Optimization of Recycling Network of Waste Mechanical and Electrical
Products Based on GAHP
Wen-yong Zhou1,1, Qing-yu Tian1,2, Yun-fei He1,3
1
School of Economics & Management, Tongji University, Shanghai, China
(1zhouwyk@126.com, 2tianqingyu513@163.com, 3edgar1122@126.com)
Abstract - Recycling network affects much the recycling
efficiency of waste mechanical and electrical products
(WMEP), but no uniform standard is in existence about how
to choose a most suitable recycling network plan. Based on
the research on the design and evaluation of recycling
network, this paper establishes an evaluating index system of
WMEP recycling network and uses the evaluation method
GAHP to optimize it. Then a numerical example is used to
prove its applicability. The value of this paper is that it
complements the research on the optimization and index
system of recycling network, is worth being extended to
other fields.
Keywords - GAHP, optimization, recycling network,
WMEP
I. INTRODUCTION
The rationality of recycling network, which is the key
ingredient of WMEP recycle, has a big effect on the
efficiency of recycling. So choosing an appropriate
recycling network scheme is to ensure the WMEP recycle
operates efficiently [1]. However, difficulties often exist in
the actual optimization process, which is often caused by
the uncertainty reflected in the aspects of WMEP’s
quantity, damaged condition, treatment methods, recycle
need and the cost of recycling and reprocessing[2].
The research on optimization of WMEP recycling
network is very few, which typically contains evaluation
index system and optimization method. The paper[3]
established an evaluation index system of recycling
logistics with four-hierarchy tree structure, also provided
the concrete explanation of evaluation index and advice of
its application. The paper[4] optimizes the logistics
network of enterprise based on the endowing weight
method of ANP. Evaluation method such as AHP, DEA,
ANP are widely used for the optimization of recycling
network in current research.
The problems and deficiencies in the existing
research reflected in two aspects: one is that most research
are around the establishment of evaluation index system,
lack of specific research on optimization and evaluation;
the other one is that most research based on the
hypothesis that the amount of the recycling object is
divinable and obeys some distribution regularity, that is
discrepant with the truth. So on the basis of the paper [5][6]
and research findings on the evaluation of recycling
network and performance evaluation of logistics system,
this paper will establish an evaluation index system of the
recycling network according to the property of WMEP
and use GAHP as the optimization method. The research
findings of this paper complement the research on the
optimization of recycling network and offer a new path
for solving the optimization problem of uncertain system.
II. The Evaluation Index System of WMEP Recycling
Network
The recycling network of WMEP is an organic whole
consists of several interconnected and interacted elements,
the performance of which reflects in the aspects of
economy, technology, environment etc. and affected by
them [7]. As a result, a reasonable evaluation index system
and optimization method is necessary for evaluating its
performance objectively and fairly.
Selecting the evaluation index is the primary and key
step of the evaluation, which should obey the basic
principle of systematic, measurable, simple, quantitative
and qualitative[8]. On the basis of the paper[9][10], we
established an evaluation index system from three aspects:
economy, society and environment, as well as five
dimensionalities: conveniences, integration, environmental
pollution, extendibility and economy. See Fig. 1.
Target
Level
Index system
Primary
Factor Conveniences
(a)
Level
Index
Level
Integration
(b)
Coverage area of
recycling stations
(a1)
Service capacity of
recycling stations
(b1)
Coverage area of
recycling centers
(a2)
Service capacity of
recycling centers
(b2)
Convenience of
Transportation
Route (a3)
Capacity of
Transportation (b3)
Environmental
Pollution (c)
Air pollution (c1)
Water pollution
(c2)
Solid waste
pollution (c3)
Noise pollution
(c4)
Energy
consumption
(c5)
Extendibility
(d)
Extendibility of
recycling stations
(d1)
Extendibility of
recycling centers
(d2)
Convenience of
Transportation
Route (d3)
Economy
(e)
Operation
cost (e1)
Dispose cost
(e2)
Constant cost
(e3)
Income level
(e4)
Fig. 1. Evaluation Index System of WEMP Recycling System
III. The Optimization Model and Calculation of
Recycling Network
As the evaluation indexes differ a lot and many can’t
be described quantitatively, the application of traditional
optimization method faces a lot of difficulties. The gray
comprehensive evaluation method which can solve the
problem of outcome bias caused by the uncertainty of the
system, is a multidimensional gray evaluation method
rooted in the Gray theory and based on the generation of
whitening function[11]. Compared with traditional weight
distribution method, analytic hierarchy process (AHP) is
more suitable for the multifactor evaluation as it can make
the deciders’ thought and decisions more numeric and
systematized[12]. Therefore, we’ll choose GAHP, the
combination of gray comprehensive evaluation method
and analytic hierarchy process as the optimization method.
