DEVELOPMENT OF SOME INTEGRATED DECISION-MAKING FRAMEWORK FOR ADVANCED MANUFACTURING TECHNOLOGY SELECTION PROBLEMS

1
DEVELOPMENT OF SOME INTEGRATED
DECISION-MAKING FRAMEWORK FOR
ADVANCED MANUFACTURING TECHNOLOGY
SELECTION PROBLEMS
Submitted by
Name of the Students University Roll No.
1. Bibek Kumar Buranwal 11600713015
2. Rosan Kumar Pattanayak 11600713037
3. Saksham Pandey 11600713038
4. Souptik Sarkar 11600713045
5. SwagatamMitra 11600713058
6. VikashMohta 11600713059
7. YashKhara 11600713060
Under the supervision of
Dr.Prasenjit Chatterjee
REPORT SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE
OF BACHELOR OF TECHNOLOGY IN MECHANICAL ENGINEERING OF MAULANA ABUL
KALAM AZAD UNIVERSITY OF TECHNOLOGY
MECHANICAL ENGINEERING DEPARTMENT
MCKV INSTITUTE OF ENGINEERING
243,G.T. ROAD(NORTH),LILUAH
HOWRAH-711204
MECHANICAL ENGINEERING DEPARTMENT

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HOWRAH-711204
CERTIFICATE OF RECOMMENDATION
We hereby recommend that the thesis prepared under our
supervision by Mr. Bibek Kumar Buranwal, Mr. Rosan Kumar
Pattanayak, Mr. VikashMohta, Mr. Souptik Sarkar, Mr.
SwagatamMitra, Mr. Yash Khara and Mr. Saksham Pandey entitled
DEVELOPMENT OF SOME INTEGRATED DECISION-
MAKING FRAMEWORK FOR ADVANCED
MANUFACTURING TECHNOLOGY SELECTION
PROBLEM be accepted in partial fulfilment of the requirements for
the degree of BACHELOR OF TECHNOLOGY IN
“MECHANICAL ENGINEERING”.
_____________________________________
Project Guide & Head of Department, Mechanical Engineering,
MCKV Institute of Engineering, Howrah

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HOWRAH-711204
Affiliated to
MAULANA ABUL KALAM AZAD UNIVERSITY OF TECHNOLOGY
(Previously known as the WEST BENGAL UNIVERSITY OF TECHNOLOGY)
CERTIFICATE OF APPROVAL*
(B.Tech. Degree in Mechanical Engineering)
This project report is hereby approved as a creditable study of an engineering subject carried out
and presented in a manner satisfactory to warrant its acceptance as a pre-requisite to the degree for
which it has been submitted. It is to be understood that by this approval, the undersigned do not
necessarily endorse or approve any statement made, opinion expressed and conclusion drawn
therein but approve the project report only for the purpose for which it has been submitted.
COMMITTEE ON FINAL 1. ----------------------------------------
EXAMINATION FOR
EVALUATION OF 2. -----------------------------------------
PROJECT REPORT
3. -----------------------------------------
4. -----------------------------------------
5. ----------------------------------------
* Only in case report is approved.

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ACKNOWLEDGMENT
It is a genuine pleasure to express our deep sense of thanks and gratitude to our
mentor and guide Dr. Prasenjit Chatterjee, Associate Professor and Head of the
Department, Department of Mechanical Engineering, MCKV Institute of Engineering,
Howrah,West Bengal. His dedication and keen interest above all his overwhelming attitude
to help his students had been solely and mainly responsible for completing our work. His
timely advice, meticulous scrutiny, scholarly advice and scientific approach have helped us
to a very great extent to accomplish this task.
We are also thankful to Dr. Goutam Paul and Mr. Soutrik Bose for their support.
We would also like to express our sincere gratitude to Dr. Ranjib Biswas for his
assistance.
We would take this opportunity to express our greatest regards to our parents for
their co- operation, understanding, and constant encouragement which were the sustaining
factors in carrying out the work successfully.
Lastly, our thanks are also due to all those who have directly and indirectly guided
us in writing this project.
BIBEK KUMAR BURANWAL
ROSAN KUMAR PATTANAYAK
SAKSHAM PANDEY
SOUPTIK SARKAR
SWAGATAM MITRA
VIKASH MOHTA
YASH KHARA

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CONTENTS
SL. NO. TOPIC PAGE NO.
1 List of Figures 6
2 List of Tables 7
3 Literature Review 9
4 4.1 Introduction to Advanced Manufacturing Technology
Selection
4.2 Aims and Objective
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5 5.1 Mathematical Model of Multi-Attributive Border
Approximation area Comparison (MABAC)
5.2 Mathematical modelling of coefficient of variation
(COV)
5.3 Mathematical model of entropy weight
5.4 Flow chart of combined Multi-Attributive Border
Approximation Area Comparison (MABAC) and Co Efficient
Of Variance (COV)
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6 Application of the combined Multi-Attributive Border
Approximation Area Comparison (MABAC) and Co Efficient
Of Variance (COV)
21
7 Case study to illustrate a robot selection problem by three
different processes.
21
8 Comparison by spearman’s rank correlation coefficient of the
three processes.
29
9 Graphical analysis of the three processes. 30
10 Case study to illustrate CNC machine selection problem by
two different processes.
31
11 Comparison by spearman’s rank correlation coefficient of the
two processes.
39
12 Results and Discussions 40
13 Conclusion 42
14 Future work 43
15 Reference 44

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1. List of Figures
FIGURE DESCRIPTION PAGE NO.
1 Graphical analysis of the three processes 30
2 Graphical analysis of the two processes 39

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2. List of Tables
TABLE DESCRIPTION PAGE No.
1 Problem Statement 21
2 Attributes for the robot selection (Criteria weights are given by
AHP method) (MABAC AHP)
21
3 Formation of Normalization matrix(MABAC AHP) 22
4 Formation of weightage matrix(MABAC AHP) 22
5 Determination of Border Approximation Area (BAA)
Matrix(MABAC AHP)
22
6 Calculation of Distance of the alternative from Border
Approximation Area (BAA) Matrix(MABAC AHP)
22
7 Calculation of Si and finally ranking them(MABAC AHP) 23
8 Attributes for the robot selection(Entropy MABAC) 23
9 Determination of the Normalization Matrix(Entropy MABAC) 23
10 Determination of Yij(Entropy MABAC) 24
11 Determination of Pij(Entropy MABAC) 24
12 Determination of lnPij(Entropy MABAC) 24
13 Determination of Pij x lnPij(Entropy MABAC) 24
14 Determination of Ej(Entropy MABAC) 25
15 Calculation of weightage method(Entropy MABAC) 25
16 Formulation of weightage matrix(Entropy MABAC) 25
Matrix(Entropy MABAC)
25
Approximation Area (BAA) Matrix(Entropy MABAC)
25
19 Calculation of Si and Ranking them accordingly(Entropy
MABAC)
26
20 Attributes for the robot selection (MABAC-COV) 26
21 Determination of the Normalization Matrix (MABAC-COV) 26
22 Determination of x bar j (MABAC-COV) 26
23 Determination of (Xij-X bar)2
(MABAC-COV) 27
24 Determination of Sj (MABAC-COV) 27
25 Determination of Delta J (MABAC-COV) 27
26 Determination of the weight Wj (MABAC-COV) 27
27 Determination of weightage matrix(MABAC-COV) 27
Matrix(MABAC-COV)
27
Approximation Area (BAA) Matrix(MABAC-COV)
28
30 Determining Si and ranking them accordingly(MABAC-COV) 28
31 Rank Comparison 29
32 Seven attributes and nine alternatives of CNC machines 31
33 Attributes for the CNC machines(Entropy MABAC) 31
34 Determination of the Normalized matrix(Entropy MABAC) 31
35 Determination of Yij(Entropy MABAC) 32
36 Determination of Pij(Entropy MABAC) 32
37 Determination of lnPij(Entropy MABAC) 32
38 Determination Pij x lnPij(Entropy MABAC) 33
39 Determining 1-Ej(Entropy MABAC) 33

