Evaluation of WMEP Disassembly Sequence Based on Entropy-TOPSIS Method
Wen-yong Zhou1, 1, Rong Rong1, 2, Yun-fei He1, 3
1
School of Economics & Management, Tongji University, Shanghai, 200092, China
(1zhouwyk@126.com, 2rongrongbaby2007@163.com,3edgar1122@126.com)
II. EVALUATION INDICATORS
Abstract - Better sequences need to be select when
evaluating the disassembly sequences of waste mechanical
and electrical product (WMEP), by which we can effectively
improve the working efficiency and reduce waste. This
paper establishes a comprehensive evaluation system for
disassembly sequence, trying to provide a reasonable way to
choose disassembly sequence. The model is designed based
on entropy-TOPSIS, so as to improve the accuracy of
evaluation, and simplify the complexity of the evaluation
process. Before the end of this paper, a numerical example is
conducted to demonstrate the feasibility and applicability of
the model.
Keywords-Disassembly sequence evaluation, Evaluation
system, Entropy-TOPSIS method, WMEP
I. INTRODUCTION
Rapid development of modern industry leads to the
growing demand of mechanical products. Mechanical
products always face the cyclic process from using to
abandoning, then recycling [1-2]. Disassembly is an
important part of green manufacturing as well as an
essential way to realize resource conservation and
sustainable development. Disassembly refers to the
process separating parts, components and connectors from
product [3].For waste mechanical and electrical product
(WMEP), reasonable disassembly sequence can lower the
cost, improve removal efficiency, and reduce secondary
environmental pollution on disassembly process [4].
Most researches focus on disassembly sequence
planning or disassembly model building. Their
achievement enrich the current research, but unfortunately,
the problem of evaluating disassembly sequences receives
little attention [5-6].In practice, feasible disassembly
sequence is not fixed, evaluating disassembly sequences
and choosing a best one is very important. Most of present
researches about the evaluation of disassembly sequences
are more based on green design [7].In addition, there are
also researches employing AHP, fuzzy evaluation method,
the gray relational analysis and other methods to evaluate
the sequence of disassembly [8].
Considering the background of remanufacturing, the
evaluation of WMEP disassembly sequence is complex
and multidimensional. While constructing a system of
disassembly sequence evaluation, this paper puts forward
a WMEP disassembly sequence evaluation model based
on entropy-TOPSIS method.
The disassembly of WMEP is a basic approach and
important part of the effectively recycling and
remanufacturing. Different disassembly sequence leads to
different costs and different value of recycling or
remanufacturing. The establishment of the evaluation
model of WMEP is designed to reduce the economic cost
and the secondary pollution of the disassembly process. In
this paper, technical, economic, environmental indicators
are taken into account to build the indexes system, reflect
the nature of the disassembly sequence more
comprehensively than previous studies which only
considering economic factor.
Technical indicators of the disassembly sequence
include security, tool change times, disassembly time and
accessibility. Security reflects whether harmful material
will be revealed and workers would get hurt. Tool change
times show the frequency of tool transformation.
Disassembly time can embody disassembly efficiency.
Accessibility means the level can be arrived by using
disassembly tool, and the size of space for operation.
Main indicators which can influence the economy of
disassembly are human consumption costs, tool
consumption costs, energy consumption costs and
recycling benefits. Different sequences need different
resource and energy, so when choosing sequence we
should take these economic indicators into account. On
one hand, we should make sure the costs lowest, the other
hand ensure high benefits.
Environmental indicators are used to judge the level
of environmental pollution. We use air pollution level,
water pollution level, noise pollution level and solid
pollution level to describe the overall pollution levels.
This paper use ten-grade to quantify the degree of
pollution.
III.EVALUATION MODEL
A. Theoretical Basis
As for the evaluation of disassembly module,
scholars studied little about disassembly sequence, but
focused more on the evaluation of detachability. There are
correlations between products’ detachability and
disassembly sequence, so the research of disassembly
sequence evaluation can learn from the efforts of
products’ detachability evaluation. Many scholars applied
lots of methods to the research of products’ detachability
evaluation, such as AHP [9], fuzzy evaluation method [10],
directed network diagram method [11], and information
entropy evaluation method [12]. Similar to the detachability
evaluation, the disassembly sequence evaluation is also
complex and multidimensional. Methods such as AHP are
subjective and hard to achieve optimization of evaluation
results. Heuristic methods such as genetic algorithms are
relatively complex. Based on the characteristics of
disassembly sequence evaluation and the requirements
that the process should be concise and the results should
be optimal, this paper connects entropy method and
TOPSIS method to structure the entropy-TOPSIS
evaluation model, it can effectively avoid the drawbacks
of Experts Grading Method which the weights are given
subjectively [13-14].
TOPSIS is a kind of multi-attribute decision making
method. The basic theory is to sort by testing the distance
between evaluation objects and the optimal/worst
solution. TOPSIS is principle- intuitive and simple in
calculation, and requires small sample size [15].Entropy
method determines the index weight according to the
amount of information that delivered from each index,
identifies the distribution and variation. Weights from
using this method are more objective than traditional
approach.
𝑃𝑖𝑗 = [𝑃1
…
𝑃𝑚 ](2)
2) Calculate entropy values, and then transform the
entropy values to weight values.
𝐻𝑗 = −
1
𝑙𝑛4
∑𝑚
𝑖=1 𝑃𝑖𝑗 × 𝑙𝑛 𝑃𝑖𝑗
(1 − 𝐻𝑗 )⁄∑4𝑗=1(1 − 𝐻𝑗 )
𝑊𝑗
=
(3)
3) Construct standardized weight matrix R.
