International journal of computer integrated manufacturing , tập 24, số 3, 2011

International Journal of Computer Integrated Manufacturing
Vol. 24, No. 3, March 2011, 189–197

An improved voting analytic hierarchy process–data envelopment analysis methodology
for suppliers selection
A. Hadi-Vencheh* and M. Niazi-Motlagh
Department of Mathematics, Islamic Azad University, Mobarakeh Branch, Mobarakeh, Isfahan, Iran
(Received 6 March 2010; final version received 3 January 2011)
Selecting an appropriate supplier is now one of the most important decisions of the purchasing department. Liu and
Hai (Liu, F.H.F. and Hai, H.L., 2005. The voting analytic hierarchy process method for selecting supplier.
International Journal of Production Economics, 97, 308–317) proposed a voting analytic hierarchy process method for
selecting suppliers. Despite its many advantages, Liu and Hai’s model (LH-model) has some shortcomings. In this
article, the authors present an extended version of the LH-model for multi-criteria supplier selection problem. An
illustrative example is presented to compare the authors’ model and the LH-model.
Keywords: data envelopment analysis (DEA); analytic hierarchy process (AHP); voting analytic hierarchy process
(VAHP); multi-criteria decision making (MCDM)

1.

Introduction

Supplier selection and evaluation is increasingly seen
as a strategic issue for companies (Ceyhun and Irem
2007). Companies need to work with different suppliers
to continue their activities. In manufacturing industries
the raw materials and component parts can equal up to
70% product cost. In such circumstances the purchasing department can play a key role in cost reduction,
and supplier selection is one of the most important
functions of purchasing management. They enhance
customer satisfaction in a value chain. Hence, strategic

partnership with better performing suppliers should be
integrated within the supply chain for improving the
performance in many directions including reducing
costs by eliminating wastages, continuously improving
quality to achieve zero defects, improving flexibility to
meet the needs of the end-customers, reducing lead
time at different stages of the supply chain, etc.
(Kumar et al. 2004, Amin and Razmi 2009). Selecting
the right supplier is always a difficult task for the
purchasing manager. This is confirmed by many
researchers (Kazerooni et al. 1997, Bevilacqua and
Petroni 2002, Humphreys et al. 2003a, Kumar et al.
2004, 2006, Ding et al. 2005, Liu and Hai 2005, Guneri
and Kuzu 2009, Hadi-Vencheh 2011). Suppliers have
varied strengths and weaknesses which require careful
assessment by the purchasers before ranking can be
given to them. So, every decision needs to be integrated
by trading off performances of different suppliers at
each supply chain stage (Liu and Hai 2005).

*Corresponding author. Email:
ISSN 0951-192X print/ISSN 1362-3052 online
Ó 2011 Taylor & Francis
DOI: 10.1080/0951192X.2011.552528


The analytic hierarchy process (AHP) has found
widespread application in decision-making problems,
involving multiple criteria in systems of many levels.
The strongest features of the AHP are that it generates

numerical priorities from the subjective knowledge
expressed in the estimates of paired comparison
matrices. The method is surely useful in evaluating
suppliers’ weights in marketing, or in ranking order,
for instance. It is, however, difficult to determine
suitable weight and order of each alternative (Lee
2009). Supplier selection is essentially a multiple
criteria decision making (MCDM) problem, which
involves multiple assessment criteria such as cost,
quality, quantity, delivery and so on. Therefore,
MCDM approaches can be used for suppliers assessment. Of the MCDM approaches, the AHP method is
particularly suitable for modelling qualitative criteria
and has found extensive applications in a wide variety
of areas such as selection, evaluation, planning and
development, decision making, forecasting, and so on.
However, due to the fact that there are some cases in
which a large number of suppliers have to be evaluated
and prioritised, while the AHP method can only
compare a very limited number of decision alternatives, the pair-wise comparison manner is obviously
infeasible in this situation.
Another way for gathering the decision makers’
opinion and selecting a candidate among a set of
candidates is preference voting. In preferential voting
systems, each voter selects m candidates from among


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A. Hadi-Vencheh and M. Niazi-Motlagh

n candidates (m n) and ranks them from the most to
the least preferred. Each candidate may receive some
votes in different ranking places. The total score of
each candidate is the weighted sum of the votes he/she
receives in different places. The winner is the one
with the biggest total score. So, the key issue of the
preference aggregation in a preferential voting system
is how to determine the weights associated with
different ranking places (Wang et al. 2007).
Liu and Hai (2005) presented a voting AHP
method henceforth LH-model, for supplier selection.
The voting AHP determines the weights of criteria not
by pair-wise comparisons but by voting. The data
envelopment analysis (DEA) method was used to
aggregate votes each criterion received in different
ranking places into an overall score of each criterion.
The overall scores were then normalised as the relative
weights of criteria. They used Noguchi’s model
(Noguchi et al. 2002) to determine weights of criteria.
Despite its many advantages LH-model has some
shortcomings. For instance, to determine the lower
bound of weights if we do not know the number of
voters we can not solve Noguchi’s model (Noguchi
et al. 2002). And for finding weights of R criteria we
have to solve Noguchi’s model, R times (one linear
programming (LP) for each criterion weight). Besides,
steps 5 and 6 of the LH-model have some obscurities
and in step 6 we need a very high number of
questionnaires and score sheets to measure supplier
performance and identify supplier priority. Of course,

inspection of questionnaires and score sheets for
determining scores is time consuming. In this article
the authors present a new voting AHP–DEA (voting
analytic hierarchy process (VAHP)–DEA) methodology to overcome shortcomings mentioned above.
The remainder of this article is organised as follows.
In section 2, the authors give a brief description of the
LH-model to provide a ground for the later development of methodology. Shortcomings of the LH-model
are presented in Section 3. The authors present our
method in Section 4 and illustrate it using a real
example. In Section 5, the authors make a comparison
between our method, LH-model and the AHP methodology proposed by Yahya and Kingsman (1999) for
supplier selection. Section 6 concludes.

overall objective of the study then specifically on
supplier rating of Dickson’s 23 criteria. The criteria
obtained from group decision fall into two categories, objective and subjective criteria. The objective criteria are those that can be evaluated using
factual data, and include quality, delivery, responsiveness, technical capability, facility, financial, etc.
Subjective criteria are those that are difficult to
quantify and thus have to be evaluated qualitatively, and include discipline, management, etc. Liu
and Hai use the chosen criteria that must be
satisfied in order to fulfil the goals of the selecting
suppliers.
2.2.

Step 2: Structure the hierarchy of the criteria

The AHP was developed to provide a simple but
theoretically multiple-criteria methodology for evaluating alternatives. Liu and Hai use the AHP to
identify subcriteria under each criterion, and to
investigate each level of the hierarchy separately.

