The analytic hierarchy process was used to determine the best laptop brand for a company to purchase for newly hired employees. Six criteria were considered: size, screen quality, CPU, price, RAM, and operating system. Six laptop brands were evaluated as alternatives. Data was collected through a questionnaire and AHP was applied in Microsoft Excel. Lenovo received the highest global weight, indicating it was the best option according to the analysis of laptop attributes and employee preferences. All consistency ratios were under 10%, showing the results were logically consistent.

1. 1
ANALYTICAL HEIRARCHY PROCESS
MANAGEMENT SCIENCE REPORT
Submitted By:- Submitted To:-
Sakshi Aggarwal Dr. Sourabh Bishnoi
19DM178 Associate Professor
PGDM Section C Statistics and Operations
Research
BIMTECH

2. i
ACKNOWLEDGEMENT
I would like to express my sincere gratitude to Dr. Sourabh Bishnoi, Associate Professor, Statistics
and Operations Research, BIMTECH for guiding me during my report. His constant support helped
me in completing my report.
I felt my heartful thanks to my family, friends and close ones for showing their confidence in me and
supporting me.
Sakshi Aggarwal
19DM179

3. ii
INDEX
1. Abstract………………………………………………………….………….………..1
2. Introduction…………………………………………………………………….…..1
3. Literature Review ………………………………………………………….…….2
4. Problem Statement…………………………………………………………..….3
5. Research Methodology………………………………………………….…….4
6. Data and Analysis……………………………………………………………..….4
7. Results………………………………………………………………………………….5
8. Conclusion……………………………………………………………………………5
9. References……………………………………………………………………..…..…6
10. Questionnaire………………………………………………………………………7

4. 1
ABSTRACT
The analytic hierarchy process (AHP) has been used in the process of purchasing a new laptop. Such
a purchasing decision usually possesses some particular features that require adjustments in the
application of the AHP method, such as the existence of a large number of very different alternatives
or the integration of qualitative and quantitative criteria. In this project, the application of AHP to
the purchase decision of a new laptop will be studied. This project reviews possible options to
enhance the decision-making outcomes in purchase decision process using the Analytic Hierarchy
Process (AHP) both from academic and practical perspectives and will examine the usability,
certainty and quality of the technique. The results of the study will also provide insight into selecting
an appropriate Laptop on the basis of different criterion.
INTRODUCTION
In this paper, the focus area is the purchase of a new laptop. The Analytic Hierarchy Process (AHP)
(Saaty, 1980) is a multi-criteria framework for decision support. The AHP relies on a hierarchic
structure to represent the problem, and is based on pairwise comparisons that use a simple scale of
intensities of preference. The support that this framework provides to structuring the decision
processes, the ease of use, the intuitiveness of the required comparisons, the flexibility and the
numerous examples of successful application are some of its main strengths.
AHP is one of the main mathematical models currently available to support the decision
theory. The multi-criteria programming made through the use of the analytic hierarchy
process is a technique for decision making in complex environments in which many variables
or criteria are considered in the prioritization and selection of alternatives or projects.
AHP was developed in the 1970s by Thomas L. Saaty and has since been extensively studied,
and is currently used in decision making for complex scenarios, where people work together
to make decisions when human perceptions, judgments, and consequences have long-term
repercussions.
The application of AHP begins with a problem being decomposed into a hierarchy of criteria
so as to be more easily analysed and compared in an independent manner. After this logical
hierarchy is constructed, the decision makers can systematically assess the alternatives by
making pair-wise comparisons for each of the chosen criteria. This comparison may use
concrete data from the alternatives or human judgments as a way to input subjacent
information.
AHP transforms the comparisons, which are most often empirical, into numerical values that
are further processed and compared. The weight of each factor allows the assessment of each
one of the elements inside the defined hierarchy. This capability of converting empirical data
into mathematical models is the main distinctive contribution of the AHP technique when
contrasted with other comparing techniques.
After all the comparisons have been made, and the relative weights between each of the
criteria to be evaluated have been established, the numerical probability of each alternative is
calculated. This probability determines the likelihood that the alternative has to fulfil the
expected goal. The higher the probability, the better the chances the alternative has to satisfy
the final goal of the portfolio.

5. 2
LITERATURE REVIEW
Some studies have been carried on which brand of laptop to buy when there are many criterions.
The criterions were decided on the behaviour of people towards different criterions which are Size,
Screen Quality, CPU, Price, RAM and Operating System. The brands of laptop was decided as per
their brand recognition in the minds of the people. Brands selected are Apple, Lenovo, Acer, Dell, HP
and ASUS. The decision on which brand to buy has been taken using Analytic Hierarchy Process
(AHP).
AHP – Theory Saaty [1977] describes the seven pillars of the AHP as follows:
● Ratio scales, proportionality and normalized ratio scales.
● Reciprocal paired comparisons.
● The sensitivity of the principal right eigenvector.
● Clustering and using pivots to extend the scale.
● To create a one-dimensional ratio scale for representing the overall outcome.
● Rank preservation and reversal.
● Integrating group judgments.