(𝑅)𝑚×𝑛
𝑊1 𝑃11
𝑊1 𝑃21
=[
…
𝑊1 𝑃𝑚1
𝑊2 𝑃12
𝑊2 𝑃22
…
𝑊2 𝑃𝑚2
𝑊3 𝑃13
𝑊3 𝑃23
…
𝑊3 𝑃𝑚3
𝑊4 𝑃14
𝑊4 𝑃24
](4)
…
𝑊4 𝑃𝑚4
4) Determine the ideal point and negative ideal point.
𝑅𝑗+ = {
𝑚𝑎𝑥 𝑟𝑖𝑗 , 𝑓𝑜𝑟𝑤𝑎𝑟𝑑𝑖𝑛𝑑𝑖𝑐𝑎𝑡𝑜𝑟
𝑖
𝑚𝑖𝑛 𝑟𝑖𝑗 ,
𝑖
𝑅𝑗− = {
B. The Evaluation Model
𝑏𝑎𝑐𝑘𝑤𝑎𝑟𝑑 𝑖𝑛𝑑𝑖𝑐𝑎𝑡𝑜𝑟
(5)
𝑚𝑖𝑛 𝑟𝑖𝑗 , 𝑓𝑜𝑟𝑤𝑎𝑟𝑑𝑖𝑛𝑑𝑖𝑐𝑎𝑡𝑜𝑟
𝑖
𝑚𝑎𝑥 𝑟𝑖𝑗 ,
𝑖
Suppose a kind of WMEP, which the number of
feasible disassembly sequence is m. Combined with
entropy method and TOPSIS method, indicator
information is shown in table I. Use Si (i =1to m) to
describe sequence 1 to sequence m.
𝑃2
𝑏𝑎𝑐𝑘𝑤𝑎𝑟𝑑 𝑖𝑛𝑑𝑖𝑐𝑎𝑡𝑜𝑟
(6)
5) Calculate the Euclidean distance from true value
to ideal point and negative ideal point. Determine the
relative proximity.
𝑑𝑖+ = √∑𝑛𝑗=1(𝑟𝑖𝑗 − 𝑅𝑗+ )2
TABLE I
(7)
INDICATORSINFORMATION
Level
indicators
Leve2 indicators
Technical
indicators
Security
u11
u21
um1
Tool change times
Disassembly time
Accessibility
Human consumption
costs
Tool consumption
costs
Energy consumption
costs
Recycling benefits
Air pollution levels
u12
u13
u14
f11
u22
u23
u24
f21
um2
um3
um4
fm1
f12
f22
fm2
f13
f23
fm3
f14
t11
f24
t21
fm4
tm1
Water pollution levels
Noise pollution levels
Solid pollution levels
t12
t13
t14
t22
t23
t24
tm2
tm3
tm4
Economic
indicators
Environmenta
l indicators
S1
S2
1) Give specific values for each evaluation indicator;
list the initial matrix U, F, T.Givean example on technical
indicators. Get standardized matrix P from
U.Suppose𝑈𝑖 = [𝑈𝑖1 𝑈𝑖2 𝑈𝑖3 𝑈𝑖4 ]𝑇 .
𝑈𝑖𝑗
= [𝑈1
𝑈2
…
𝑈𝑚 ](1)
𝑑𝑖− = √∑𝑛𝑗=1(𝑟𝑖𝑗 − 𝑅𝑗− )2
Sm
𝐶𝑖 =
𝑑𝑖−
𝑑𝑖+ +𝑑𝑖−
(8)
(9)
6) Make the relative proximity matrix as the initial
matrix of first indicators.
𝐶𝑖 = [𝑐𝑖1
𝑐𝑖2
𝑐𝑖3 ]𝑇 𝑈 , = [𝐶1
𝐶2
…
𝐶𝑚 ](10)
7) Use above method to calculate the first indicators,
and then get final relative proximity.
IV. NUMERICAL EXAMPLE
One product has been study for three sequences:
sequence 1, sequence 2, and sequence 3. Through the
prediction and the actual experts (workers) scoring, data
of indicators are shown by s1, s2, s3.
s1 = (8,3,34,6,450,80,120,75,4,7,6,5)
s2 = (6,4,48,8,540,105,160,96,5,4,4,5)
s3 = (9,4,57,7,630,116,210,68,6,6,5,8)
Step 1. Use formula (1) and (2) to get standardized
matrix of technical indicators, then calculate the weight
from (3). W = (0.2509,0.2467,0.2574,0.2450).
Step 2. By using formula (4) to (6), we can confirm
the ideal point and negative ideal point of technical
indicator. Then use formula (7) to (9) to calculate relative
proximity. Using the same method, we can get the relative
proximity of economic indicator and environmental
indicator. Total results are shown in table II.
TABLE II
RELATIVEPROXIMITY OFLEVEL1
Relativ
e proximity
s1
s2
s3
Technical
indicator
0.386
0.4473
0.6858
Economic
indicator
0.7426
0.5672
0
Environment
al indicator
0.4918
0.8143
0.2528
Step3. According to formula (7) to (9), we use above
method and data of table 2to get the final relative
proximity of three sequences : c1 = 0.9173 , c2 =
0.7497 , c3 = 0.025 . Since c1 > c2 > c3 , so we choose
sequence 1 as the best sequence.
V. CONCLUSION
This paper analyzed the disassembly process of
WMEP, took technical, economic, environmental
indicators into account to establish an evaluation index
system. The paper connected entropy method and
TOPSIS method to structure the entropy-TOPSIS
evaluation model. The model can simplify the complexity
of the evaluation, and improve the whole efficiency of
remanufacturing process.
In this paper, there are still shortcomings, pending
further study. For example, indicators in this paper just
come from manufacturer, ignored the concern indicators
of other stakeholders. In addition, disadvantages of using
the method to evaluate disassembly sequence also need to
be further analyzed by more empirical research.
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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