They structure the problem into a hierarchy. On the
top level is the overall goal of selection suppliers. On
the second level are criteria that contribute to the
goal. On the third level are criteria that are
decomposed into subcriteria, and on the bottom (or
fourth) level are candidate suppliers that are to be
evaluated in terms of the subcriteria of the third
level.

2.3. Step 3: Prioritise the order of criteria
or subcriteria
2.3.1.

The first stage

In this section, the authors give a brief description of
LH-model for selecting suppliers.

In this step, Liu and Hai (2005) suppose that there are
n managers (or voters) in the study, and they will select
different orders of criteria or subcriteria for the
candidates. Every manager votes 1 to S S R, R
is the number of criteria. For this purpose, assume
there are R criteria. The criteria will be regarded as
candidates. Hence, they get R orders from 1 to R and
sum every vote in a table. It commonly happens that,
when one has to select among many objects, a
particular object is rated as the best in one evaluation,
while others are selected by other evaluation methods.
The managers get the order of criteria but not the

weights. The weight of each ranking is determined
automatically by the total votes each candidate
obtains.

2.1. Step 1: Select suppliers’ criteria
All managers and supervisors of a company are
used in this step. They were first briefed about the

2.3.2. The second stage
Liu and Hai use the same methodology to find the
orders of subcriteria.

2.

The LH-model (Liu and Hai 2005)


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International Journal of Computer Integrated Manufacturing
2.4. Step 4: Calculate the weights of criteria
or subcriteria
2.4.1. The first stage
At the first stage of this step Liu and Hai (2005) use
Noguchi’s voting and ranking model (model 1) to
develop criteria varied level from hierarchy analysis
process. This model is as follows:
yrr ¼ max

X

urs xrs

ðs¼1$SÞ

s:t: yrp ¼

X

urp xrp

1; p ¼ 1; 2; . . . ; r

ðs¼1$SÞ

ur1 ! 2ur2 ! . . . ! Surs
1
urs ! e ¼
ð1 þ 2 þ . . . þ SÞ Â n
2
¼
n  SðS þ 1Þ

ð1Þ

2.4.2. The second stage
In this stage, Liu and Hai (2005) use the voting data of
subcriteria and the same method to determine weights
of the second level criteria. The second level gives the
normalised values for all factors. The sum of weights

for the factors of criteria must add up to 1. So a criteria
performance will be made up from weighting its
subcriteria weights.

2.4.3. The third stage
The values in the bottom level are the global weight for
each of factors; they are the factor weight multiplied by
the criterion weight, so for a factor the value is criteria
weight multiply by subcriteria weight. As the actual
performance data are collected for the factor value,
these weights in the bottom level can be used directly
to calculate the overall rating of the suppliers and to
provide a performance score that can be derived for
each factor.

2.5.

their judgement on the qualitative scale of adjectival
descriptors. The general performance score guidelines
are given in Table 1.
Therefore each supplier can be awarded a score
from 0 to 10 on each subcriterion.
2.6.

Step 6: Identify supplier priority

Simple score sheets were provided to assist the
manager to record the scores for each supplier on
each of the factors. Once the scores for each factor
have been determined, then it is relatively easy to

calculate the resulting supplier rating scores. Mathematically, the supplier rating is equivalent to the sum
of the product of each factor weight and the supplier
performance score on that factor.
3.

Issues on LH-model

In what follows the authors express ambiguities and
shortcomings of VAHP methodology presented by Liu
and Hai (2005). Firstly, it uses Noguchi’s strong
ordering, despite it has useful properties, this model
has a main deficiency, that is, it uses the term 2/
nS(Sþ1) to bound urs and make it greater than zero.
There is a question: if we do not know the number of
voters (n), what should we do?
Secondly, in step 4 to obtain the weight of each
criteria and subcriteria selection suppliers, we have to
solve the model RþP times, where R is the number of
criteria and P is the number of subcriteria. Clearly this
is time consuming.
Thirdly, in step 5, the managers have to compare
each supplier with respect to each factor and award a
score from 0 to 10 to each supplier on each factor. This
one by one assessment is time consuming, too.
Fourthly, in step 6, it has not been identified that
the scores which are applied to calculate the resulting
supplier rating scores are the average of managers
scores or for each manager scores we calculate the total
scores and then average all of managers total scores to
obtain resulting supplier rating scores.

Step 5: Measure supplier performance

This step requires the managers to assess the performance of all suppliers on the factors identified as
important for supplier scores. A major problem was
thus to ensure consistency between the managers and
avoid any bias creeping in. A set of standard guidelines
was set up after discussions with the managers (or
voters) of the company. It is agreed that all performance scores would be based on an 11-point grade
scale. Each grade would have an adjective descriptor
and an associated point score or range of point scores.
The managers preferred, in the first instance, to make

4. Proposed six step procedure
In this section, using a real example, the authors
propose a new six-step procedure for supplier selection. The authors illustrate our method by a real case
Table 1.

Supplier criteria score guideline.

Grade

Very
dissatisfied

Poor

Acceptable

Good

Very
satisfied

Scores

0/1

2/3

5

7/8

9/10


192

A. Hadi-Vencheh and M. Niazi-Motlagh

study to better describe the model. The case study is
related to the supplier selection of the Tiam Win
Company. Tiam Win Company concentrates on
producing door and window in Shahr-e-kord, Iran.
This company, to produce its products, is required to
purchase several kind of profile such as aluminium,
PVC, UPVC and so on with different sizes. Hence,
Tiam Win Company buys its profiles from different
suppliers with respect to demand of customers and its

type of home and industrial customers. Overall, Tiam
Win Company possesses several suppliers from different countries, namely Germany, Italy, Turkey and
Iran. The aforementioned company, to evaluate five
suppliers, applied our procedure as follows:
The problem is to select one of five candidate
suppliers. The first step is the structuring of the
problem into a hierarchy (see Figure 1). On the top
level is the overall goal of selection suppliers. On the
second level are seven criteria that contribute to the
goal. On the third level are seven criteria that are
decomposed into 13 subcriteria, and on the bottom (or
fourth) level are five candidate suppliers that are to be
evaluated in terms of the subcriteria of the third level.

categories, objective and subjective criteria. The
objective criteria are those that can be evaluated using
factual data, and include quality, financial, responsiveness, accessibility and technical capability. The authors
will use the above seven criteria that must be satisfied
in order to fulfil the goals of the selecting suppliers.

4.1.

