Selecting Best Tractor Ranking Wise by Software using MADM(Multiple –Attribute Decision Making Approach)

International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395 -0056
Volume: 04 Issue: 06 | June -2017 www.irjet.net p-ISSN: 2395-0072
© 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 1951
Selecting best tractor ranking wise by software using MADM
(Multiple –attribute decision making approach)
Raman Gupta1
1 Student (M.Tech), Mechanical Engineering Department, PCET Lalru, Punjab, India
----------------------------------------------------------------------***---------------------------------------------------------------------
Abstract – An extension of TOPSIS (Technique for order
performance by similarity to ideal solution), a Multi-
attribute decision making (MADM) technique, to a group
decision environment investigated. TOPSIS is a useful
technique in dealing with MADM problems in the real world.
MADM is a practical tool for selection and ranking a number
of alternatives its applications are numerous. In classical
MADM methods, the ratings and the weights of the criteria
are known precisely. Since human judgments including
preferences are often vague and cannot be expressed by
exact numerical values, the application of fuzzy concepts in
decision making is deemed to be relevant. In recent years
TOPSIS has been successfully applied to the areas of human
resources, management, transportation, product design,
manufacturing, water management, quality control and
many more areas. We design a model of TOPSIS for the
fuzzy environment with the introduction of appropriate
negations for ideal solutions. This paper represents an
optimization model to determine attribute weights for
MADM problems with incomplete weight information. In
this method, a series of mathematical programming models
are constructed and transformed into a single mathematical
programming model to determine the weight of attributes.
A concrete problem for selecting best tractor is discussed in
the paper, describes the complete process of method.
Key Words: Tractor, TOPSIS, MADM, Best Tractor,
Software Selection, Best Automobile
1. INTRODUCTION
”Multi-attribute decision making (MADM) is the most well-
known branch of decision making. It is branch of a general
class of operations research models that deals with
decision problems under the presence of a number of
decisions criteria. The MADM approach requires that the
selection be made among decision alternatives described
by the attributes. MADM problems are assumed to have a
predetermined, limited number of decision alternatives.
Solving a MADM problem involves sorting and ranking.
MADM approaches can be viewed as alternative methods
for combining the information in a problem’s decision
matrix together with additional information from the
decision make to a determine a final ranking or selection
from among the alternatives.
A MADM problem with m criteria and n alternatives can
present according to C1…Cm and A1…An as criteria and
alternatives, respectively. Moreover, A MADM
methodology is shown as ‘decision table’ (table 1). Each
row and column presents the alternatives and criteria,
respectively. The score aij describes the value and amount
of alternative Aj against criterion Ci. In addition, weights
W1…Wm should be assigned to every criterion. Weight
presents the importance of criterion Ci to the decision, and
is assumed to be positive. After filling the decision table by
decision-maker experience, a MADM technique must be
selected in order to rank and select alternatives.
Table -1: Decision Table
. .
. .
. . . . .
. . . . .
. .
Zhang Yao & Fan Zhiping [1] developed a method attribute
decision making based on incomplete linguistic judgment
matrix. This matrix is transformed into incomplete fuzzy
judgment matrix and an optimization model is developed
on the basis of incomplete fuzzy judgment matrix provided
by the decision maker and the decision matrix to
determine attribute weights by lagrange multiplier
method. Then the overall values of all alternatives are
calculated to rank them.
Jian Ma [2] gives an approach to multiple attribute
decision making based on preference information on
alternatives, where multiple decision makers gives theory
preference information on alternatives in different
formats. To reflect decision makers preference
information, an optimization model is constructed to
assess attribute weights and then to rank the alternatives
or select the most desirable one.