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40 Determining the weight(Entropy MABAC) 34
41 Determining the weightage matrix(Entropy MABAC) 34
Matrix(Entropy MABAC)
34
Approximation Area (BAA) Matrix(Entropy MABAC)
35
44 Calculation of Si and then ranking them accordingly(Entropy
MABAC)
35
45 Attributes for the CNC machines (MABAC-COV) 35
46 Determination of the Normalized matrix(MABAC-COV) 36
47 Calculation of x bar j(MABAC-COV) 36
48 Calculation of xij- x bar(MABAC-COV) 36
49 Determination of (Xij-X bar)2
(MABAC-COV) 37
50 Determination of Sj(MABAC-COV) 37
51 Determination of Delta j(MABAC-COV) 37
52 Determination of Weightage Wj(MABAC-COV) 37
53 Determination of weightage matrix(MABAC-COV) 37
Matrix(MABAC-COV)
38
Approximation Area (BAA) Matrix (MABAC-COV)
38
56 Determination of Si and ranking them accordingly (MABAC-
COV)
38
57 Rank Comparison 39

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3. Literature Review
Pamučar, Dragan, and Goran Ćirović (2015):-Explain the application of the new
DEMATEL–MABAC model in the process of making investment decisions on the
acquisition of manipulative transport (Forklifts) in logistics centres. The DEMATEL
method was used to obtain the weight coefficients of criteria, on the basis of which the
alternatives were evaluated. The evaluation and selection of Forklifts was carried out using
a new multi-criteria method – the MABAC (Multi-Attributive Border Approximation
area Comparison) method. They explain a practical application and a sensitivity analysis of
the MABAC method. In the first stage, a stability analysis was carried out on the solution
reached by the MABAC method, depending on changes made to the weights of the criteria.
In the second and third stages, a consistency analysis of the results from the MABAC
method was carried out depending on both the changes in the measurement units in which
the values of individual criteria are presented and on the formulation of the criteria.
Pei-Yue, Li, Qian Hui, and Wu Jian-Hua. Groundwater quality assessment is an essential
study which plays important roles in the rational development and utilization of
groundwater. Groundwater quality greatly influences the health of local people. However,
most traditional water quality comprehensive assessment methods which have complicated
formulas are difficult to apply in water quality assessment. In this paper, a novel method for
groundwater quality assessment called set pair analysis was introduced and entropy weight
was assigned to each index to improve the assessment model. The calculation steps are
depicted in the paper and take groundwater quality assessment in Dongsheng City as a case
study. The assessment results indicated that groundwater qualities in the study area were
relatively good, Set Pair Analysis method, which was an optimal method for groundwater
quality assessment and worth promoting, was easy to use and calculation processes which
use almost all the relative information were simple, results were reasonable, reliable and
intuitive.
Deng, Hepu, This paper presents a similarity-based approach to ranking multi criteria
alternatives for solving discrete multi criteria problems. The approach effectively makes
use of the ideal solution concept in such a way that the most preferred alternative should
have the highest degree of similarity to the positive ideal solution and the lowest degree of
similarity to the negative-ideal solution. The overall performance index of each alternative
across all criteria is determined based on the concept of the degree of similarity between
each alternative and the ideal solution using alternative gradient and magnitude. An
example is presented to demonstrate the applicability of the proposed approach. A
comparative analysis between the proposed approach and the technique for order preference
by similarity to ideal solution is conducted for demonstrating the merits of the proposed
approach for solving discrete multi criteria analysis problems.
Xia, Fei, Huan Wei, and Lian Wu Yang. The aim of this paper is to put forward a new
material selection method based on COPRAS method. The method combines the COPRAS
method and coefficient of variation method. The new method is simple and easy to use, and
coefficient of variation method can objectively determine the attributes weights. Thus it can
be easily accepted by decision makers. Finally, a practical example is used to demonstrate
the feasibility and effectiveness of the proposed method.
Yusuf Tansel. The selection of Computer-Integrated Manufacturing (CIM) technologies
becomes more complex as the decision makers in the manufacturing organization have to

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assess a wide range of alternatives based on a set of attributes. Although, a lot of Multi-
Attribute Decision-Making (MADM) methods are available to deal with selection
applications, this explains aims to explore the applicability of an integrated TOPSIS and
DoE method to solve different CIM selection problems in real-time industrial applications.
Four CIM selection problems, which include selection of (a) an industrial robot, (b) a rapid
prototyping process, (c) a CNC machine tool and (d) plant layout design, are considered in
this paper. TOPSIS method and Design of Experiment (DoE) are used together to identify
critical selection attributes and their interactions of all these cases by fitting a polynomial to
the experimental data in a multiple linear regression analysis. This mathematical model
development process involves TOPSIS experiments with the model.
Chen, Mei-Fang, and Gwo-Hshiung Tzeng. As international corporate activities increase,
their staffing involves more strategic concerns. However, foreign assignments have many
differences, and dissatisfaction with the host country is a known cause of expatriate failure.
From the point of view of an expatriate candidate, the decision of whether to take an
expatriate assignment can be regarded as a FMCDM (fuzzy multiple criteria decision
making) problem. They describes a fuzzy AHP (fuzzy analytic hierarchy process) to
determine the weighting of subjective judgments. Using the Sugeno integral for λ-fuzzy
measure, and using the non additive fuzzy integral technique to evaluate the synthetic
utility values of the alternatives and the fuzzy weights, then the best host country alternative
can be derived with the grey relation model. The authors further combine the grey relation
model based on the concepts of TOPSIS (technique for order preference by similarity to
ideal solution) to evaluate and select the best alternative. A real case of expatriate
assignment decision-making was used to demonstrate that the grey relation model
combined with the ideas of TOPSIS results in a satisfactory and effective evaluation.

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4. INTRODUCTION
4. Introduction to Advanced Manufacturing Technology Selection
The problem of selection and justification of advanced manufacturing technologies
(AMT) is a multi-attribute problem which involves both tangible and intangible factors. To
select the best manufacturing technology that achieves most of the company requirements,
it is necessary to use an appropriate selection approach that takes into consideration the
different quantitative and qualitative factors of company objectives and AMT benefits. In
this paper, a methodology for the selection of AMT is presented to assist the decision
maker in selecting technologies that meet their needs. The suggested methodology
combines two databases for the manufacturing company and AMT information, and multi-
criteria decision making (MCDM) tools.
Multiple-criteria decision-making (MCDM) or multiple-criteria decision
analysis (MCDA) is a sub-discipline of operations research that explicitly evaluates
multiple conflicting criteria in decision making (both in daily life or in professional
settings). Conflicting criteria are typical in evaluating options: cost or price is usually one
of the main criteria, and some measure of quality is typically another criterion, easily in
conflict with the cost. In order to survive in the present day global competitive
environment, it now becomes essential for the manufacturing organisations to take timely
and accurate decisions regarding effective use of their scarce resources. Various multi-
criteria decision-making (MCDM) methods are now available to help those organisations in
choosing the best decisive course of actions. In this project work, the applicability of some
newly developed MCDM methods will be explored while solving some discrete
manufacturing decision making problems. Integrated decision-making framework will also
be developed for effective decision-making. Ranking performances of these methods will
also be compared. Decision making that deals with several aspects of a finite set of
available alternatives in a given situation is often referred to as multi criteria analysis.