Let us suppose that managers (or voters) in the study
will select different orders of criteria or subcriteria for
the candidates. Every manager votes 1 to S R, R is
the number of criteria. For this purpose, let us assume
seven criteria including (1) quality, (2) Background, (3)
financial, (4) responsiveness, (5) accessibility, (6)
technical capability and (7) management. These criteria
will be regarded as candidates. We will get seven orders

from 1 to 7 and a sum of every vote is shown in Table 2.
It commonly happens that, when one has to select
among many objects, a particular object is rated as the

Step 1: Select suppliers’ criteria

The authors suppose the number of managers or voters
is unknown. They were first briefed about the overall
objective of the study then specifically on supplier
rating of Dickson’s 23 criteria (Dickson 1966) and the
other supplier selection criteria researches such as
(Lehmann and O’Shaughnessy 1974, Abratt 1986,
Weber et al. 1991, Min and Galle 1999, Stavropolous
2000, Ghodsypour and O’Brien 2001, Humphreys
et al. 2003b, Chen et al. 2006, Lin and Chang 2008).
The criteria obtained from group decision fall into two

Figure 1.

Hierarchy of suppliers’ selection.

4.2.

Step 2: Structure the hierarchy of the criteria

The AHP was developed to provide a simple but
theoretically multiple-criteria methodology for evaluating alternatives. The authors use the AHP to identify
subcriteria under each criterion, and to investigate
each level of the hierarchy separately. The 13
subcriteria are quality-related certificates, factory

audit, performance history, reputation, after sale
service, on time delivery, conveyance way, distance,
product rang, design capability, attitude, communication system and E-Commerce.

4.3. Step 3: Prioritise the order of criteria or
subcriteria
4.3.1. The first stage


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International Journal of Computer Integrated Manufacturing
Table 2.

Priority votes of seven criteria from respondents in the first stage.

Criteria

First

Second

Third

Fourth

Fifth

Sixth

Seventh

18
7
8
1
0
5
8

8
3
14
10
3
8
1

7
9
10
10
2
4
5

6
8
1
5

13
11
3

2
7
2
12
8
7
9

1
7
5
8
12
4
10

5
6
7
1
9
8
11

Quality
Background

Financial
Responsiveness
Accessibility
Technical capability
Management

Table 3. Priority votes of subcriteria from respondents in
the second stage.
Criteria
Quality-related certificates
Factory audit
Conveyance way
Distance
Performance history
Reputation
Product range
Design capability
After sales service
On time delivery
Attitude
E-Commerce
Communication system

Table 4.

First

Second

13

34
23
24
40
7
30
17
19
28
6
24
17

34
13
24
23
7
40
17
30
28
19
21
6
20

Third

max a þ ws

s:t: a

yr ¼

S
X

xrs ws

r ¼ 1; 2; . . . ; R

s¼1

w1 ! 2w2 ! . . . ! Sws ! 0
S
X

ð2Þ

ws ¼ 1;

s¼1

20
17
10

Weights of seven criteria in the first stage.
Propose model

develop criteria varied level from hierarchy analysis
process.

Noguchi’s model

Criteria

Weight

Normal

Weight

Normal

Quality
Background
Financial
Responsiveness
Accessibility
Technical capability
Management

10.4573
6.5271
8.0285
5.5767
3.9734
6.2837
6.1534

0.2225
0.1389
0.1708
0.1187
0.0845
0.1337
0.1309

1.0000
0.5884
0.7677
0.5410
0.3800
0.6242
0.6009

0.2221
0.1307
0.1705
0.1202
0.0844
0.1386
0.1335

best in one evaluation, while others are selected by
other evaluation methods. The managers get the order
of criteria but not the weights. The weight of each
ranking is determined automatically by the total votes
each candidate obtains.

where xrs is the total votes of the rth criteria for the s th
place. The above model maximises the minimum of the
total scores of the R criteria and determines a common
set of weights for all the criteria. In fact, this model
maximises a (the minimum of the total scores) and the
minimum weight ws at the same time and determines
the most favourable weight for all criteria. Indeed, ws is
added as a component of the objective function to
force ws not to equal to 0.
4.4.1.

The first stage

The authors use the data of Table 2 and find the
weights of seven criteria by Equation (2). Table 4
shows that weight for quality, background, financial,
responsiveness, accessibility, technical capability and
management are 10.4573, 6.5271, 8.0285, 5.5767,
3.9734, 6.2837, and 6.1534, respectively. After normalising these data, the results are 0.2225, 0.1389, 0.1708,
0.1187, 0.0845, 0.1337 and 0.1309.

The authors use the same methodology to find the
orders of these subcriteria, presented in Table 3.

4.4.2. The second stage
The authors use the data of Table 3 and the same
method. Table 5 shows the weights of the second level
criteria. The sum of weights for the factors of criteria
must add up to 1.

4.4. Calculate the weights of criteria or subcriteria
In this article, instead of Noguchi’s model, the authors
propose the following model. This model is used to

4.4.3. The third stage
The authors obtain the global weight for each of the
factors by multiplying factor weight by the criterion

4.3.2. The second stage


194

A. Hadi-Vencheh and M. Niazi-Motlagh

weight, so for factory audit factor the value is 0.5745
times 0.2225. As the actual performance data are
collected for the factor value, these weights in the
Table 6 can be used directly to calculate the overall
rating of the suppliers and to provide a performance
score that can be derived for each factor.

4.5. Step5: Calculate supplier performance with
respect to factors
4.5.1. The first stage
This step again requires the managers to assess the
performance of all suppliers on the 14 factors identified
as important for supplier scores. A major problem was

Table 5.

Weights of 13 subcriteria in the second stage.
Propose model

Noguchi’s model

Criteria

Weight

Normal

Weight

Normal

Quality-related
certificates
Factory audit
Performance history
Reputation
After sales service
On time delivery
Conveyance way
Distance
Product range
Design capability
Attitude
E-Commerce

Communication
system

20.0000

0.4255

0.7407

0.4255

27.0000
29.0000
18.0000
22.0000
25.0000
23.3333
23.6667
25.6667
21.3333
12.6364
17.8182
16.5455

0.5745
0.6170
0.3890
0.4681
0.5320
0.4965

0.5035
0.5461
0.4539
0.2689
0.3791
0.3520

1.0000
1.0000
0.6207
0.8800
1.0000
0.9859
1.0000
1.0000
0.8312
0.7092
1.0000
0.9752

0.5745
0.6170
0.3830
0.4681
0.5319
0.4965
0.5035
0.5461
0.4539
0.2642

0.3725
0.3633

Table 6.

thus to ensure consistency between the managers and
avoid any bias creeping in. For this purpose, the
authors apply voting method like the authors used in
step 3, that is, for each factor, every manager orders
the suppliers and votes 1 to T (T P, P is the number
of suppliers) with respect to that factor. Therefore to
assist the manager to record the votes the authors
provide a questionnaire with 14 columns and each
column has P rows and at the top of each column the
authors write the title of each factor. While managers
or experts vote and record their idea, we gather the
sheets. For each factor the authors prepare a table and
enter the votes associated with that factor in it. For
instance, Table 7 shows the priority votes of five
suppliers with respect to performance history.
4.5.2.