Patricia A. Berger [3] describes the development of a
multi-attribute decision model that generates depictions
of the agricultural landscape for use in alternative future
studies. The model first evaluates any changes in the land
base due to conversion of farmland to non-agricultural
uses, and then uses field descriptions, crop characteristics,
and the decision paradigm of an agricultural producer to
determine the preferred crop for each field under a
particular policy scenario.
Celik Parkan & Ming-Lu Wul [4] presents a decision-
making and performance measurement models with
applications to robot selection. This model demonstrates
the use of and compares some of the current multi-
attribute decision making (MADM) and performance
measurement methods through a robots selection
problem. The final selection is made on the basis of the
rankings obtained by averaging the results of OCRA,
TOPSIS, and a utility model.
1.1 TOPSIS
Technique for order preference by similarity to ideal
solutions (TOPSIS) is one of the technique for solving
decision-making problems. This technique is suggested by
Yoon & Hwang in 1981. Any problems of the type of the
multi-attribute decision with M alternative and N criteria
can be evaluated in a geometric system with ‘m’ points in
‘n’ dimensional space. Based on the idea the best
alternative should have the shortest distance from a
positive ideal solution (the best possible) and the longest
distance from negative ideal solution (the worst possible).
The TOPSIS technique consists of following steps.
Step 1: Normalize the decision matrix: The normalization
of the decision matrix is done using the below
transformation for each nij :
Then, weights should be multiplied to normalized matrix.
Step 2: Determine the positive and negative ideal
alternatives:
Error! Reference source not found. = {Error! Reference
source not found. , Error! Reference source not found. , … ,
Error! Reference source not found.} = {(Error! Reference
source not found. | j ϵ J ) , (Error! Reference source not
found. | j ϵ J’ | i = 1 , 2 , … , m)}
J = { j = 1 ,2 , … , n | j f or positive attributes }
Positive attribute: The one which has the best attribute
values (more is better).
J’ = { j = 1 , 2 , … , n | j f or negative attributes }
Negative attribute: The one which has the worst attribute
values (less is better).
In addition, the weighted normalized decision matrix
should be calculated with multiplying the normalized
decision matrix by its associated weights. The weighted
normalized value Error! Reference source not found. is
calculated as: Error! Reference source not found. = Error!
Reference source not found.
Where Error! Reference source not found. represents the
weight of the jth attributes or criterion.
Error! Reference source not found. = {Error! Reference
source not found. , Error! Reference source not found. , … ,
Error! Reference source not found. } = {( Error! Reference
source not found. | j ϵ J ) , (Error! Reference source not
found. | j ϵ J’ | i = 1,2, … , m)}
J = { j = 1,2, … , n | j f or positive attributes}
J’ = { j = 1,2, … , n | j f or negative attributes}
Step 3: Obtain the separation measure (based on
Euclidean distance) of the existing alternatives from ideal
and negative one (the separation between alternatives will
be found according to distance measure called normalized
Euclidean distance (Szmidt & Kacprzyk, 2000)):
dError! Reference source not found.= {Error! Reference
source not found. - Error! Reference source not found. ; i =
1,2, … , m
dError! Reference source not found.= {Error! Reference
source not found. - Error! Reference source not found. ; i =
1,2, … , m
Step 4: Calculate the relative closeness to the ideal
alternatives:
clError! Reference source not found. = dError! Reference
source not found. / ( dError! Reference source not found. +
dError! Reference source not found. ) ; 0 ≤ clError!
Reference source not found.≤ 1 : i = 1,2, … , m
Step 5: Rank the alternatives: based on the relative
closeness to the ideal alternative, the most is the clError!
Reference source not found., the better is the alternative
Error! Reference source not found..

2. PROBLEM FORMULATION
India is a republic and democratic country celebrating its
66th republic day in year 2015. Therefore becoming an
advanced country from day to day, year to year there are
lots of many up gradations in every field of technology.
Today demand for all kind of products is increasing day by
day with many options available hence increasing the
competition day by day.
Basically, people in India have a single kind of mentality
i.e. A person should have as much as he/she can have in
lest amount of rupees. But in technical aspects, the
product should be good in terms of technical aspects
according to the requirement of applications. Therefore
this paper will help to find out the best product according
to the need of required applications.
To carry out the research work in this paper total 6
numbers models have been selected and all the models
selected are of same power. The tractor models which
have been compared in the paper have been shown in
table 2.
Table -2: Models with make
S.No Model Name Tractor Make
1 DI 740 III S3 International Tractors Limited
(ITL)
2 744 FE Punjab Tractors Limited (PTL)
3 5045 D John Deere India Private Limited
(John Deere)
4 EICHER 5150 Tractors and Farm Equipment
Limited (TAFE)
5 2042 DI Indo Farm Equipment Limited
(Indo Farm)
6 PREET 4549 Preet Group of Companies (Preet)
The technical attributes of the above listed models have
been discussed below in the paper.
2.1 Technical attributes
The research has been carried out in this paper to find the
best tractor among the six selected tractors.
Configurations of all the six tractors have been collected
and same have been shown in table 3 in the comparison
form. Total six configurations have been compared in the
table 3.
Table -3: Comparison of tractor configurations
Make ITL PTL John
Deere
TAFE Indo
Farm
Preet
Specs
Model DI 740
III S3
744FE 5045 D EICHER
5150
2042DI PREET
4549
Power
(In HP)
45 HP 45 HP 45 HP 45 HP 45 HP 45 HP
Engine (In
CC)
2780 3136 2615 2500 2476 2892
Lift
(In KG)
1200 1500 1400 1500 1400 1800
PTO
(In RPM)
1000 1000 540 625 1000 540
Gears
(In NOS.)
10 10 12 10 10 10
Ground
Clearance
(In MM)
425 400 420 355 380 415
Tractor
Price
(In Lacs)
3.16 3.26 3.26 3.14 2.90 3.09
3. METHODOLOGY
To carry out the research work MADM approach has been
used, the work has been carried out in total four number
of different phases. All the phases has been described in
the paper research work has been done in the different
phases.
3.1 Survey
The first initiatory step to carry out the research work is
to collect the attributes i.e. data on which the research
could be done. The data has been collected on tractors for
which six numbers of companies has been surveyed.
Survey has been done in the companies like –
International tractors limited, Punjab tractors limited,
John deere, Tafe, Indofram and Preet tractors.
3.2 Data segregation and preparation
After the data (attributes) has been collected, it is
necessary to segregate the data in a tabular form so as to
compare the attributes. This has already been shown in
table 3.
3.3 Manual comparison of technical attributes
The manual comparison has been done by using TOPSIS of
MADM approach. However, to perform the manual
comparison there are some steps for manual comparison ,
equations are used for manual comparison and there are
also some rules for manual comparison.
There are total six steps for manual comparison that are
given below:
Step 1: Prepare decision matrix
Step 2: Normalize the matrix
Step 3: Assign the weightage to the attributes