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4.2 AIMS AND OBJECTIVES
The past researchers have adopted different decision-making tools for evaluating,
justifying and selecting materials and advanced manufacturing technologies, but all those
methods are either very complicated or require lengthy computations and sometimes need
the help of linear programming tools to solve the developed models. Also, for the decision-
making problems with large number of attributes and smaller number of alternatives, those
approaches may occasionally give poor results. The present project work takes this
opportunity to explore the application feasibility and potentiality of some multi-criteria
decision-making (MCDM) methods to provide more precise and accurate rankings of the
feasible alternatives. According to the best of our knowledge, there have been very few
applications of these methods for decision-making in manufacturing environment.
Vicious global competition has forced the manufacturing organizations to improve
their quality and responsiveness in a cost-effective manner. The use of Advance
Manufacturing Technology Selection organizational objectives. A wrong alternative
selection may result in loss of productivity and profitability. The complexity of the
selection process makes multi-criteria analysis an invaluable tool in the engineering design
process. Thus, the main purpose of this project work is to explore the applicability of some
newly developed MCDM methods namely Multi Attributive Border Approximation area
Comparison (MABAC) model, Co-efficient Of Variance(COV) model and Spearman
Analysis etc while solving some Advanced Manufacturing Technology Selection Problems
decision-making problems as mentioned below and to develop integrated decision-making
framework for effective and rationale decision-making. Ranking performances of these
methods will also be compared to reveal the computational easiness and demonstrate how
the developed models can be effectively applied for decision-making in various
manufacturing situations, like:

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a) Robot Selection
b) CNC Machine Selection
c) EDM Selecion
All the considered methods will be applied to different manufacturing situations as
already mentioned and the results will be compared for better visualization.

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5.1 Mathematical Model of Multi-Attributive Border Approximation area
Comparison (MABAC)
Step 1.Formation of the initial decision matrix (X). Here alternatives in the form of vectors
Ai = (x i1, xi2. . .xin), where xij is the value of the ith alternative according to the jth criterion
(i = 1, 2 . . . m; j = 1, 2 . . . n).
…………………………………………(1)
Where m indicates the number of the alternatives, n indicates the total number of criteria.
Step 2. Normalization of the elements from the initial matrix (X).
…………………………………….(2)
The elements of the normalized matrix (N) are determinedusing the equation:
(a) For Benefit type criteria (a higher value of the criterion ispreferable)
………………………………………………………………………..(3)
(b) For Cost type criteria (a lower value of the criterion ispreferable)
………………………………………………………………………(4)
where xij, xi
+
and xi
-
are the elements from the initial decision matrix(X), for which xi
+
and
xi
-
are defined as:
xi
+
= max(x1, x2, . . ., xn), and is the maximum value of theobserved criterion according to
the alternatives.
xi
-
= min(x1, x2, . . ., xn), and is the minimum value of the observed criterion according to the
alternatives.

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Step 3.Calculation of the elements from the weighted matrix (V). The elements from the
weighted matrix (V) are calculated on the basis of the expression.
…………………………………………………………………….(5)
where nij are the elements of the normalized matrix (N), wi is the weight coefficients of the
criteria. Using Eq. (17) we obtain the weighted matrix V
….(6)
Step 4. Determining the border approximation area matrix (G). The border approximation
area (BAA) for each criterion is determined according to the Equation below
……………………………………………………………….(7)
where vij are the elements of the weighted matrix (V), and m is the total number of
alternatives. After calculating the value gi for each criterion, a border approximation area
matrix G (19) is formed with the format n _ 1 (n is the total number of criteria according to
which the selection is made from the alternatives offered).
………………………………………………….(8)
Step 5. Calculation of the distance of the alternative from the border approximation area for
the matrix elements (Q)
……………………………………………….(9)
The distance of the alternatives from the border approximation area (qij) is determined as
the difference between the elements in the weighted matrix (V) and the value of the border
approximation area (G).

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…………(10)
where gi is the border approximation area for criterion Ci, vij is the weighted matrix of the
elements (V), n is the number of criteria, m is the number of alternatives.
Step 6:- Determine Si = ∑ ij …………………………………(11)
Step 7 :- Determine the rank according to the highest value of Si.

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5.2 Mathematical model of Co-efficient of Variance (COV)
Step 1.Formation of the initial decision matrix (X). Here alternatives in the form of vectors
Ai = (x i1, xi2, . . .,xin), where xij is the value of the ith alternative according to the jth
criterion
(i = 1, 2, . . ., m; j = 1, 2, . . ., n).
………………………………………(12)
Step 2:- Determine x bar, x (∑ ij)/m …………………………………………..(13)
Step 3:- Determine sj, sj=
………………………………….(14)
Step 4:-Determine 𝛿, 𝛿j= ………………………………………(15)
Step 5:- Finally Determine weights of criteria by Wj= ………(16)

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5.3 MATHEMATICAL MODEL OF ENTROPY WEIGHT (Wj)
Step 1:- Formation of the initial decision matrix (X).
Here alternatives in the form of vectors Ai = (x i1, xi2, . . .,xin), where xij is the value of the
ith alternative according to the jth criterion
(i = 1, 2, . . ., m; j = 1, 2, . . ., n).
………………………………….(17)
Step 2:- Conversion of decision matrix into Normalized Matrix.
I:-Efficiency type (Beneficial Type)
………………………….(18)
II:-Cost type (Non Beneficial Type)
……(19)
III:- After transformation the standard grade matrix Y can be obtained and shown as
…………………….(20)
Step 3:- Determining the ratio of index value of the j index in i sample is
……………………………(21)
Step 4:- Determination of information entropy
………………………(22)

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Step 5:- Determination of Entropy weight
……………………………….(23)

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5.4 FLOW CHART OF COMBINED MULTI-ATTRIBUTIVE BORDER
APPROXIMATION AREA COMPARISON (MABAC) AND CO
EFFICIENT OF VARIANCE (COV)
1. Formation of initial decision
matrix
2. Normalization of decision
matrix
3. Calculation of weight by
COV method
4. Calculation of weighted
matrix (V)
5. Calculation of Border
Approximation Area (BAA)
matrix (G)
6. Calculation of the distance
of the alternative from the
border approximation area for
the matrix elements(Q)
Q=V-G
7. Calculation of Si
8. Finally determine the rank
according to highest value of
Si

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6. APPLICATION OF THE COMBINED MULTI-ATTRIBUTIVE
BORDER APPROXIMATION AREA COMPARISON (MABAC) AND
CO EFFICIENT OF VARIANCE (COV)
7. CASE STUDY TO ILLUSTRATE A ROBOT SELECTION PROBLEM BY TWO
DIFFERENT PROCESSES.
Question:-A case study is presented to illustrate the MACBAC and COV application and
validity of its results in the robot selection problem. Forthe robot selection problem, the
factors are determined based on thestudy as on following table. We considered the selection
problem of the most suitable industrial robot for an industrial application. The industrial
robot selection problem consists of five attributes and seven alternative robots, as shown in
Table. Among these five attributes, load capacity (LC), maximum tip speed (MTS),
memory capacity (MC), and manipulator reach (MR) are beneficial attributes (where higher
values are preferable), whereas, repeatability (RE) is a non-beneficial attribute (where lower
value is preferable).
Table 1:- Problem Statement
Serial
No.
Load
Capacity
(LC)
Repeatability
(RE)
Maximum tip speed
(MTS)
Memory
capacity(MC)
Manipulator
reach (MR
1 60 40 2540 500 990
2 6.35 15 1016 3000 1041
3 6.8 10 1727 1500 1676
4 10 20 1000 2000 965
5 2.5 10 560 500 915
6 4.5 8 1016 350 505
7 3 10 177 1000 920
Solution by MABAC-AHP Method
Step 1 (Table 2):- Attributes for the robot selection (Criteria weights are given by AHP
method)
Alternatives LC RE MTS MC MR
1 60 40 2540 500 990
2 6.35 15 1016 3000 1041
3 6.8 10 1727 1500 1676
4 10 20 1000 2000 965
5 2.5 10 560 500 915
6 4.5 8 1016 350 505
7 3 10 177 1000 920
WEIGHTAGE 0.1761 0.2042 0.2668 0.243 0.2286
MAX 60 40 2540 3000 1676
MIN 2.5 8 177 350 505