The second stage

By using the data of the last stage and the Equation (2)
the authors obtain the score of each supplier with
respect to each factor. The authors show this method
in Table 7 and found the weight of suppliers with
respect to performance history as shown in Table 8.
Table 9 shows the scores of each supplier

with respect to each factor that was obtained by the
same methodology.
4.6. Step 6: Identify supplier priority
Whenever the scores for each factor are determined,
then it is relatively easy to calculate the resulting
supplier rating scores. An example of this is shown in
Table 10. Mathematically, the supplier rating is
equivalent to the sum of the product of each factor
global weight and the supplier performance score on

Global weight of 14 factors.
Global weights

Criteria

Sub-criteria

Quality

Quality-related
certificates
Factory audit
Performance
history
Reputation
Financial
After sales service
On time delivery
Conveyance way
Distance

Product range
Design capability
Attitude
E-Commerce
Communication
system

Background
Financial
Responsiveness
Accessibility
Technical
capability
Management

Proposed
model

LH-model

0.0947

0.0945

0.1278
0.0857

0.1276
0.0806

0.0532
0.1708
0.0555
0.0631
0.0420
0.0426
0.0730
0.0607
0.0352
0.0496
0.0461

0.0501
0.1705
0.0562
0.0639
0.0419
0.0425
0.0757
0.0629
0.0353
0.0497
0.0485

Table 7. Priority votes of five suppliers with respect to
performance history from managers.
Suppliers

First

Second

Third

Fourth

Fifth

Supplier
Supplier
Supplier
Supplier
Supplier

11
9
18
4
5

13
12
7
11
4

2
9
9
15

12

8
14
10
13
2

13
3
3
4
24

1
2
3
4
5

Table 8. The weights of suppliers with respect to performance history.
Suppliers

Weight

Supplier
Supplier
Supplier
Supplier
Supplier

9.9708
9.6788
12.088
8.1241
7.1387

1
2
3
4
5


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International Journal of Computer Integrated Manufacturing
Table 9.

The scores of suppliers with respect to 14 factors.

Factors
Quality-related certificates
Factory audit
Performance history
Reputation
Financial
After sales service
On time delivery
Conveyance way

Distance
Product range
Design capability
Attitude
E-Commerce
Communication system

Table 10.

Supplier 1

Supplier 2

Supplier 3

Supplier 4

Supplier 5

9.7591
9.6423
9.9708
10.5468
12.8925
7.4562
8.0211
9.6531
6.7452
8.7795
11.8529

10.8854
9.8021
9.6076

11.5766
10.8102
9.6788
9.0253
12.0251
10.2567
9.7301
8.9564
8.6491
13.2178
9.9812
14.5806
10.0988
8.2904

14.6350
8.5401
12.0876
14.0685
6.4521
6.0325
4.8597
6.6028
3.0912
16.3945
11.8567

4.3828
18.0079
9.6522

5.5328
8.6277
8.1241
6.1532
8.0256
11.2051
11.1350
10.2958
15.4219
3.4197
7.3703
7.0921
5.0017
8.4985

5.4964
9.3796
7.1387
7.2062
7.6047
12.0495
13.2541
11.4919
13.0926
5.1885
5.9389

10.0591
4.0895
10.9513

Rating of supplier-1.

Criteria

Sub-criteria

Weights

Scores

Sub-totals

Quality

Quality-related certificates
Factory audit
Performance history
Reputation
Financial
After sales service
On time delivery
Conveyance way
Distance
Product range
Design capability
Attitude

E-Commerce
Communication system

0.0947
0.1278
0.0857
0.0532
0.1708
0.0555
0.0631
0.0420
0.0426
0.0730
0.0607
0.0352
0.0496
0.0461

9.7591
9.6423
9.9708
10.5468
12.8925
7.4562
8.0211
9.6531
6.7452
8.7795
11.8529
10.8854

9.8021
9.6076

0.9240
1.2325
0.8544
0.5609
2.2023
0.4141
0.5062
0.4051
0.2871
0.6410
0.7193
0.3832
0.4865
0.4428
10.0595

Background
Financial
Responsiveness
Accessibility
Technical capability
Management
Total score

that factor. The supplier rating value for supplier-1 is
obtained by summing up the products of the respective
elements in columns 3 and 4 for each row and given in

the final column. The rating method used in supplier-1
can also be used to find the total scores of the other five
suppliers. The supplier with the highest supplier rating
value should be regarded as the best performing
supplier and the rest can be ranked accordingly.
Table 11 shows the rating value of each supplier and
its rank in the proposed method as well.
4.7.

Comparison

In this section the authors make a comparison between
our method, LH-model and the AHP method proposed by Yahya and Kingsman (1999). In what follows
the authors compare the three methods, step by step:
As we see in Table 12, steps 1 and 2 are the same in the
three methods. Step 3 is the same in the proposed
method and LH-model but differs from AHP. In fact
this is the main difference between voting approaches

Table 11. Ranking using proposed model and a comparison of our and LH-model.
Score

Ranking

Suppliers

Proposed
model

LH-model

Proposed
model

LH-model

Supplier
Supplier
Supplier
Supplier
Supplier

10.0595
10.7365
9.8233
8.0212
8.3597

5.9466
5.8895
6.4066
4.7043
4.9643

2
1
3
5
4

2
3
1
5
4

1
2
3
4
5

and the AHP. This is why the authors call these
approaches VAHP. In this step, the voting methods
use voting to prioritise the order of alternatives but
AHP method uses comparison matrices that take
time, so if the number of criteria increase, pairwise
comparisons are certainly impossible to be made. The
traditional AHP method can only compare a very
limited number of decision alternatives, which is
usually not more than 15. When there are hundreds


196

A. Hadi-Vencheh and M. Niazi-Motlagh

Table 12.
model.
Step

1
2
3
4

Differences between LH-model and proposed
Old VAHP

Proposed VAHP

Select suppliers, criteria
Structure the hierarchy
of the criteria
Prioritise the order of
criteria or subcriteria
Calculate the weights
(Noguchi’s ordering)

Select suppliers, criteria
Structure the hierarchy
of the criteria
Prioritise the order of
criteria or subcriteria
Calculate the global
weights using model
(2)
Calculate suppliers
weights with respect to
factors
Identify supplier priority

5

Measure supplier
performance

6

Identify supplier priority

or thousands of alternatives to be compared, the pairwise comparison manner provided by the traditional
AHP is obviously infeasible. To overcome this
difficulty, the authors combine the AHP with a new
voting DEA model and propose an integrated VAHP–
DEA methodology in this article. The purpose of step
4 is the same as all of methods but the ways is different.
The LH-model uses Noguchi’s model which has some
shortcomings mentioned before. The authors proposed
a new DEA model which overcomes those shortcomings. In step 5, AHP and LH-model use comparing
scores but the authors used again ‘voting’ and
proposed a model (2) to measure supplier performance, it gives rise to avoid any bias creeping in and is
easy. Finally, step 6 is the same as in the three
methods. So the difference of LH-model and proposed
VAHP is steps 3, 4 and 5.
5.

