistency of the
data collected.
N=4
From the calculations we can infer that the data is quite consistent and can be
observed that the consistency index is less than 10% as prescribed in the
process. Since the data is consistent, there is no need to repeat the entire
Criteria PRICE MILEAGE LOOKS COLOR
PRICE 1 3.63 5.43 5.24
MILEAGE 0.28 1 0.40 2.00
LOOKS 0.18 2.50 1 4.16
COLOR 0.19 0.50 0.24 1
SUM 1.65 7.63 7 12.4
PairWise Matrix of CRITERIA by synthesing using Geometric Mean
Criteria PRICE MILEAGE LOOKS COLOR Criteria Weights
PRICE 0.61 0.48 0.77 0.42 0.57
MILEAGE 0.17 0.13 0.06 0.16 0.13
LOOKS 0.11 0.33 0.14 0.34 0.23
COLOR 0.12 0.07 0.03 0.08 0.07
4.26
0.0881
0.90
9.79% ACCEPTABLE
Constant
Consistency Ratio (CR)
ƛ max
Consistency Index (CI)

10. process to get the consistency indexless than 10%. Wecan now moveon to the
next step of calculation of alternatives.
Main inference from STEP 3: Price is given the utmost importance by the
respondent whichis placedat 57% of the total share, It is thenfollowedby the
Looks which is given the second importance at 23% followedby Colour, Price
accordingly.
STEP 4 (PRICEto Alternatives): From hereonwards each criterion of selecting a
Bike is rated with respect to all the alternatives which are Apache, Enfield, R15
.All the above three steps are repeated for each criterion. First Criterion of the
Appearance is chosen and compared against all the other brands.
PRICE APACHE ENFIELD R15
APACHE 1 0.24 5.19
ENFIELD 4.16 1 7.56
R15 0.19 0.13 1
Sum 5.35 1.37 13.75
Pairwise Matrix of PRICE by using Geometric Mean
PRICE APACHE ENFIELD R15 Criteria Weights
APACHE 0.19 0.18 0.38 0.25
ENFIELD 0.78 0.73 0.55 0.69
R15 0.04 0.10 0.07 0.07
Normalised Matrix
Criteria Weights 0.25 0.69 0.07
PRICE APACHE ENFIELD R15 Sum Sum/Weight
APACHE 0.25 0.16 0.35 0.77 3.11
ENFIELD 1.03 0.69 0.52 2.23 3.25
R15 0.05 0.09 0.07 0.21 3.02
Weighted Normalised Matrix

11. Main inference: Price wise ENFIELD is given the utmost importance by then
followed by the APACHE which is given the second importance followed by
R15 accordingly.
STEP 5 (MILEAGE to Alternatives): Second Criterion of the Comfort is chosen
and compared against all the other brands alternatives APACHE, ENFIELD, R15
Main inference: MILEAGE wise R15 is given the utmost importance by then
followed by the APACHE which is given the second importance followed by
ENFIELD accordingly.
STEP 6 (LOOKS to Alternatives): Second Criterion of the Comfort is chosen and
compared against all the other brands alternatives APACHE, ENFIELD, R15.
MILEAGE APACHE ENFIELD R15
APACHE 1 3.30 0.23
ENFIELD 0.30 1 0.17
R15 4.35 5.77 1
Sum 5.65 10.07 1.40
MILEAGE APACHE ENFIELD R15 Criteria Weights
APACHE 0.18 0.33 0.16 0.22
ENFIELD 0.05 0.10 0.12 0.09
R15 0.77 0.57 0.71 0.69
Criteria Weights 0.22 0.09 0.69
MILEAGE APACHE ENFIELD R15 Sum Sum/Weight
APACHE 0.22 0.30 0.16 0.68 3.06
ENFIELD 0.07 0.09 0.12 0.28 3.01
R15 0.97 0.53 0.69 2.18 3.18
3.09
0.0431
0.58
7.43% ACCEPTABLE
Pairwise Matrix of MILEAGE by using Geometric Mean
Normalised Matrix
Weighted Normalised Matrix
ƛ max
Consistency Index (CI)
Constant
Consistency Ratio (CR)
3.13
0.0632
0.90
7.03% ACCEPTABLE
ƛ max
Consistency Index (CI)
Constant
Consistency Ratio (CR)