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Step 2 (Table 3):- Formation of Normalization matrix (by eqn. 2)
Normalization LC RE MTS MC MR
1 1 0 1 0.056604 0.414176
2 0.066956522 0.78125 0.355057 1 0.457728
3 0.074782609 0.9375 0.655946 0.433962 1
4 0.130434783 0.625 0.348286 0.622642 0.392827
5 0 0.9375 0.162082 0.056604 0.350128
6 0.034782609 1 0.355057 0 0
7 0.008695652 0.9375 0 0.245283 0.354398
Step 3(Table 4):- Formation of weightage matrix (by eqn. 6)
Weightage matrix LC RE MTS MC MR
1 0.3522 0.2042 0.5336 0.256755 0.323281
2 0.187891043 0.363731 0.361529 0.486 0.333237
3 0.189269217 0.395638 0.441806 0.348453 0.4572
4 0.199069565 0.331825 0.359723 0.394302 0.3184
5 0.1761 0.395638 0.310044 0.256755 0.308639
6 0.182225217 0.4084 0.361529 0.243 0.2286
7 0.177631304 0.395638 0.2668 0.302604 0.309615
Step 4 (Table 5):- Determination of Border Approximation Area (BAA) Matrix (by eqn. 7)
BAA LC RE MTS MC MR
G 0.203013045 0.34842 0.368167 0.317283 0.319864
Step 5 (Table 6):- Calculation of Distance of the alternative from Border Approximation
Area (BAA) Matrix. (by eqn. 10)
Q = V - G LC RE MTS MC MR
1 0.149186955 -0.14422 0.165433 -0.06053 0.003416
2 -0.015122002 0.015311 -0.00664 0.168717 0.013372
3 -0.013743828 0.047217 0.07364 0.03117 0.137336
4 -0.00394348 -0.0166 -0.00844 0.077019 -0.00146
5 -0.026913045 0.047217 -0.05812 -0.06053 -0.01123
6 -0.020787828 0.05998 -0.00664 -0.07428 -0.09126
7 -0.025381741 0.047217 -0.10137 -0.01468 -0.01025

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Step 6 (Table 7):- Calculation of Si and finally ranking them. (by eqn. 11)
Alternative Si Rank
1 0.113288067 3
2 0.175640992 2
3 0.275618631 1
4 0.046572083 4
5 -0.109572261 6
6 -0.132992805 7
7 -0.104459315 5
2.Solution by Entropy MABAC method
Step 1(Table 8):- Attributes for the robot selection
Attributes LC RE MTS MC MR
1 60 40 2540 500 990
2 6.35 15 1016 3000 1041
3 6.8 10 1727 1500 1676
4 10 20 1000 2000 965
5 2.5 10 560 500 915
6 4.5 8 1016 350 505
7 3 10 177 1000 920
MAX 60 40 2540 3000 1676
MIN 2.5 8 177 350 505
Step 2(Table 9):- Determination of the Normalization Matrix (by eqn. 2)
1 1 0 1 0.056604 0.414176
2 0.066957 0.78125 0.355057 1 0.457728
3 0.074783 0.9375 0.655946 0.433962 1
4 0.130435 0.625 0.348286 0.622642 0.392827
5 0 0.9375 0.162082 0.056604 0.350128
6 0.034783 1 0.355057 0 0
7 0.008696 0.9375 0 0.245283 0.354398
MAX 1 1 1 1 1
MIN 0 0 0 0 0

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Step 3(Table 10):- Determination of Yij (by eqn. 20)
Yij LC RE MTS MC MR
1 1 0 1 0.056604 0.414176
2 0.066957 0.78125 0.355057 1 0.457728
3 0.074783 0.9375 0.655946 0.433962 1
4 0.130435 0.625 0.348286 0.622642 0.392827
5 0 0.9375 0.162082 0.056604 0.350128
6 0.034783 1 0.355057 0 0
7 0.008696 0.9375 0 0.245283 0.354398
SUM 1.315652 5.21875 2.876428 2.415094 2.969257
Step 4(Table 11):- Determination of Pij (by eqn. 21)
Pij LC RE MTS MC MR
1 0.760079 0 0.347653 0.023438 0.139488
2 0.050892 0.149701 0.123437 0.414063 0.154156
3 0.056841 0.179641 0.228042 0.179688 0.336785
4 0.099141 0.11976 0.121083 0.257813 0.132298
5 0 0.179641 0.056348 0.023438 0.117918
6 0.026438 0.191617 0.123437 0 0
7 0.006609 0.179641 0 0.101563 0.119356
Step 5(Table 12):- Determination of lnPij
LnPij LC RE MTS MC MR
1 -0.27433 0 -1.05655 -3.75342 -1.96978
2 -2.97804 -1.89912 -2.09203 -0.88174 -1.86979
3 -2.8675 -1.7168 -1.47823 -1.71654 -1.08831
4 -2.31121 -2.12226 -2.11128 -1.35552 -2.0227
5 0 -1.7168 -2.8762 -3.75342 -2.13777
6 -3.63297 -1.65226 -2.09203 0 0
7 -5.01926 -1.7168 0 -2.28708 -2.12565
M=7 ln m= 1.94591 - (1/(ln m)=-0.5139
Step 6 (Table 13):- Determination of Pij x lnPij
Pij * lnPij LC RE MTS MC MR
1 -0.20851 0 -0.36731 -0.08797 -0.27476
2 -0.15156 -0.2843 -0.25823 -0.36509 -0.28824
3 -0.16299 -0.30841 -0.3371 -0.30844 -0.36653
4 -0.22914 -0.25416 -0.25564 -0.34947 -0.2676
5 0 -0.30841 -0.16207 -0.08797 -0.25208
6 -0.09605 -0.3166 -0.25823 0 0

25
7 -0.03317 -0.30841 0 -0.23228 -0.25371
SUM -0.88142 -1.78028 -1.63859 -1.43123 -1.70291
Step 7(Table 14):- Determination of Ej (by eqn. 22)
Ej 0.452961 0.914884 0.842066 0.735506 0.875125
Step 8(Table 15):- Calculation of weightage method (by eqn. 23)
WEIGHT 0.463805 0.072165 0.133904 0.22425 0.105875
Step 9(Table 16):- Formulation of weightage matrix (by eqn. 5)
WAIGHTAGE
MATRIX LC RE MTS MC MR
1 0.927610917 0.072165 0.267807 0.236944 0.149726
2 0.494860259 0.128545 0.181447 0.448501 0.154337
3 0.498490041 0.13982 0.221737 0.321567 0.21175
4 0.524301823 0.117269 0.18054 0.363878 0.147466
5 0.463805458 0.13982 0.155607 0.236944 0.142945
6 0.479937822 0.144331 0.181447 0.22425 0.105875
7 0.467838549 0.13982 0.133904 0.279255 0.143397
Step 10(Table 17):- Determination of Border Approximation Area (BAA) Matrix (by
eqn.7)
BAA LC RE MTS MC MR
G 0.53468801 0.123134 0.184778 0.292802 0.148144
Step 11(Table 18):- Calculation of Distance of the alternative from Border Approximation
Q = V – G LC RE MTS MC MR
1 0.392922907 -0.05097 0.083029 -0.05586 0.001582
2 -0.039827751 0.005411 -0.00333 0.155699 0.006193
3 -0.03619797 0.016687 0.036959 0.028765 0.063606
4 -0.010386187 -0.00586 -0.00424 0.071076 -0.00068
5 -0.070882552 0.016687 -0.02917 -0.05586 -0.0052
6 -0.054750188 0.021197 -0.00333 -0.06855 -0.04227
7 -0.066849461 0.016687 -0.05087 -0.01355 -0.00475

26
Step 12(Table 19):- Calculation of Si and Ranking them accordingly. (by eqn.11)
Alternative Si Rank
1 0.370707943 1
2 0.12414445 2
3 0.109819018 3
4 0.049909212 4
5 -0.144423797 6
6 -0.147704344 7
7 -0.119330604 5
3. Solution by MABAC-COV method.
Step 1(Table 20):- Attributes for the robot selection
1 60 40 2540 500 990
2 6.35 15 1016 3000 1041
3 6.8 10 1727 1500 1676
4 10 20 1000 2000 965
5 2.5 10 560 500 915
6 4.5 8 1016 350 505
7 3 10 177 1000 920
MAX 60 40 2540 3000 1676
MIN 2.5 8 177 350 505
Step 2(Table 21):- Determination of the Normalization Matrix (by eqn. 2)
LC RE MTS MC MR
1 1 0 1 0.056604 0.414176
2 0.066957 0.78125 0.355057 1 0.457728
3 0.074783 0.9375 0.655946 0.433962 1
4 0.130435 0.625 0.348286 0.622642 0.392827
5 0 0.9375 0.162082 0.056604 0.350128
6 0.034783 1 0.355057 0 0
7 0.008696 0.9375 0 0.245283 0.354398
Step 3 (Table 22):- Determination of x bar j (by eqn. 13)
Alternatives LC RE MTS MC MR
1 1 0 1 0.056604 0.414176
2 0.066957 0.78125 0.355057 1 0.457728
3 0.074783 0.9375 0.655946 0.433962 1
4 0.130435 0.625 0.348286 0.622642 0.392827