Conclusion

Outsourcing decisions are an integral aspect of the
logistics function. Traditionally, they have dealt primarily with the supply of raw materials and component

parts and some services such as transportation. In
recent years, with the increase in contract logistics,
many firms are outsourcing activities that were once
performed in-house. To remain competitive with these
third-party providers, logistics managers must use more
sophisticated techniques when performing their duties.
In this article, the authors proposed a new weighting
procedure instead of AHPs’ paired comparison for
selecting suppliers. The proposed model uses an
integrated VAHP–DEA methodology to evaluate
alternatives. It provides a simpler calculation of the
weights to be used and for scoring the performance of
suppliers. It is shown that the new integrated VAHP–
DEA methodology is simple enough, easy to use,
applicable to any number of decision alternatives, and
particularly useful and effective for complex MCDM
problems with a large number of decision alternatives,

where pair-wise comparisons are certainly impossible
to be made. It is expected that in the near future this
method will be applied effectively to various issues
such as policy making, business strategies and
performance assessment.
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International Journal of Computer Integrated Manufacturing
Vol. 24, No. 3, March 2011, 198–210

Optimisation of weld deposition efficiency in pulsed MIG welding using hybrid neuro-based
techniques
Kamal Pal, Sandip Bhattacharya and Surjya K. Pal*

Department of Mechanical Engineering, Indian Institute of Mechanical Engineering, Kharagpur 721 302, West Bengal, India
(Received 12 January 2010; final version received 6 November 2010)
The weld quality depends primarily on the degree of arc stability and the bead characteristics in gas metal arc
welding. The weld deposition has to be enhanced to make the process economically feasible. This article addresses
modelling and optimisation of deposition efficiency in highly non-linear pulsed metal inert gas welding. The design
of experiments was performed using central composite response surface methodology for the model development.
The back propagation neural network technique was found to be better than the response surface regression model.
Two global optimisation techniques, namely, genetic algorithm and differential evolution, were then applied to
maximise the deposition efficiency. The capability to identify the hidden optimum solutions using differential
evolution technique was found to be better than genetic algorithm.
Keywords: peak voltage; pulse frequency; pulse on-time; torch angle; arc stability; optimisation; neuro-GA; neuroDE

1.

Introduction

The arc stability, in gas metal arc welding (GMAW),
depends on material transfer behaviour and arc shape
variation. The deposition efficiency is an economic
factor, such as weld productivity. It increases with the
reduction of spatter, caused by higher arc stability, in
pulsed gas metal arc welding (P-GMAW). P-GMAW
is widely used, especially in thin sheet metal joining. It
provides a stable spray transfer with reduced heat
input (Smati 1986, Thamodharan et al. 1999). There
are various pulse parameters, in addition to normal arc
welding parameters in P-GMAW. The arc stability, as
well as weld quality, can be significantly improved by
controlling the pulse parameters (Tong et al. 2001,
Ghosh et al. 2007). The arc stability is best for one

droplet per pulse (ODPP) condition with the droplet
diameter close to the electrode wire diameter (Amin
1983, Allum 1985, Kim 1989). This can be achieved by
selecting the appropriate amplitude and duration of
peak current, which is higher than transition current to
ensure detachment (Mike and Kemppi 1989). Significant efforts have been made to achieve ODPP
conditions in P-GMAW (Zhang et al. 2000, De
Miranda et al. 2007).
Various mathematical models have been developed
to monitor the arc stability (Benyounis and Olabi
2008). The conventional techniques focus mainly on
the mean or the variance of the performance characteristics. The dual response approach considers both

*Corresponding author. Email:
ISSN 0951-192X print/ISSN 1362-3052 online
Ó 2011 Taylor & Francis
DOI: 10.1080/0951192X.2010.542181


mean and variance to develop the model (Kim and
Rhee 2004). The model has been further used for
optimisation. However, GMAW processes are highly
dynamic and non-linear with a multitude of uncontrollable factors, which suggests the need for an adaptive
intelligent system to characterise and then further
monitor the process. Thus, various evolutionary
algorithms and computational networks have also
been developed, which considers the uncertainty
features of the process. These tools may improve the
model, with the occurrence of incremental learning as
new data become available. Thus, these techniques are

used in a wide variety of applications, from classification and pattern recognition to optimisation and
control. In recent years, soft computing tools have
also been used with numerical techniques to predict
and optimise GMAW parameters more accurately
(Moon and Na 1997, Kim and Rhee 2002, Olabi et al.
2006).
Most of the conventional robust process design
techniques have been used to maximise the process
performance while minimising the expected loss (Allen
et al. 2001). The response surface methodology (RSM)
and Taguchi method have been applied widely in
GMAW optimisation (Song et al. 2005, Hsiao et al.
2008, Balasubramanian et al. 2009, Giridharan and
Murugan 2009, Kumar and Sundarrajan 2009). However, these techniques are limited to regular experimental regions. This limitation can be overcome with


International Journal of Computer Integrated Manufacturing
the introduction of genetic algorithm (GA) (Correia
et al. 2005). It can generate global optimum point
rather than local optimum solutions (Tarng et al. 1999,
Huang et al. 2007). However, there is a risk of
insufficient sweeping of the search space with improper
parameter settings in GA (Correia et al. 2004). The
controlled random search algorithm similar to GA has
been used to overcome these difficulties (Kim et al.
2005). The adaptive gradient descent neural network
has also been found to be useful in GMAW optimisation (Meng and Buffer 1997). The GA technique has
been applied on the trained neural network model,
called neuro-GA, to improve the optimisation capability (Tseng 2006, Park and Rhee 2008).
In recent years, the differential evolution (DE)

technique has been applied to improve the training of
gradient decent artificial neural networks (ANNs) (Du
et al. 2007, Slowik and Bialko 2008). The neuro-DE
algorithm has been applied to various areas such as
weather forecasting (Abdul-Kader 2009) and bankruptcy prediction in banks (Chauhan et al. 2009). The
DE approach has been also used for tuning the PID
controller of MIMO systems (Iruthayarajan and
Baskar 2009), highway network capacity optimisation
(Koh 2009) and reliability-redundancy optimisation
(Coelho 2009). This approach has been found to be
more useful than GA for better convergence in case of
non-linear systems (Subudhi et al. 2008).
In the present work, the design of experiments was
performed using half fractional central composite
RSM in pulsed metal inert gas welding (P-MIGW).
The welding torch angle (yt), welding speed (S) and
wire feed rate (F), along with three pulse parameters,
namely, peak voltage (Vp), pulse frequency (fp) and
pulse on-time (tp), were considered for development of

Figure 1.