Step 4: Multiply the weightage to the normalized matrix.
Step 5: Apply TOPSIS i.e. calculate Ideal positive &
Negative alternatives
Step 6: Calculate the relative closeness i.e. 1.
There are total five numbers of different equations used
for the manual comparison and those are given below in
table 4.
Table -4: Equations used in manual comparison
Sr. No. Area of applying
equation
Equation
1. To prepare normalize
matrix
2. Multiplying weightage
and normalize matrix
=
3. Calculating ideal
positive attribute
= { -
4. Calculating ideal
negative attribute
= { -
5. Relative closeness C = / ( + )
There are also some rules for comparison while using
TOPSIS technique. These rules should be always kept in
mind while making comparison. Total three rules have
been given below in this paper.
Rule 1: The rows and column of decision matrix should be
of same quantity i.e. the number of companies
(alternative) should be same to the number of
specifications (attributes). Therefore in the work content
total 6 (six) different attributes have been considered of
total 6 (six) different companies.
Rule 2: The specifications (attributes) should be
considered of common platform. Therefore, in the work
content the specification of 45 HP tractor model has been
considered of six different companies.
Rule 3: Weightage should be assigned to every type of
specification such that the sum of all the specifications
should come out to b one (1) only. Weightage can be
assigned according to the need of consumer. It is not
necessary to assign a fix weightage to any kind of
specification.
The weightages to the specifications will be assigned by
the consumer. The higher weightage can be assigned to
the specifications which is on most priority and similarly
the weightage will continue to decrease to the least
priority specification (attribute).
The weightages assigned should be such that the sum of
these weightages should comes out to be one (1) only.
Table 5 shows the weightage assigned to the specifications
(attributes).
Table -5: Weightage assigned to specifications (attributes)
Sr. No. Specification (Attribute) Weightage assigned
1. Engine displacement 0.25
2. Hydraulic lift capacity 0.18
3. Power take off 0.15
4. Gear speeds 0.12
5. Ground Clearance 0.10
6. Tractor Price 0.20
Manual comparison of the problem has been done below
in the paper by using TOPSIS technique of MADM
approach. The calculation will be done as per the six
discussed steps.
Step 1: Prepare the decision matrix
Step 2: Normalize the decision matrix: The above
discussed equation will be used to normalize the prepared
decision matrix ,and the normalized matrix (Error!
Reference source not found.) is given below.
Step 3: Assign weightage (Error! Reference source not
found.) to the attributes
= 0.25
= 0.18
= 0.15
= 0.12
= 0.10
= 0.20
The weightage matrix (Error! Reference source not
found.) is mentioned below