27
5 0 0.9375 0.162082 0.056604 0.350128
6 0.034783 1 0.355057 0 0
7 0.008696 0.9375 0 0.245283 0.354398
X bar j 0.18795 0.745536 0.410918 0.345013 0.42418
Step 4 (Table 23):- Determination of (Xij-X bar)2
(Xij-X bar)2
LC RE MTS MC MR
1 0.659425 0.555824 0.347017 0.08318 0.0001
2 0.014639 0.001276 0.00312 0.429007 0.001126
3 0.012807 0.03685 0.060038 0.007912 0.331569
4 0.003308 0.014529 0.003923 0.077077 0.000983
5 0.035325 0.03685 0.061919 0.08318 0.005484
6 0.02346 0.064752 0.00312 0.119034 0.179928
7 0.032132 0.03685 0.168854 0.009946 0.004869
sum/m 0.111585 0.106704 0.09257 0.11562 0.074866
Step 5(Table 24):- Determination of Sj (by eqn. 14)
Sj 0.334044 0.326656 0.304254 0.340029 0.273616
Step 6(Table 25):- Determination of Delta J (by eqn. 15)
Delta j 1.777299 0.43815 0.740424 0.985552 0.645047
Step 7(Table 26):- Determination of the weight Wj (by eqn. 16)
Wj 0.387509 0.095531 0.161437 0.214882 0.140641
Step 8(Table 27):- Determination of weightage matrix (by eqn. 6)
Weightage matrix LC RE MTS MC MR
1 0.775017781 0.095531 0.322873 0.227046 0.198891
2 0.413455138 0.170164 0.218756 0.429765 0.205017
3 0.416487816 0.185091 0.26733 0.308133 0.281282
4 0.438053528 0.155238 0.217663 0.348677 0.195889
5 0.38750889 0.185091 0.187602 0.227046 0.189884
6 0.40098746 0.191062 0.218756 0.214882 0.140641
7 0.390878533 0.185091 0.161437 0.267589 0.190484
Step 9(Table 28):- Determination of Border Approximation Area (BAA) Matrix (by eqn. 7)
BAA LC RE MTS MC MR
G 0.446731175 0.163001 0.222772 0.28057 0.19679

28
Step 10(Table 29):- Calculation of Distance of the alternative from Border Approximation
Q = V – G LC RE MTS MC MR
1 0.328286606 -0.06747 0.100101 -0.05352 0.002102
2 -0.033276037 0.007163 -0.00402 0.149195 0.008227
3 -0.030243359 0.02209 0.044558 0.027563 0.084493
4 -0.008677647 -0.00776 -0.00511 0.068107 -0.0009
5 -0.059222285 0.02209 -0.03517 -0.05352 -0.00691
6 -0.045743715 0.02806 -0.00402 -0.06569 -0.05615
7 -0.055852642 0.02209 -0.06134 -0.01298 -0.00631
Step 11(Table 30):- Determining Si and ranking them accordingly (by eqn. 11)
Alternative Si Rank
1 0.309494443 1
2 0.127292567 3
3 0.148460536 2
4 0.045655572 4
5 -0.132732528 6
6 -0.143535657 7
7 -0.11438448 5

29
8. COMPARISON BY SPEARMAN’S RANK CORRELATION
COEFFICIENT OF THE THREE PROCESSES.
SPEARMAN’S RANK CORRELATION COEFFICIENT
The Spearman’s rank correlation coefficient measures the relation among nonlinear
datasets. Its purpose is to quantify the strength of linear relationship between two variables.
If there are no repeated data values, a perfect Spearman correlation of +1 or −1 occurs
when each of the variables is a Perfect monotone function of the Spearman’s rank
correlation is computed by Equation
RS = 1-
∑
Where:
Rs: Spearman‟s rank coefficient
di: Difference between ranks of each case
n: Number of pairs of values.
TABLE 31:- RANK COMPARISON
Methods Used/
Alternatives
Rank by
Topsis +
DOE
Rank by
MABAC+AHP
Rank by
MABAC+ENTROPY
Rank by
MABAC+COV
1 1 3 1 1
2 3 2 2 3
3 2 1 3 2
4 4 4 4 4
5 6 6 6 6
6 5 7 7 7
7 7 5 5 5
Sperman's rank co-
efficient - 0.75 0.821428571 0.857142857

30
9. GRAPHICAL ANALYSIS
FIG.1: GRAPHICAL ANALYSIS OF THE THREE PROCESSES
0
1
2
3
4
5
6
7
8
1 2 3 4 5 6 7
Rank
Alternatives
Rank comparison
Rank by Topsis + DOE Rank by MABAC+AHP Rank by MABAC+ENTROPY Rank by MABAC+COV

31
10. CASE STUDY TO ILLUSTRATE CNC MACHINE SELECTION PROBLEM BY
TWO DIFFERENT PROCESSES.
Question:- A case study is presented to illustrate the MACBAC and COV application and
validity of its results in the CNC machine selection problem. Forthe CNC machine
selection problem, the factors are determined based on thestudy as on following table. We
considered the selection problem of the most suitable industrial CNC machine for an
industrial application. The industrial CNC machine selection problem consists of seven
attributes and nine alternative CNC machine, as shown in Table. Among these seven
attributes, Area, Cost and Spindle motor power are non-beneficiary whereas, Max diameter,
Max spindle speed, No. of tools and Rapid transverse X-axis are all beneficiary attributes.
Table 32:- Seven attributes and nine alternatives of CNC machines.
1.Solution by Entropy MABAC method
Step 1 (Table 33):- Attributes for the CNC machines
Alternatives Area Cost
Spindle motor
power
Max
Diameter
Max Spindle
speed
No of
tools
Rapid traverse
X axis
BNE 34S5 5595200 1 7.5 50 7000 12 10
SKT28LM 6650040 6 22 300 3500 12 20
T-42 5279169 3 11 315 6000 12 24
ST30SS 11370315 4 22.4 406 4500 24 24
DS30 11370316 5 22.4 457 4000 12 24
LH-55N 33429309 7 45 650 1200 12 5
LOC-650 24235325 7 22.4 650 500 12 5
LU300 2ST 6047500 2 22.4 370 5000 20 20
LB-35II
{M} 600T
10466900 4 30 490 3200 12 15
MAX 33429309 7 45 650 7000 24 24
MIN 5279169 1 7.5 50 500 12 5
Spindle
motor power
Max
Diameter
Max Spindle
speed
No of tools
Rapid
traverse X
axis
BNE 34S5 0.988773377 1 1 0 1 0 0.263157895
SKT28LM 0.95130145 0.166666667 0.613333333 0.416666667 0.461538462 0 0.789473684
T-42 1 0.666666667 0.906666667 0.441666667 0.846153846 0 1
ST30SS 0.783619335 0.5 0.602666667 0.593333333 0.615384615 1 1
DS30 0.7836193 0.333333333 0.602666667 0.678333333 0.538461538 0 1
LH-55N 0 0 0 1 0.107692308 0 0
LOC-650 0.326605267 0 0.602666667 1 0 0 0
LU300 2ST 0.972705962 0.833333333 0.602666667 0.533333333 0.692307692 0.666666667 0.789473684
LB-35II
{M} 600T
0.815712071 0.5 0.4 0.733333333 0.415384615 0 0.526315789