199

the deposition efficiency model using RSM as well as
back propagation neural network (BPNN). The
response surface method was found to be inadequate.
Therefore, the optimisation of process parameters for
maximum deposition efficiency was processed with two
different implementations, GA and DE on the developed BPNN model.

2.

Experimental procedure

In this work, a voltage-controlled P-MIGW machine
(FRONIOUS make with TRANSARC 500 power
source and FRONIUS VR131 control unit) was used.
The experiments were carried out on 6-mm mild steel
plates using copper-coated mild steel filler wire (ESAB,
S-6 wire, 1.2-mm diameter), using Butt welding
method. The schematic diagram of the experimental
set-up at 08 torch angle (perpendicular welding) is
shown in Figure 1. A four-roller drive system fed the
electrode wire to the welding gun. The design of
experiments was performed using central composite
RSM.
The chemical composition of the work material was
obtained by optical emission spectroscopy analysis as
shown in Table 1. Pure argon (99.9%) was used as
shielding gas at a pressure of 10 kgf/cm2 with flow rate
of 15 L/min. The welding torch tip to base plate
distance was maintained at 15 mm. Six process
parameters: welding speed (S), wire feed rate (Fw),
pulse frequency (fp), pulse on-time (tp), peak voltage
(Vp) and torch angle (yt) were considered in this
investigation.
The specimens were prepared with a V-shaped
groove having the groove angle, the root face and the
root gap of 608, 1.5 and 0.5 mm, respectively. The faces

Schematic diagram of the experimental set-up in perpendicular welding.


200

K. Pal et al.

of each pair of specimens were cleaned by a surface
grinder. Each pair of plates was tack welded at the two
ends to make a Butt weld joint. The weight of each pair
of plates before (Wi) and after (Wf) welding was
measured by electronic balance (A and D Company
Limited, GF-3000) weighting equipment. The deposition efficiency (Zd) can be expressed as the ratio of
actual enhancement of a pair of base plates’ weight due
to welding to its theoretical value (Wd) related to wire
feed rate (F) as per Equation (1), where, ‘l’ and ‘tw’
indicate the mass per unit length of the electrode wire
and welding time duration, respectively.
Zd ¼

3.

Wf À Wi Wf À Wi
¼
Wd
tw Fl

ð1Þ

Development of design of experiments

Various trial experiments were carried out to set the
range of each process parameter for acceptable weld
quality. In the present work, RSM was used as design
of experiment technique. Half fractional central
composite RSM (a¼2.378) with nine centre point
experiments were designed. The coded value of the
upper and lower level for each process parameter was
þ2.378 and 72.378, respectively. The levels and their
corresponding actual values are shown in Table 2. The
negative value of torch angle indicated backhand
welding, whereas positive value showed forehand
welding as shown in Figure 2. The torch perpendicular
condition was represented by 08 torch angle. The
actual values of each parameter were adjusted as per
available settings in the welding machine and the
motor attached with welding table.
The coded design matrix containing a total of 53
experiments developed using MINITAB software
(release 13.31, Minitab Inc. 2002), is shown in Table
3. However, the experiments were performed randomly
Table 1.
C
0.208

Chemical composition (wt %) of the base plate.
Si

Mn

P

S

Ta

Cr

Ni

0.171

0.489

0.088

0.047

0.018

0.008

0.007

Table 2.

to avoid the possibility of systematic error in the
process.
4. Modelling of deposition efficiency
The pulse parameters highly influence the arc stability

in P-GMAW (Pal et al. 2009a). The torch position and
its direction during welding also affect the weld quality
and deposition efficiency (Nouri et al. 2007, Kannan
and Yoganandh 2009, Pal et al. 2009a). The process
inputs with corresponding deposition efficiency of the
53 number of experiments are shown in Table 4. A
total of nine centre point experiments (experiment no.
35, 37, 39, 40, 41, 48, 51, 52 and 53) having same
process parameter values were used to check the
repeatability of the deposition efficiency.
The ANN was also considered, along with mathematical models due to non-linear nature of the arc
during welding. In this work, RSM and BPNN
technique were used to develop the model of deposition efficiency.
4.1.

Development of mathematical model

A response surface is a functional mapping of various
process parameters to a single output feature. In the
present research, a second-order polynomial response
surface model was developed using 53 sets of data to
correlate six input process parameters: S, Fw, yt, Vp, fp
and tp with the output variable, deposition efficiency.
The commercially available software, MINITAB, was
used for the model development and further statistical
analysis to check the adequacy of the model.
The significant and insignificant coefficients were
calculated using ‘student’s t-test’ by comparing their
values with standard tabulated data at their corresponding degree of freedom and 95% confidence level.
When the calculated value of ‘t’ corresponding to a

coefficient exceeds the standard tabulated value, the
coefficient may be considered as significant. The
significant regression coefficients were recalculated to
develop the final model (Equation (2)). The adequacy
of the model was tested with 95% confidence level
using the analysis of variance (ANOVA) technique.

Process parameters and their levels.
Level

Process parameter
Torch angle
Welding speed
Wire feed rate
Peak voltage
Pulse frequency
Pulse on-time

Symbol

Unit

72.378

71

0

þ1

þ2.378

yt
S
F
Vp
fp
tp

deg
mm/s
m/min
Volt
Hz
ms

735
4.6
6.3
27.0
80
2.6

715
5.8
7.3
30.4
105
3.4

0
7.7
8.0
33.0
124
4.0

15
8.8
8.7
35.6
144
4.6

35
9.9
9.7
39.0
172
5.4


International Journal of Computer Integrated Manufacturing

Figure 2.

201

Schematic representation of different torch angles in P-MIGW.