6. 3
PROBLEM STATEMENT
GOAL : To undertake a purchase decision on the brand of laptops to be bought for newly recruited
employees in a Company.
SELECTION : The selection of a brand of laptop is based on the following 6 criterions:
1. Size
2. Screen Quality
3. CPU
4. Price
5. RAM
6. Operating System
These are the criterion which affects the choices made by an individual when they undertake a
purchase decision of a new laptop.
ALTERNATIVES : Below listed are the 6 alternatives that an individual can choose based on the
above-mentioned criterions.
1. Apple
2. Lenovo
3. Acer
4. Dell
5. HP
6. ASUS

7. 4
RESEARCH METHODOLOGY
This study evaluates the purchase decision based on 6 criterions and 6 alternatives available
to the company. For doing the analysis 5 employees were asked to fill out questionnaire and
this primary data was used to conduct analysis using Analytical Hierarchy Process (AHP) in
Microsoft Excel.
Sample Size: 5
Source of Data: Questionnaire
Type of Data: Primary Data
DATA AND ANALYSIS
As initially stated in the problem statement, the goal was to find out the most preferred
Brand of Laptop (alternative) among the 6 chosen features in a laptop (criterions). This was done
through comparison analysis and normalization. For this purpose, Analytic Hierarchy Process is used
because the preferences in an AHP are determined on the basis of pairwise comparisons,
which involves the evaluation of each element with all the other elements at a given
hierarchical level.
Step 1: Input the responses from five questionnaires collected. Take geometric mean of each
question that was answered. Geometric Mean is used instead of arithmetic mean because it is less
affected by extreme values and is an appropriate measure for data that involves ratios.
Step 2: The first step is to prepare a pairwise comparison matrix of all the criterion by
assigning a numerical value from 1 to 9, where 1 indicates equal preference and 9
indicates extremely important.
Step 3: Normalize the pairwise comparison matrix and assign weight to each criterion. For example,
the Size was compared with Screen Quality, CPU, Price, RAM and Operating System. Also, a
numerical value was also assigned at this stage by comparing the 2 criteria. This data will be in
Worksheet “Criterion” in Microsoft Excel.
Step 4: Give the relative importance of the various alternatives with respect to individual criteria.
Here we make pairwise comparison of the alternatives based on every criterion individually. After
assigning a numerical value in the similar fashion, we normalize these tables and here also, we find
out the weighted average of each alternative for each criterion individually. For example, the Size
criteria from choosing between the alternative Apple and Lenovo, after that the chosen
numerical value is divided by sum of the first alternative, which is the normalized
value. This data will be in different Worksheets named “Size”, “Screen Quality”, “CPU”, “Price”,
“RAM” and “Operating System” in Microsoft Excel.
Step 5: Create a table and write the weighted average of each criteria and also the weighted average
of each alternative that was individually calculated for each criterion individually. Thus, matrix
multiplication is performed to find the most preferred alternative.
Step 6: In the end, by arranging and totalling the global weight for each of the alternatives, we can
interpret which alternative to go for. Each alternative has a global weight which is fit to all
the judgments about all those aspects of Size, Screen Quality, CPU, Price, RAM and Operating
System. This data will be in Worksheet named “Global Weights”.

8. 5
Step 7: In addition to creating tables, the consistency of each matrix is checked. For this, Consistency
Ratio (CR) is calculated which should be less than 10% (Saaty, 1980). The CR coefficient is calculated
as follows. First the Consistency Index (CI) needs to be estimated. This is done by adding the
columns in the judgment matrix and multiply the resulting vector by the vector of priorities obtained
earlier. This yields an approximation of the maximum eigenvalue, denoted by λmax. Then, the CI
value is calculated by using the formula: CI = (λmax - n)/(n - 1). Next the Random Index is calculated
by using the formula: RI = 1.98*(n - 2)/n. Consistency Ratio (CR) is obtained by dividing the
Consistency Ratio by Random Index. Here n refers to the order of matrix i.e. n=6.
RESULTS
Consistency of each matrix created :
Worksheets Criterion Size Screen
Quality
CPU Price RAM Operating
System
Consistency Index 0.0540 0.0470 0.0239 0.0307 0.0316 0.0196 0.0322
Random Index 1.32 1.32 1.32 1.32 1.32 1.32 1.32
Consistency Ratio 0.0409 0.0356 0.0181 0.0232 0.0240 0.0148 0.0244
Ranking of various alternatives on the basis of different criterions :
Alternative Percentage Rank
HP 21.58% 1
Dell 18.75% 2
Apple 18.52% 3
ASUS 14.97% 4
Lenovo 13.76% 5
Acer 12.43% 6
CONCLUSION
As mentioned earlier, that Consistency Ratio (CR) should be less than 10% or 0.1. It can be seen that
in every matrix i.e. Criterion, Size, Screen Quality, CPU, Price, RAM and Operating System, the
Consistency Ratio is less than 10% or 0.1. This means that such inconsistency is acceptable.
Example :- Consistency Ratio of Criterion Matrix is 0.0409 or 4.09% which means that 4.09%
inconsistency is acceptable. Inconsistency occurs because there are different perceptions a person
makes while selecting a new laptop.
By considering the global weights, it can be seen that HP got 1st
Rank (highest preference) on the
basis of different criterions.
Dell and Apple got a rank of 2nd
and 3rd
respectively though there is only a slight difference in
percentage.
ASUS occupied 4th
Rank and Lenovo occupied 5th
Rank.
Acer is the less preferred brand when compared different criterions.
The Company should consider buying HP laptops for their employees as they are the highly
preferred laptops compared to other alternatives on the basis of different criterions.

9. 6
REFERENCES
1. Sharma Pinki (2012). A study of brand choice of laptops by management and engineering students.
Retrieved from http://www.researchersworld.com/vol3/issue4/vol3_issue4_2/Paper_07.pdf
2. Danesh D., Ryan M.J. & Abbasi A. (2015). Using Analytic Hierarchy Process as a Decision-Making Tool
in Project Portfolio Management. Retrieved from https://publications.waset.org/10003073/pdf
3. Klutho Steven (2013). Mathematical Decision Making: An Overview of the Analytic Hierarchy Process.
Retrieved from https://www.whitman.edu/Documents/Academics/Mathematics/Klutho.pdf