32
Step 2(Table 34):- Determination of the Normalized matrix (by eqn. 2)
Normalization Area Cost
Spindle
motor power
Max
Diameter
Max Spindle
speed
No of tools
Rapid
traverse X
axis
BNE 34S5 0.98877338 1 1 0 1 0 0.263157895
SKT28LM 0.95130145 0.166667 0.613333333 0.416666667 0.461538462 0 0.789473684
T-42 1 0.666667 0.906666667 0.441666667 0.846153846 0 1
ST30SS 0.78361934 0.5 0.602666667 0.593333333 0.615384615 1 1
DS30 0.7836193 0.333333 0.602666667 0.678333333 0.538461538 0 1
LH-55N 0 0 0 1 0.107692308 0 0
LOC-650 0.32660527 0 0.602666667 1 0 0 0
LU300 2ST 0.97270596 0.833333 0.602666667 0.533333333 0.692307692 0.66666667 0.789473684
LB-35II {M}
600T
0.81571207 0.5 0.4 0.733333333 0.415384615 0 0.526315789
Step 3(Table 35):- Determination of Yij (by eqn. 20)
Step 4(Table 36):- Determination of Pij (by eqn. 21)
Pij
Area Cost
Spindle motor
power
Max
Diameter
Max Spindle
speed
No of
tools
Rapid traverse
X axis
BNE 34S5 0.149308834 0.25 0.187593797 0 0.213815789 0 0.049019608
SKT28LM 0.143650419 0.041666667 0.115057529 0.077208153 0.098684211 0 0.147058824
T-42 0.1510041 0.166666667 0.170085043 0.081840642 0.180921053 0 0.18627451
ST30SS 0.118329732 0.125 0.113056528 0.10994441 0.131578947 0.6 0.18627451
DS30 0.118329727 0.083333333 0.113056528 0.125694873 0.115131579 0 0.18627451
LH-55N 0 0 0 0.185299568 0.023026316 0 0
LOC-650 0.049318734 0 0.113056528 0.185299568 0 0 0
LU300
2ST
0.146882588 0.208333333 0.113056528 0.098826436 0.148026316 0.4 0.147058824
LB-35II
{M} 600T
0.123175867 0.125 0.075037519 0.13588635 0.088815789 0 0.098039216
Yij
Area Cost
Spindle
motor power
Max
Diameter
Max Spindle
speed
No of tools
Rapid
traverse X
axis
BNE 34S5 0.988773377 1 1 0 1 0 0.263157895
SKT28LM 0.95130145 0.166666667 0.613333333 0.416666667 0.461538462 0 0.789473684
T-42 1 0.666666667 0.906666667 0.441666667 0.846153846 0 1
ST30SS 0.783619335 0.5 0.602666667 0.593333333 0.615384615 1 1
DS30 0.7836193 0.333333333 0.602666667 0.678333333 0.538461538 0 1
LH-55N 0 0 0 1 0.107692308 0 0
LOC-650 0.326605267 0 0.602666667 1 0 0 0
LU300 2ST 0.972705962 0.833333333 0.602666667 0.533333333 0.692307692 0.666666667 0.789473684
LB-35II
{M} 600T
0.815712071 0.5 0.4 0.733333333 0.415384615 0 0.526315789
SUM 6.622336763 4 5.330666667 5.396666667 4.676923077 1.666666667 5.368421053

33
Step 5(Table 37):- Determination of lnPij
lnPij
Area Cost
Spindle
motor power
Max
Diameter
Max Spindle
speed
No of tools
Rapid
traverse X
axis
E 34S5 -1.90173841
-
1.386294361
-
1.673476309
0
-
1.542640432
0
-
3.015534901
SKT28LM
-
1.940372578
-3.17805383
-
2.162323026
-
2.561250216
-2.31583032 0
-
1.916922612
T-42
-
1.890448293
-
1.791759469
-
1.771456717
-
2.502981308
-
1.709694516
0
-
1.680533834
ST30SS
-
2.134280211
-
2.079441542
-
2.179867335
-
2.207780403
-
2.028148247
-
0.510825624
-
1.680533834
DS30
-
2.134280256
-2.48490665
-
2.179867335
-
2.073897949
-2.16167964 0
-
1.680533834
LH-55N 0 0 0
-
1.685781479
-
3.771117552
0 0
LOC-650
-
3.009451264
0
-
2.179867335
-
1.685781479
0 0 0
LU300
2ST
-
1.918121733
-
1.568615918
-
2.179867335
-
2.314390138
-
1.910365212
-
0.916290732
-
1.916922612
LB-35II
{M} 600T
-
2.094142133
-
2.079441542
-2.58976704
-
1.995936407
-
2.421190835
0 -2.32238772
M=9 -(1/ln m)= -0.455119613
Step 6(Table 38):- Determination Pij x lnPij
Pij * lnPij
Area Cost
Spindle
motor power
Max
Diameter
Max Spindle
speed
No of tools
Rapid
traverse X
axis
BNE 34S5
-
0.283946344
-0.34657359
-
0.313933775
0
-
0.329840882
0
-
0.147820338
SKT28LM
-
0.278735334
-0.13241891
-
0.248791544
-
0.197749399
-
0.228535887
0
-
0.281900384
T-42
-
0.285465442
-
0.298626578
-
0.301298291
-
0.204845598
-
0.309319732
0
-
0.313040616
ST30SS
-
0.252548806
-
0.259930193
-
0.246448233
-
0.242733114
-
0.266861611
-
0.306495374
-
0.313040616
DS30 -0.2525488
-
0.207075554
-
0.246448233
-0.26067834 -0.24887759 0
-
0.313040616
LH-55N 0 0 0
-
0.312374579
-
0.086834944
0 0
LOC-650
-
0.148422327
0
-
0.246448233
-
0.312374579
0 0 0
LU300
2ST
-
0.281738684
-
0.326794983
-
0.246448233
-
0.228722929
-
0.282784324
-
0.366516293
-
0.281900384
LB-35II
{M} 600T
-
0.257947772
-
0.259930193
-
0.194329693
-
0.271220512
-
0.215039976
0
-
0.227685071
SUM
-
2.041353509
-
1.831350001
-
2.044146234
-
2.030699051
-
1.968094945
-
0.673011667
-
1.878428026

34
Step 7 (Table 39):- Determining 1-Ej (by eqn. 22)
Ej 0.07093998 0.166516696 0.069668956 0.075789033 0.10428139 0.69369919 0.145090563
Step 8(Table 40):- Determining the weight (by eqn. 23)
EIGHT 0.0534998040.1255795460.0525412530.0571567450.0786444240.5231573260.109420902
Step 9(Table 41):- Determining the weightage matrix (by eqn. 6)
WEIGHTAGE
MATRIX
Area Cost
Spindle
motor power
Max
Diameter
Max Spindle
speed
No of tools
Rapid
traverse X
axis
BNE 34S5 0.10639899 0.251159 0.105082507 0.057156745 0.157288847 0.52315733 0.138215876
SKT28LM 0.10439424 0.146509 0.084766555 0.080972056 0.11494185 0.52315733 0.195805825
T-42 0.10699961 0.209299 0.100178656 0.082400974 0.145189705 0.52315733 0.218841804
ST30SS 0.09542328 0.188369 0.084206115 0.091069747 0.127040992 1.04631465 0.218841804
DS30 0.09542328 0.167439 0.084206115 0.095928071 0.120991421 0.52315733 0.218841804
LH-55N 0.0534998 0.12558 0.052541253 0.11431349 0.087113823 0.52315733 0.109420902
LOC-650 0.07097312 0.12558 0.084206115 0.11431349 0.078644424 0.52315733 0.109420902
LU300 2ST 0.10553938 0.230229 0.084206115 0.087640343 0.133090563 0.87192888 0.195805825
LB-35II {M}
600T
0.09714024 0.188369 0.073557755 0.099071692 0.111312107 0.52315733 0.16701085
BAA
Area Cost
Spindle
motor power
Max
Diameter
Max Spindle
speed
No of tools
Rapid
traverse X
axis
G 0.09084164 0.176489 0.082309161 0.08975444 0.116957571 0.59803961 0.168765165
Step 11(Table 43):- Calculation of Distance of the alternative from Border Approximation Area
(BAA) Matrix (by eqn. 10)
Q = V - G Area Cost
Spindle
motor power
Max
Diameter
Max Spindle
speed
No of tools
Rapid traverse
X axis
BNE 34S5
0.01555734 0.07467 0.022773345
-
0.032597694 0.040331276 -0.0748823 -0.030549289
SKT28LM
0.0135526
-
0.02998 0.002457394
-
0.008782384
-
0.002015721 -0.0748823 0.02704066
T-42
0.01615797 0.03281 0.017869495
-
0.007353465 0.028232134 -0.0748823 0.050076639
ST30SS
0.00458164 0.01188 0.001896954 0.001315308 0.010083421 0.44827504 0.050076639
DS30
0.00458164
-
0.00905 0.001896954 0.006173631 0.00403385 -0.0748823 0.050076639