Zd ¼ 265:76 À 0:74at À 6:66S À 9:43F À 3:66VP
2

2

À 0:73fp À 10:35tp þ 0:58S þ 0:72F þ

0:01V2P

þ 1:11t2p þ 0:01at S þ 0:04at F À 0:01at tp þ 0:01SVP
À 0:01Sfp À 0:08Stp þ 0:03Ffp À 1:42Ftp þ 0:01VP fp
þ 0:36VP tp þ 0:02fp tp
ð2Þ
The ANOVA result of the reduced model is shown in
Table 5. The acceptance of these models mainly depends
on P, F and R2 values. P value indicates the probability
of significance of the model, which should be less than
0.05 at 95% confidence level. The P value of the reduced
modified regression equation was found to be improved
from 0.112 (initial full model) to 0.035 (less than 0.05).
The F value of the model has to be higher than the
tabulated F value at 95% confidence level at respective
degrees of freedom of the regression model. The F-value
criterion for initial regression model was not satisfied.
This criteria was fulfilled in the modified model as F
value was 2.05 which is more than tabulated F value
(F0.05,24,28 ¼1.91), as shown in Table 5. The lack-of-fit is
another essential criterion for accepting the developed
model. This source of variation should not be predominant. Hence, the F ratio should be less than the
tabulated F ratio at a specified confidence level (95%)

for the lack-of-fit consideration. It was also found to be
satisfied as F value was 1.03 (F0.05,24,20 ¼2.08). However,
the R2 value (63.8) was found to be poor. Therefore, this
response surface regression model was not highly
adequate to represent the relationship between the
deposition efficiency with process parameters.
4.2. Development of ANN model
ANNs are computational models inspired by the central
nervous system comprising neurons. The multi-layered

perceptrons, generally trained using the error back
propagation algorithm, has been popularly used in
weld modelling (Kim et al. 2001; 2002; Pal et al. 2008).
The network is built up of numerous individual units
called neurons. A typical feed forward network is
arranged into an input layer, an output layer and any
number of hidden layers. Each layer comprises a
variable number of nodes as neurons. In this research,
a code for multi-neuron, multi-layered ANN model was
developed in C programming language, for mapping the
P-MIGW process parameters to weld deposition efficiency. A schematic representation of fully connected
multi-neuron, single hidden layered ANN architecture,
which was employed in this research, is shown in Figure
3. The input layer comprises six nodes corresponding to
six input parameters and the output layer has only one
node corresponding to deposition efficiency. The number of nodes in the hidden layer was varied from 1 to 30
to obtain the optimal prediction accuracy.
The summation of the products of weight of each
node of previous layer (wji) and the corresponding
inputs (yi) gives us the input of jth neuron. Each

neuron accepts the weighted sum of inputs (I) to it and
outputs a single value (O) depending on its transfer
function (f) (Equation (3)). The log-sigmoidal transfer
function was used in this work as the activation
function for the hidden layer to establish the nonlinearity of the process.
X
O ¼ fðIÞ ¼ fð
wji yi Þ
ð3Þ
The outputs of any layer, other than the output
layer were used as the inputs of the succeeding layer.
Thus, the network provides a non-linear mapping
between input parameters and output features. Each
network was trained using a set of known input and
output values. Training algorithms change the interneuron weights in such a way that the error function


202

K. Pal et al.

Table 3.
Serial
no.
1
2
3
4
5
6

7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36

37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53

Coded design matrix using RSM.

Table 4.
sponses.

Detailed experimental design matrix with re-

Process parameters
yt

S

F

Vp

fp

tp

0
0
1
1
0
1
1
0
71
71
71
1
71
72.378
1
1
1
1
71
71
1
0

0
0
0
1
0
1
0
2.378
71
1
71
71
0
0
0
0
0
1
0
71
71
0
71
71
0
1
71
0
71
71

1

0
0
1
1
0
71
71
0
1
71
1
71
71
0
1
1
1
1
1
1
71
0
0
0
0
71
0
1

0
0
1
71
71
71
0
0
2.378
72.378
0
71
0
71
1
0
71
71
0
71
1
0
71
1
1

0
0
1
71

0
71
1
0
1
71
71
1
1
0
1
71
71
1
71
1
1
0
0
0
0
71
0
1
0
0
1
1
1
71

0
72.378
0
0
2.378
71
0
71
1
0
1
1
0
71
71
0
71
71
71

0
0
71
1
0
71
71
0
1
1

1
71
71
0
1
71
71
71
71
71
1
0
0
0
0
71
0
1
0
0
71
1
71
71
72.378
0
0
0
0
1

0
1
1
2.378
1
1
0
1
1
0
71
71
1

0
2.378
1
71
0
71
71
0
1
71
71
1
1
0
71
1

71
71
71
71
1
0
0
72.378
0
1
0
1
0
0
1
71
71
71
0
0
0
0
0
71
0
1
71
0
1
71

0
1
1
0
1
1
1

0
0
71
1
0
1
71
72.378
71
1
71
1
71
0
71
1
71
1
1
71
71
2.378

0
0
0
71
0
1
0
0
1
1
1
71
0
0
0
0
0
71
0
71
1
0
1
71
0
1
1
0
1
71

71

(E), which is related to the difference between the
target values (Ti) and the actual output (Oi) values
(Equation (4)), is reduced.
E¼

N
1X
ðTi À Oi Þ2
N i¼1

ð4Þ

F
S
Vp
(mm/ (m/
Experiment yt
fp
tp
min) (Volt) (Hz) (ms)
s)
no.
(deg)
1
2
3
4
5

6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35

36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53

715
715
715
715
715
715
715
715
715
715
715

715
715
715
715
715
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
735
35
0
0
0
0
0
0
0

0
0
0
0
0
0
0
0
0
0
0
0

5.8
5.8
5.8
5.8
5.8
5.8
5.8
5.8
8.8
8.8
8.8
8.8
8.8
8.8
8.8
8.8
5.8

5.8
5.8
5.8
5.8
5.8
5.8
5.8
8.8
8.8
8.8
8.8
8.8
8.8
8.8
8.8
7.7
7.7
7.7
9.9
7.7
4.6
7.7
7.7
7.7
7.7
7.7
7.7
7.7
7.7
7.7

7.7
7.7
7.7
7.7
7.7
7.7

7.3
8.7
8.7
8.7
7.3
7.3
8.7
7.3
8.7
8.7
7.3
8.7
7.3
8.7
7.3
7.3
7.3
8.7
7.3
7.3
8.7
7.3
8.7

8.7
8.7
7.3
7.3
7.3
7.3
8.7
8.7
8.7
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
6.3
9.7
8
8
8

30.4
35.6
30.4
35.6
35.6
35.6
30.4
30.4
30.4
35.6
35.6
30.4
30.4
35.6
30.4
35.6
35.6
35.6
30.4
30.4
35.6
35.6
30.4
30.4
30.4
35.6
30.4
30.4
35.6

35.6
35.6
30.4
33
33
33
33
33
33
33
33
33
33
27
39
33
33
33
33
33
33
33
33
33

144
144
144
105
144

105
105
105
144
144
105
105
105
105
144
144
105
105
144
105
144
144
105
144
144
144
105
144
105
144
105
105
124
124
124

