On the Selection of Optimum Blend of WPO – Combinatorial Mathematics Based Approach

International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 04 Issue: 08 | Aug -2017 www.irjet.net p-ISSN: 2395-0072
© 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 857
On the Selection of Optimum Blend of WPO – Combinatorial
Mathematics Based Approach
Geetha.N.K1, Sekar.P2
1Assistant Professor, Department of Mathematics, Sri Krishna College of Engineering and Technology,
Coimbatore, India 641008
2Dean, Faculty of Science and Humanities, SRM University, Chennai, India 600089.
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Abstract - This paper presents the methodologyofselection
of optimum blend using combinatorial mathematics based
approach from blends of waste plastic oil designated as
WPO10, WPO20 and WPO30 based on the performance
parameters like brake power, specific fuel consumption,
mechanical efficiency, brake thermal and indicated thermal
efficiency. It is found that WPO20 at 10kg load forms the
optimum blend out of all the test fuels.
Key Words: Waste plastic oil, Combinatorial mathematics
based approach, CMBA, Blend
1. INTRODUCTION
With the rapid depletion of fossil fuels at a faster rate, an
alternative fuel is needed to fulfill the needs of mankind.Out
of the various alternative fuels, Waste Plastic Oil (WPO) is
acclaimed to be a suitable alternative fuel as the properties
of WPO are very close to diesel [1-3]. Researchers haveputa
lot of effort in production and characterization of WPO and
its use as fuel on engines in neat and blend form [4-6].
The present study deals with the selectionofoptimumblend
of WPO-Diesel. The statistical data for the present study if
taken from the experimental results of Ankit et al. [7]. The
blends of WPO are designated as WPO10 (10%WPO+
90%Diesel), WPO20 (20%WPO+80%Diesel) and WPO30
(30%WPO+70%Diesel). The load on the engine is varied as
2kg, 4kg, 6kg, 8kg and 10kg. the results of experimental
investigation are shown in Table1.
Table - 1: Experimental results
Exp No. Blend
Load
(kg)
BP
(kW)
SFC
Kg/kWh)
Mech
Efficiency (%)
BTE
(%)
ITE
(%)
1 WPO 10 2 0.43 0.71 17.21 12 69.72
2 WPO 10 4 0.87 0.43 29.36 20.13 68.55
3 WPO 10 6 1.3 0.34 38.4 24.99 65.08
4 WPO 10 8 1.74 0.27 45.39 32.07 70.66
5 WPO 10 10 2.17 0.24 50.96 35.03 68.75
6 WPO 20 2 0.43 0.71 18.77 12.16 64.78
7 WPO 20 4 0.87 0.41 31.6 20.94 66.25
8 WPO 20 6 1.3 0.33 40.94 26.29 64.23
9 WPO 20 8 1.74 0.27 48.03 31.74 66.08
10 WPO 20 10 2.17 0.24 53.6 36.41 67.93
11 WPO 30 2 0.43 0.71 16.74 12.12 72.42
12 WPO 30 4 0.87 0.42 26.68 20.21 70.46
13 WPO 30 6 1.3 0.32 37.63 27.06 71.93
14 WPO 30 8 1.74 0.27 44.58 31.57 70.83
15 WPO 30 10 2.17 0.24 50.13 36.08 71.98

2. COMBINATORIAL MATHEMATICS BASED
APPROACH
Combinatorial mathematics based approach (CMBA) is an
integration of combinatorial mathematics matrix function
and analytic hierarchy process and a [8]. The step wise
procedure of CMBA is shown below:
Step 1: Decision matrix
Decision matrix is a collection of data for each experiment
and is same as shown in Table1.
Step 2: Normalization
The size of the matrix is equal to the number of attributes
considered. Normalization is to set the attribute data on
same scale so that, comparisons can be made easier [9]. Let
xij is the normalized value of yij for attribute i, then,
)(max ijj
ij
ij
y
y
x 
; if jth attribute is beneficial
ij
ijj
ij
y
y
x
)(min