35
LH-55N
-
0.03734184
-
0.05091
-
0.029767908 0.024559051
-
0.029843748 -0.0748823
-
0.059344263
LOC-650
-
0.01986852
-
0.05091 0.001896954 0.024559051
-
0.038313147 -0.0748823
-
0.059344263
LU300
2ST 0.01469774 0.05374 0.001896954
-
0.002114097 0.016132992 0.27388927 0.02704066
LB-35II
{M} 600T 0.0062986 0.01188
-
0.008751407 0.009317252
-
0.005645464 -0.0748823
-
0.001754314
Step 12(Table 44):- Calculation of Si and then ranking them accordingly. (by eqn.11)
Alternative Si Rank
BNE 34S5 0.01530281 4
SKT28LM -0.07260924 7
T-42 0.06291075 3
ST30SS 0.52810934 1
DS30 -0.01716916 5
LH-55N -0.25753043 9
LOC-650 -0.21686165 8
LU300 2ST 0.3852837 2
LB-35II {M} 600T -0.06353728 6
2.Solution MABAC-COV method
Step 1(Table 45):- Attributes for the CNC machines
Spindle motor
power
Max
Diameter
Max Spindle
speed
No of
tools
Rapid traverse
X axis
BNE 34S5 5595200 1 7.5 50 7000 12 10
SKT28LM 6650040 6 22 300 3500 12 20
T-42 5279169 3 11 315 6000 12 24
ST30SS 11370315 4 22.4 406 4500 24 24
DS30 11370316 5 22.4 457 4000 12 24
LH-55N 33429309 7 45 650 1200 12 5
LOC-650 24235325 7 22.4 650 500 12 5
LU300 2ST 6047500 2 22.4 370 5000 20 20
LB-35II
{M} 600T
10466900 4 30 490 3200 12 15
MAX 33429309 7 45 650 7000 24 24
MIN 5279169 1 7.5 50 500 12 5

36
Step 2(Table 46):- Determination of the Normalized matrix (by eqn. 2)
Normalization Area Cost
Spindle
motor power
Max
Diameter
Max Spindle
speed
No of tools
Rapid
traverse X
axis
BNE 34S5 0.98877338 1 1 0 1 0 0.263157895
SKT28LM 0.95130145 0.166667 0.613333333 0.416666667 0.461538462 0 0.789473684
T-42 1 0.666667 0.906666667 0.441666667 0.846153846 0 1
ST30SS 0.78361934 0.5 0.602666667 0.593333333 0.615384615 1 1
DS30 0.7836193 0.333333 0.602666667 0.678333333 0.538461538 0 1
LH-55N 0 0 0 1 0.107692308 0 0
LOC-650 0.32660527 0 0.602666667 1 0 0 0
LU300 2ST 0.97270596 0.833333 0.602666667 0.533333333 0.692307692 0.66666667 0.789473684
LB-35II {M}
600T
0.81571207 0.5 0.4 0.733333333 0.415384615 0 0.526315789
Step 3(Table 47):- Calculation of x bar j. (by eqn. 13)
Spindle
motor power
Max
Diameter
Max Spindle
speed
No of tools
Rapid
traverse X
axis
BNE 34S5 0.988773377 1 1 0 1 0 0.263157895
SKT28LM 0.95130145 0.166667 0.613333333 0.416666667 0.461538462 0 0.789473684
T-42 1 0.666667 0.906666667 0.441666667 0.846153846 0 1
ST30SS 0.783619335 0.5 0.602666667 0.593333333 0.615384615 1 1
DS30 0.7836193 0.333333 0.602666667 0.678333333 0.538461538 0 1
LH-55N 0 0 0 1 0.107692308 0 0
LOC-650 0.326605267 0 0.602666667 1 0 0 0
LU300 2ST 0.972705962 0.833333 0.602666667 0.533333333 0.692307692 0.66666667 0.789473684
LB-35II
{M} 600T
0.815712071 0.5 0.4 0.733333333 0.415384615 0 0.526315789
X bar j 0.735815196 0.444444 0.592296296 0.59962963 0.51965812 0.18518519 0.596491228
Step 4(Table 48):- Calculation of xij- x bar
Xij-X bar
Area Cost
Spindle
motor power
Max
Diameter
Max Spindle
speed
No of tools
Rapid
traverse X
axis
BNE 34S5 0.252958181 0.555556 0.407703704 -0.59962963 0.48034188 -0.1851852
-
0.333333333
SKT28LM 0.215486254 -0.27778 0.021037037
-
0.182962963
-
0.058119658
-0.1851852 0.192982456
T-42 0.264184804 0.222222 0.31437037
-
0.157962963
0.326495726 -0.1851852 0.403508772
ST30SS 0.04780414 0.055556 0.01037037
-
0.006296296
0.095726496 0.81481481 0.403508772
DS30 0.047804104 -0.11111 0.01037037 0.078703704 0.018803419 -0.1851852 0.403508772
LH-55N -0.7358152 -0.44444
-
0.592296296
0.40037037
-
0.411965812
-0.1851852
-
0.596491228
LOC-650 -0.40920993 -0.44444 0.01037037 0.40037037 -0.51965812 -0.1851852 -

37
0.596491228
LU300
2ST
0.236890766 0.388889 0.01037037
-
0.066296296
0.172649573 0.48148148 0.192982456
LB-35II
{M} 600T
0.079896875 0.055556
-
0.192296296
0.133703704
-
0.104273504
-0.1851852
-
0.070175439
Step 5(Table 49):- Determination of (Xij-X bar)2
(Xij-X
bar)2
Area Cost
Spindle
motor power
Max
Diameter
Max Spindle
speed
No of tools
Rapid
traverse X
axis
BNE 34S5 0.063987842 0.308642 0.16622231 0.359555693 0.230728322 0.03429355 0.111111111
SKT28LM 0.046434326 0.07716 0.000442557 0.033475446 0.003377895 0.03429355 0.037242228
T-42 0.069793611 0.049383 0.09882873 0.024952298 0.106599459 0.03429355 0.162819329
ST30SS 0.002285236 0.003086 0.000107545 3.96433E-05 0.009163562 0.66392318 0.162819329
DS30 0.002285232 0.012346 0.000107545 0.006194273 0.000353569 0.03429355 0.162819329
LH-55N 0.541424002 0.197531 0.350814903 0.160296433 0.16971583 0.03429355 0.355801785
LOC-650 0.167452766 0.197531 0.000107545 0.160296433 0.270044561 0.03429355 0.355801785
LU300
2ST
0.056117235 0.151235 0.000107545 0.004395199 0.029807875 0.23182442 0.037242228
LB-35II
{M} 600T
0.006383511 0.003086 0.036977866 0.01787668 0.010872964 0.03429355 0.004924592
sum/m 0.106240418 0.111111 0.072635171 0.085231344 0.092296004 0.12620027 0.15450908
Step 6(Table 50):- Determination of Sj (by eqn. 14)
Sj 0.325945421 0.333333 0.269509131 0.291944077 0.303802574 0.35524678 0.39307643
Step 7(Table 51):- Determination of Delta j (by eqn. 15)
delta j 0.442971854 0.75 0.45502417 0.486874002 0.584620085 1.91833261 0.658981074
Step 8(Table 52):- Determination of Weightage Wj (by eqn. 16)
Wj 0.083630029 0.141595 0.085905423 0.091918451 0.110372237 0.36216796 0.124411079
Step 9(Table 53):- Determination of weightage matrix (by eqn. 5)
WEIGHTAGE
MATRIX
Area Cost
Spindle
motor power
Max
Diameter
Max Spindle
speed
No of tools
Rapid
traverse X
axis
BNE 34S5 0.16632117 0.28319 0.171810846 0.091918451 0.220744475 0.36216796 0.157150836
SKT28LM 0.1631874 0.165194 0.138594082 0.130217806 0.16131327 0.36216796 0.222630351
T-42 0.16726006 0.235991 0.163793006 0.132515767 0.20376413 0.36216796 0.248822157
ST30SS 0.14916414 0.212392 0.137677758 0.146456732 0.178293614 0.72433591 0.248822157
DS30 0.14916413 0.188793 0.137677758 0.154269801 0.169803442 0.36216796 0.248822157