124
124
124
124
124
124
172
124
124
80
124
124
124
124
124
124
124
124

4.6
4.6
3.4
3.4
3.4
4.6
4.6
3.4
4.6
3.4
3.4

3.4
4.6
4.6
3.4
4.6
3.4
4.6
3.4
4.6
3.4
4.6
3.4
4.6
3.4
3.4
3.4
4.6
4.6
4.6
3.4
4.6
4
4
4
4
4
4
4
4
4

4
4
4
4
2.6
5.4
4
4
4
4
4
4

Zd
(%)
91.35
90.4
88.04
88.67
92.78
93.17
89.99
89.54
90.77
91.71
90.09
89.42
90.04
92.53
89.87

91.09
82.68
84.86
84.65
85.48
93.66
93.8
89.59
88.72
89.35
87.18
89.8
88.44
90.47
93.63
86.63
84.3
87.71
81.98
87.24
92.48
88.41
90.91
86.32
88.13
86.94
89.28
83.58
93.04
88.65

90.52
89.49
84.2
90.76
89.04
86.46
91.94
90.71

The entire ‘knowledge’ of the network is stored as
the inter-neuron weights. The present work uses the
gradient descent error back-propagation algorithm
(Werbos 1974) to train the network. The network is
adjusted to reduce the overall mean square error


International Journal of Computer Integrated Manufacturing
(MSE) in back-propagation training (Werbos 1990).
The synaptic weights between nodes are modified from
Wold to Wnew according to an error correction chain
rule (Equation (5)) during the backward pass, based on
the gradient descent technique to minimise the MSE
between actual pth output (Opk) and desired pth output
(Tpk) for the total number of training pattern (N) as
per Equation (6).
Wnew ¼ Wold À Z

Table 5.

@E

@Wi

ð5Þ

ANOVA table for deposition efficiency (Zd) model.

Source

DF

Seq
SS

Regression
Linear
Square
Interaction
Residual error
Lack-of-fit
Pure error
Total

24
6
6
12
28
20
8
52

277.93
132.31
73.93
71.69
158.02
113.94
44.09
435.95

Adj
SS

Adj
MS

F

277.93 11.580 2.05 0.035
41.64 6.940 1.23 0.321
74.04 12.340 2.19 0.074
71.69 5.974 1.06 0.428
158.02 5.644
113.94 5.697 1.03 0.512
44.09 5.511

F0.05,24,28¼1.91; F0.05,24,20¼2.08.

Figure 3.

P

Schematic representation of ANN model.

MSE ¼

N X
P 
2
1 X
Tkp À Okp
2N k¼1 p¼1

203

ð6Þ

The learning rate was adjusted to reduce MSE. The
momentum coefficient (a) was also used to maintain
the stability of Z with adequate learning according to
delta rule.
In this work, the BPNN model was developed
based on the same experimental dataset which was
used to develop response surface regression model. The
whole dataset was normalised between 0.1 and 0.9. The
performance of the BPNN model depends on the
network parameters, like number of neurons in hidden
layer (h), learning rate (Z) and momentum coefficient
(a). Therefore, achieving optimal architecture is quite a
difficult task. Several trials were made to finally obtain

the optimal architecture, which can provide the
minimum MSE. The full experimental dataset was
divided into a ‘training dataset’ and a ‘testing dataset’.
The testing patterns were randomly chosen from the
total dataset. The overtraining problem was avoided
by using cross-validation of ‘training patterns’ and
‘testing patterns’ from the complete experimental


204

K. Pal et al.

dataset during training. This process was repeated
using random selection of different subsets of data to
check the generalisation capability of the network.
Finally, six randomly chosen experimental data
(experiment no. 5, 12, 20, 31, 39 and 49, highlighted
as italics in Table 4) were used as ‘testing dataset’. The
networks were compared on the basis of their
prediction accuracy in testing by training up to a
maximum of 100,000 iterations or until MSE in testing
reaches 0.005. Once the models have been developed
using 46 numbers of training patterns, they have been
validated by the testing dataset to test the prediction
capability of the networks. The optimum architecture
was found by varying the number of neurons in the
hidden layer along with the variation of Z and a. This
evaluation was carried out by the determination of
MSE in testing based on the absolute value of the

deposition efficiency. It has been found that 6-8-1
architecture provides the best data fitting capability
with Z and a being 0.8, and 0.5, respectively. This
optimum architecture provided the minimum MSE in
training and testing as 0.0136 and 0.0063, respectively.
4.3. Comparison of the developed BPNN and RSM
model
Prediction capability of the developed models was
indicated by error percentage in prediction of deposition efficiency in this case. The percentage of prediction
error was calculated by Equation (7).
Prediction errorð%Þ ¼
ðExperimental value À Predicted valueÞ
 100
Experimental value
ð7Þ
Thus, prediction error of each six testing patterns is
shown in Figure 4 using BPNN model as well as RSM
regression model. It indicated that the percentage error
for all the testing patterns is within in between +5%
using BPNN model, whereas it was more than 10% in
case of RSM model.
The mean absolute prediction error was obtained
by averaging the prediction error of all six testing
patterns. It was calculated as per Equation 8.
Mean absolute prediction error ð%Þ ¼


6

1X

ðExperimental valuei À Predicted valuei Þ
 100




6 i¼1
Experimental valuei
ð8Þ
Thus, the mean absolute prediction error was
7.87% using reduced response surface regression

Figure 4. Comparison of prediction error in ANN and
RSM model.

model, which was found to be improved to 1.67%
using BPNN model. Based on the detailed analysis, it
may be concluded that BPNN is more accurate than
RSM model. Therefore, BPNN model was used for
parametric study and further optimisation of deposition efficiency.
5. Parametric study on deposition efficiency
The effect of each process parameter on deposition
efficiency was investigated keeping other parameters
constant at a specific level coded by 72.378 to þ2.378
as discussed in Section 3. The BPNN model was used
to predict the deposition efficiency with the variation of

each process parameter at these respective levels. The
influence of torch angle, peak voltage and pulse
frequency was found to be predominant at a particular
parametric level. As the torch angle became positive
(forehand welding) deposition efficiency was found to
be reduced due to high amount of spatter caused by
improper gas shielding (Figure 5(a)). The deposition
efficiency increased with an enhancement of peak
voltage as well as pulse frequency due the better arc
stability (Figure 5d and e). However, the deposition
efficiency was not significantly influenced by pulse ontime, except at high negative torch angle (backhand
welding) as shown in Figure 5f. It improved slightly at
either low welding speed or low wire feed rate, except
in backhand welding (Figure 5b and c).
This parametric investigation indicated that the
deposition efficiency increased significantly with higher
peak voltage, higher pulse frequency and higher pulse
on-time along with negative torch angle. However, it
may be improved with different parametric combinations using optimisation techniques.