A. Weight distributing process of AHP
According to the evaluation index system established
in the foregoing chapter and AHP, we will calculate the
weight matrix of indexes on the primary factor level
which can be marked as W= ( ,
,
,
) and
the index level, marked as
=( ,
), x=(a, b, c,
d, e).
a. Establish the determination matrix
Quantificat the importance of each index according
to the standard nine-point preference scoring system
suggested by Saaty[13] to establish the determination matrix.
b. Get the weight matrix
Step 1. Normalize every determination matrix:
(1)
Step 5. Let
represents the weight of
that
belongs to the recycling network “t”, which is relegated to
gray-grade “e” by experts and get the weight matrix of the
gray evaluation :
=
(5)
/
Step 6. Calculate the synthetical weight vector of the
gray evaluation of recycling network “t” based on ,
which is represented as:
(6)
=
Step 7. Assign each gray-grade by grade levels to
generate the equating vector H=( ,
), on the
basis of which we can get the synthetical evaluation value
of the recycling network “t”.
(7)
=
So we can figure out the synthetical evaluation
vector V=[ ,
] of all recyckling networks.
According to V, we can get the evaluation grades of
all the recycling network schemes to judge their
rationality and choose the most suitable scheme.
=
IV. A Numerical Example
Step 2. Sum up the normalized numbers of the
determination matrix by the row:
(2)
=
Step 3. Normalize
and get the weight matrix
W can be figured out in the same way.
=
/
.
(3)
B. Evaluating process of gray comprehensive evaluation
method
Step 1. Determine the grade system of all the indexes
on the index level according to the industry standard,
historical data, decision makers’ experience and
preference.
Step 2. Organize experts to grade the indexes on the
index level of all recycling network scheme, the quantity
of which is t(t=1,2⋯n ), based on the grade standard and
then get the evaluation sample matrix D.
Step 3. Let e(e=1, 2, ⋯, g) represents the serial
number of gray-grade of evaluation. Establish whitening
function based on the grade system and figure out the
gray-grade of each index.
Step 4. Let
represents the gray-grade coefficient
of the grade of index which belongs to the gray-grade
of evaluation with the serial number e.
=
(4)
One recycling corporate came up with 5 feasible
schemes of constructing recycling network. The
optimizating process based on the model of GAHP
introduced in the forgoing chapter is as follows.
Step 1. Figure out the weight of each index according
to the basic model of AHP and formula 1~4. If the
uniformity check is passed, we can get the weight vector
W and
as follows:
W=[0.129,0.065,0.258,0.032,0.516]
=[0.444,0.444,0.111]
=[0.286,0.571,0.143]
=[0.133,0.044,0.531,0.027,0.265]
=[0.286,0.143,0.571]
=[0.279,0.093,0.0700.558]
Step 2. Determine the grade system shown in TABLE
on the 5-point method[14].
I based
TABLE I
Grade System
Grade
Evaluation
Index:
5.0-4.0
4.0-3.0
3.0-2.0
2.0-0.0
Excellent
Good
General
Bad
Step 3. Organize experts to grade the index e
according to the TABLE I For the contrary indexes like
cost and pollution, the grade should obey the reversed
principle. The sample matrix of evaluation D is:
D=
Step 4. Confirm four gray-grades of evaluation,
choose four gray levels and establish whitening function
using construction method of trigonometric endpoint
type[15]. The whitening function is as follows:
1
0
1
3 4
2
0
（a）
8
1
1
0 1
4
（b）
3
（c）
6
0
2
4
（d）
Fig. 2. The Whitening Function
Step 5. Calculate the weight vector of the gray
evaluation of the whole index system in the 5 recycling
networks based on the formula 4 to 6, the result is as
follows.
Assign each gray-grade by grade levels shown in
TABLE I, we can figure out H=[5, 4, 3, 2].
Besides, we can figure out the synthetical evaluation
vector V=[3.623, 3.571, 3.877, 3.800, 4.030 ].
The result shows that the highest grade is the fifth
scheme, 4.030 and prove the effectiveness of this model
for the result agrees with the actual situation.
V. CONCLUSION
The optimization of recycling network is a complex
job as its uncertainty may lead to the result deviation.
While the GAHP model can solve these problems for its
property of multilevel and multifactor and also reduce the
subjective influence from experts. This paper establishes
an evaluation index system of WEMP recycling network
based on the principle of measurable, simple, etc. and
practices GAHP, which is of good maneuverability and
promotional value, in a numerical example. However,
there are some shortages in this paper need to be
improved in further research, which reflected in that the
optimization model depends much on the experts’
judgment, which may affect the conclusion subjectively.
ACKNOWLEDGMENT
This work was supported by a grant from the program
on "Twelfth Five-Year" Plan for Chinese National
Science and Technology Development, the project on
"Technology Standard Development and Evaluation
Research of Scrap Metal Products Recycling" (No.
2011BAC10B08).
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