Step 4: Multiplying the weightage matrix (Error! Reference
source not found.) and normalized matrix (Error!
Reference source not found.) to form weight normalized
matrix (Error! Reference source not found.). The weight
normalized matrix (Error! Reference source not found.).
Step 5: Apply TOPSIS, calculate ideal positive and negative
attributes
Take out Error! Reference source not found. array
[Highest (+ve) value in column] from weight normalized
matrix Error! Reference source not found.).
Take out Error! Reference source not found. array
[Highest (-ve) value in column] from weight normalized
matrix Error! Reference source not found.).
Now, calculate ideal positive (Error! Reference source not
found.) & ideal negative (Error! Reference source not
found.) alternative.
Ideal positive alternative, Error! Reference source not
found. = [Error! Reference source not found. - Error!
Reference source not found. Error! Reference source not
found.
Ideal negative alternative, Error! Reference source not
found. = [Error! Reference source not found. - Error!
Reference source not found. Error! Reference source not
found.
Prepare, separation measurement matrix by using ideal
positive (Error! Reference source not found.).
Put all the values in the matrix (Error! Reference source
not found.)
Now, add all the rows
Error! Reference source not found. =Error! Reference
source not found. Error! Reference source not found.
Error! Reference source not found. = 0.422565, Error!
Reference source not found. = 0.424401, Error! Reference
source not found. = 0.42525, Error! Reference
source not found. = 0.426342, Error! Reference source not
found. = 0.425802, Error! Reference source not found. = 0
Prepare, separation measurement matrix by using ideal
positive (Error! Reference source not found.).
Put all the values in the matrix (Error! Reference source
not found.)
Now, add all the rows
Error! Reference source not found. =Error! Reference
source not found. Error! Reference source not found.
Reference source not found. = 0.001965, Error! Reference
source not found. = 0.001122, Error! Reference source not
found. = 0, Error! Reference source not found. = 0.000540,
Error! Reference source not found. = 0.426342
Step 6: Calculate the relative closeness (Error! Reference
source not found.) by using the below mentioned formula
Error! Reference source not found. = Error! Reference
source not found. ; 0 < Error! Reference source not found.
< 1
Reference source not found. = 0.0046087, Error!
Reference source not found. = 0.0026315, Error!
Reference source not found. = 0, Error! Reference source
not found. = 0.0012665, Error! Reference source not
found. = 1
Hence, based upon the relative closeness calculated,
ranking is shown in table 6.
Table -6: Calculated tractor ranking after manual
comparison.
Ranking Model Make
1st PREET 4549 PREET Tractors
2nd DI 740 III S3 International Tractors Limited
3rd 744 FE Punjab Tractors Limited

4th 5045 D JOHN DEERE
5th 2042 DI INDOFARM
6th EICHER 5150 TAFE
3.4 Software comparison of technical attributes
After doing the manual comparison of the attributes, to
prove out the work the comparison can also be done with
the software. Author, has developed a software on the
platform of Dotnet. Snapshots of the comparison is shown
figures 1 to 10.
Fig -1: Enter the numbers of tractors to be compared
Fig -2: Enter companies name
Fig -3: Enter the name of specifications to be compared
Fig -4: Enter the values of matrix
Fig -5: Assign the weightage to the specifications
Fig -6: Normalized matrix
N
Fig -7: Weightage normalized matrix

We
Fig -8: Ideal positive measurement matrix
Fig -9: Ideal negative measurement matrix
Fig -10: Relative closeness and ranking
4. CONCLUSION
After the manual comparison of attributes by using MADM
approach and TOPSIS, it has been truly diversified the
range for selecting any best option in any area of
application. Here in this paper, the comparison has been
done to select a best tractor and to prepare the ranking,
similarly this technique can be used to select any best
automobile or any other items which have their own
particular specifications. Thus the conclusion here comes
that MADM approach using TOPSIS can be used in any
term or in any area of field to select any of the best option.
ACKNOWLEDGEMENT
The constant guidance and encouragement received from
Mr. Raman Arora, assistant professor of mechanical
engineering department of PCET, Lalru has been of great
help in carrying the research work and is acknowledged
with reverential thanks.
REFERENCES
[1] Zhang Yao and Fan Zhiping, “Method for multiple
attribute decision making based on incomplete
linguistic judgment matrix”, Science Direct, Year
2008, Vol-19, Issue 2, 298-303.
[2] Jian Ma, “An Approach to Multiple Attribute Decision
Making Based on Preference Information on
Alternatives”, Elsevier North-Holland, Year 2002,
Vol.-131, Issue 1, 101-106.
[3] Particia A. Berger, “Generating Agricultural
Landscape for Alternative Futures Analysis: A
Multiple Attribute Decision-Making Model”,
Pergamon Press, Year 1998.
[4] Celik Parkan and Ming-Llu Wul, “Decision-making
and performance measurement models with
applications to robot selection”, Year 1999, Vol-36,
Issue 3,503-523.

Selecting Best Tractor Ranking Wise by Software using MADM(Multiple –Attribute Decision Making Approach)

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