; if, jth attribute is non-beneficial
The normalized values of attributes are shown in Table 2.
Table – 2: Normalized values of attributes
Exp No. Blend
Load
(kg)
BP
(kW)
SFC
Kg/kWh)
Mech
Efficiency (%)
BTE
(%)
ITE
(%)
1 WPO 10 2 0.198 1.000 0.321 0.330 0.963
2 WPO 10 4 0.401 0.606 0.548 0.553 0.947
3 WPO 10 6 0.599 0.479 0.716 0.686 0.899
4 WPO 10 8 0.802 0.380 0.847 0.881 0.976
5 WPO 10 10 1.000 0.338 0.951 0.962 0.949
6 WPO 20 2 0.198 1.000 0.350 0.334 0.895
7 WPO 20 4 0.401 0.577 0.590 0.575 0.915
8 WPO 20 6 0.599 0.465 0.764 0.722 0.887
9 WPO 20 8 0.802 0.380 0.896 0.872 0.912
10 WPO 20 10 1.000 0.338 1.000 1.000 0.938
11 WPO 30 2 0.198 1.000 0.312 0.333 1.000
12 WPO 30 4 0.401 0.592 0.498 0.555 0.973
13 WPO 30 6 0.599 0.451 0.702 0.743 0.993
14 WPO 30 8 0.802 0.380 0.832 0.867 0.978
15 WPO 30 10 1.000 0.338 0.935 0.991 0.994
Step 3: Relative Importance
After analyzing the attributes, the relative importance of
attributes is assigned. Table 3 shows the scale for pairwise
comparison [10].
The geometric mean approach of AHP is used to determine
the relative normalized weights of the attributes and the
consistency check is carried out. It is required that the
consistency ratio value of the relative importance of
attributes should be less than 0.10 [11]. The consistency
ratio in the present study is found to be 0.068. The
consistency evaluation is shown in Table 4.
Step 4: Formation of alternate selection attribute matrix
The alternative selection matrix is formed by keeping the
normalized values for attributes for the alternative as
diagonal elements. The matrix is represented by, B.
B= (1)
Step 5: Permanent function
The permanent function used in Combinatorial mathematics
characterizes the configuration of a system [12]. The
characteristic permanent function for the standardmatrixis
shown in Eq. 2.

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Table – 3: Scale for pairwise comparison
Degree of importance Definition
1 Equal
2 Intermediate between 1 and 3
3 Moderately preferable
5 Strongly preferable
7 Very strongly preferable
9 Extremely strongly preferable
½, 1/3, ¼, 1/5, 1/6, 1/7, 1/8, 1/9 Reciprocals of 2, 3, 4, 5, 6, 7, 8 and 9
Table – 4: Consistency evaluation
BP
(kW)
SFC
Kg/kWh)
Mech Efficiency
(%)
BTE
(%)
ITE
(%)
Tota
l
Averag
e
Consistency
Measure
BP (kW) 0.353 0.444 0.343 0.235 0.222
1.59
8
0.320 5.259
SFC (Kg/kWh) 0.118 0.222 0.343 0.235 0.222
1.14
0
0.228 5.435
Mech Efficiency
(%)
0.176 0.111 0.171 0.353 0.222
1.03
4
0.207 5.360
BTE (%) 0.176 0.111 0.057 0.118 0.222
0.68
5
0.137 5.090
ITE (%) 0.176 0.111 0.086 0.059 0.111
0.54
3
0.109 5.102
CI 0.062
RI 0.91
CR 0.068

Step 6: Rank of alternatives
The rank of alternatives is based on the permanent function
value of the alternative selection matrix, also called as Index
score. The alternative for which the value of Index score is
highest is the best choice for the considereddecisionmaking
problem. The Index score for all alternatives is sorted and
ranked as shown in Table 5.
Table – 5: Index score for alternatives
Exp No. Blend Load (kg) Index score Rank
10 WPO 20 10 141.4409 1
15 WPO 30 10 141.2131 2
5 WPO 10 10 139.798 3
4 WPO 10 8 132.5319 4
14 WPO 30 8 131.9812 5
9 WPO 20 8 131.8858 6
13 WPO 30 6 123.9184 7
8 WPO 20 6 122.7776 8
3 WPO 10 6 121.7662 9
2 WPO 10 4 115.2242 10
7 WPO 20 4 115.138 11
12 WPO 30 4 114.5299 12
11 WPO 30 2 111.311 13
1 WPO 10 2 110.7055 14
6 WPO 20 2 110.0223 15
3. CONCLUSION
The proposed CMBA is adapted to select optimum blend of
waste plastic oil. The computation used is comparatively
simple compared to other multi attribute decision making
methods. The measures of the attributes and their relative
importance are used together to rank the alternatives.
Hence, it provides a better evaluation. The use of permanent
concept characterizes theconsideredapproachasitcontains
all possible structural componentsoftheattributesandtheir
relative importance hence, no information is lost. This
method can deal with problems consideringboth qualitative
and quantitative attributes. The uniqueness of CMBA is that
it offers a general procedure thatcanbeapplicabletodiverse
selection problems that incorporates vagueness and a
number of selection attributes. The approach is logical,
simple and convenient to implement.
NOMENCLATURE
BP: Brake power
SFC: Specific fuel consumption
BTE: Brake thermal efficiency
ITE: Indicated thermal efficiency
CMBA: Combinatorial mathematics based approach
WPO: Waste plastic oil
WPO10:10%WPO+90%Diesel
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