38
LH-55N 0.08363003 0.141595 0.085905423 0.183836903 0.122258478 0.36216796 0.124411079
LOC-650 0.11094404 0.141595 0.137677758 0.183836903 0.110372237 0.36216796 0.124411079
LU300 2ST 0.16497746 0.259591 0.137677758 0.140941625 0.186783786 0.60361326 0.222630351
LB-35II {M}
600T
0.15184805 0.212392 0.120267592 0.159325316 0.156219167 0.36216796 0.189890594
BAA
Area Cost
Spindle
motor power
Max
Diameter
Max Spindle
speed
No of tools
Rapid
traverse X
axis
G 0.14200219 0.198997 0.134576221 0.144341478 0.164142201 0.41400698 0.191885241
Step 11(Table 55):- Calculation of Distance of the alternative from BAA Matrix (by eqn. 10)
Step 12 (Table 56):- Determination of Si and ranking them accordingly (by eqn. 11)
Alternative Si Rank
BNE 34S5 0.06335229 4
SKT28LM -0.04664627 7
T-42 0.12436335 3
ST30SS 0.40719145 1
DS30 0.02074725 5
LH-55N -0.2861464 9
LOC-650 -0.2189463 8
LU300 2ST 0.32626365 2
LB-35II {M} 600T -0.03784018 6
Q = V – G Area Cost
Spindle
motor power
Max
Diameter
Max Spindle
speed
No of tools
Rapid
traverse X
axis
BNE 34S5
0.02431899 0.084193 0.037234625
-
0.052423027 0.056602274 -0.051839
-
0.034734405
SKT28LM
0.02118521 -0.0338 0.004017862
-
0.014123672
-
0.002828931 -0.051839 0.03074511
T-42
0.02525787 0.036995 0.029216786
-
0.011825711 0.039621929 -0.051839 0.056936916
ST30SS 0.00716195 0.013395 0.003101537 0.002115254 0.014151413 0.31032894 0.056936916
DS30 0.00716195 -0.0102 0.003101537 0.009928323 0.005661241 -0.051839 0.056936916
LH-55N
-
0.05837216 -0.0574
-
0.048670798 0.039495424
-
0.041883723 -0.051839
-
0.067474163
LOC-650
-
0.03105815 -0.0574 0.003101537 0.039495424
-
0.053769964 -0.051839
-
0.067474163
LU300
2ST 0.02297527 0.060594 0.003101537
-
0.003399853 0.022641585 0.18960628 0.03074511
LB-35II
{M} 600T 0.00984587 0.013395
-
0.014308629 0.014983837
-
0.007923034 -0.051839
-
0.001994648

39
11. COMPARISON
(Table 57):- RANK COMPARISON
Alternatives Rank by MABAC+ENTROPY Rank by MABAC+COV
1 4 4
2 7 7
3 3 3
4 1 1
5 5 5
6 9 9
7 8 8
8 2 2
9 6 6
FIG.2:- Rank Comparison by Graphical Analysis
0
1
2
3
4
5
6
7
8
9
10
1 2 3 4 5 6 7 8 9
Rank
Altrnatives
Rank Comparison
Rank by MABAC+ENTROPY Rank by MABAC+COV

40
12. RESULTS AND DISCUSSIONS
We used the MABAC-COV and TOPSIS –DOE as a trial method in selection of Robot
from the Seven robots given to us to find out the best robot among them. After applying the
Spearman’s Co-relation we find out that the our spearman’s co-relation co-efficient is more
than .8.Our Spearman’s Co-relation for this method is around .86 . So the trial method on
the robot selection was a success. The result table is given below.
Methods Used/
Alternatives
Rank by
Topsis + DOE
Rank by
MABAC+AHP
Rank by
MABAC+ENTROPY
Rank by
MABAC+COV
1 1 3 1 1
2 3 2 2 3
3 2 1 3 2
4 4 4 4 4
5 6 6 6 6
6 5 7 7 7
7 7 5 5 5
Sperman's rank co-
efficient - 0.75 0.821428571 0.857142857
The Graphical analysis is given below
After the success in the Robot selection by the use of MABAC-COV and MABAC-
Entropy method we used it in the selection of Industrial CNC machines. We were provided
with nine CNC machines and we applied the mentioned method on it. Finally, after finding
out the ranking by this process we compared our relation using the Spearman’s Co-relation
we find out that the CNC machine ST30SS is ranked as the number one. So it is the best
alternative CNC machine among all the nine CNC machine given to us. The result table is
given below.
0
1
2
3
4
5
6
7
8
1 2 3 4 5 6 7
Rank
Alternatives
Rank comparison
Rank by Topsis + DOE Rank by MABAC+AHP Rank by MABAC+ENTROPY Rank by MABAC+COV

41
Alternatives Rank by MABAC+ENTROPY Rank by MABAC+COV
1 4 4
2 7 7
3 3 3
4 1 1
5 5 5
6 9 9
7 8 8
8 2 2
9 6 6
The graphical analysis is given below
0
1
2
3
4
5
6
7
8
9
10
1 2 3 4 5 6 7 8 9
Rank
Altrnatives
Rank Comparison
Rank by MABAC+ENTROPY Rank by MABAC+COV

42
13 CONCLUSIONS
In our project we used various MCDM processes, after analysing their results we found that
MABAC-COV gives the best result among all others processes. Therefore, Integrated
MABAC-COV can be considered as one of the best methods in Advanced Manufacturing
Technology (AMT) selection.

43
14. FUTURE SCOPE
The research presented in this thesis seems to have raised more questions that it has
answered. There are several lines of research arising from this work which would be
pursued. So, far we have examined only the CNC machines of the industry. There are many
areas in the industry where we can use our MCDM process and find out the best material
among the various types of materials given to us for a particular type of job. It would be
fascinating to examine the different industry results.

44
15. REFERENCE
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logistics centers using Multi-Attributive Border Approximation area Comparison
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entropy weight in groundwater quality assessment-a case study in Dongsheng City,
Northwest China." Journal of Chemistry 8.2 (2011): 851-858.
Deng, Hepu. "A similarity-based approach to ranking multi criteria
alternatives." International Conference on Intelligent Computing. Springer Berlin
Heidelberg, 2007.
Xia, Fei, Huan Wei, and Lian Wu Yang. "Improved COPRAS Method and Application in
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İç, Yusuf Tansel. "An experimental design approach using TOPSIS method for the
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Chen, Mei-Fang, and Gwo-Hshiung Tzeng. "Combining grey relation and TOPSIS
concepts for selecting an expatriate host country." Mathematical and Computer
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Athawale, Vijay Manikrao, and Shankar Chakraborty. "Material selection using multi-
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Chen, Mei-Fang, and Gwo-HshiungTzeng. "Combining grey relation and TOPSIS concepts
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(2004): 1473-1490.
Pei-Yue, Li, QianHui, and Wu Jian-Hua. "Application of set pair analysis method based on
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