12. Main inference:LOOKS wise APACHE is given the utmost importance by then
followed by the ENFIELD which is given the second importance followed by
R15 accordingly.
STEP 7 (COLOR to Alternatives): Second Criterion of the Comfort is chosen and
compared against all the other brands alternatives APACHE, ENFIELD, R15.
LOOKS APACHE ENFIELD R15
APACHE 1 2.71 6.46
ENFIELD 0.37 1 5.77
R15 0.15 0.17 1
SUM 1.52 3.89 13.23
LOOKS APACHE ENFIELD R15 Criteria Weights
APACHE 0.66 0.70 0.49 0.61
ENFIELD 0.24 0.26 0.44 0.31
R15 0.10 0.04 0.08 0.07
Criteria Weights 0.61 0.31 0.07
LOOKS APACHE ENFIELD R15 Sum Sum/Weight
APACHE 0.61 0.85 0.48 1.94 3.15
ENFIELD 0.23 0.31 0.43 0.96 3.09
R15 0.10 0.05 0.07 0.22 3.02
3.09
0.0443
0.58
7.64% ACCEPTABLE
Pairwise Matrix of LOOKS by using Geometric Mean
Normalised Matrix
Weighted Normalised Matrix
ƛ max
Consistency Index (CI)
Constant
Consistency Ratio (CR)

13. Maininference:COLORS wise ENFIELDis giventhe utmostimportance by then
followed by the APACHE which is given the second importance followed by
R15 accordingly.
STEP 8: In the last and final step to find out the global weighted average we
multiply the weighted average of each criteria against the weighted average
given to each criteria of each brand. Once each of these are multiplied the final
preference of the respondents can be derived using the table.
Main inference: It is observed from the survey that ENFIELD is the most
preferred bike with criteria such as Price, Mileage, Color, Looks. The
observations show that 53% of the respondents have chosen over the other
COLOR APACHE ENFIELD R15
APACHE 1 0.14 2.62
ENFIELD 6.95 1 6.95
R15 0.38 0.14 1
Sum 8.33 1.29 10.57
COLOR APACHE ENFIELD R15 Criteria Weights
APACHE 0.12 0.11 0.25 0.16
ENFIELD 0.83 0.78 0.66 0.76
R15 0.05 0.11 0.09 0.08
Criteria Weights 0.16 0.76 0.08
Age APACHE ENFIELD R15 Sum Sum/Weight
APACHE 0.16 0.11 0.22 0.49 3.06
ENFIELD 1.11 0.76 0.58 2.45 3.24
R15 0.06 0.11 0.08 0.25 3.02
3.11
0.0534
0.58
9.21%
Pairwise Matrix of COLOR by using Geometric Mean
Normalised Matrix
Weighted Normalised Matrix
ƛ max
Consistency Index (CI)
Constant
Consistency Ratio (CR)
Criteria Weights APACHE ENFIELD R15 APACHE ENFIELD R15
PRICE 0.57 0.25 0.69 0.07 0.14 0.39 0.04
MILEAGE 0.13 0.22 0.09 0.69 0.03 0.01 0.09
LOOKS 0.23 0.61 0.31 0.07 0.14 0.07 0.02
COLOR 0.07 0.16 0.76 0.08 0.01 0.06 0.01
0.32 0.53 0.15SUM
ORIGINAL SCORE WEIGHTED SCORE

14. brands, while the other two brands i.e. APACHE and R15 are very low
compared to the choice of Enfield.
Summary
The following table shows the ranking order of each criteria against along each
alternative for a better understanding and interpretation of the report.
In nutshell, the most preferred Bike among all criteria and among all the
alternatives, Enfield is the clear winner and is the most preferred bike brand by
the chosen 3 respondents.
References
 Introduction to management science. Sweeney, Anderson
 Wikipedia
 https://www.pmi.org/learning
 https://cran.r-project.org/web/packages/ahp/
Criteria Weights APACHE ENFIELD R15 APACHE ENFIELD R15
PRICE 0.57 0.25 0.69 0.07 0.14 0.39 0.04
MILEAGE 0.13 0.22 0.09 0.69 0.03 0.01 0.09
LOOKS 0.23 0.61 0.31 0.07 0.14 0.07 0.02
COLOR 0.07 0.16 0.76 0.08 0.01 0.06 0.01
0.32 0.53 0.15
RANK 2 1 3
SUM
ORIGINAL SCORE WEIGHTED SCORE