The international journal of advanced manufacturing technology, tập 60, số 5 8, 2012

Int J Adv Manuf Technol (2012) 60:421–436
DOI 10.1007/s00170-011-3636-4

ORIGINAL ARTICLE

Enhancing total agility level through assessment and product
mapping: A case study in the manufacturing
of refrigeration air dryer
C. G. Sreenivasa & S. R. Devadasan & R. Murugesh

Received: 10 October 2010 / Accepted: 9 September 2011 / Published online: 27 September 2011
# Springer-Verlag London Limited 2011

Abstract The world’s manufacturing community has been
questing for ways to face the onslaught of competition. One
of those ways is the adoption of agile manufacturing (AM)
paradigm. AM paradigm enables a company to quickly
respond to the customers’ dynamic demands. In order to
implement AM paradigm, a model named “model for
enhancing total agility level” (METAL) is proposed in this
paper. METAL enunciates the assessing of the total agility
level (TAL), identifying the weak AM criteria and
subsequently strengthening them. The practicality of METAL has been explored in an air dryer manufacturing
company. During this case study, refrigeration air dryer
was considered as AM capable product. After assessment,
three weak AM criteria were identified. Proposals were
drawn to strengthen these three weak AM criteria. These
proposals envisage the strengthening of the weak AM
criteria through the removal of nonvalue adding activities,
utilization of mathematical models, and creation of web

portal. The reassessment has indicated the possibility of
enhancing the TAL value in the above company through the
implementation of these proposals. The experience of
carrying out this research has revealed that the deployment
C. G. Sreenivasa (*)
University B.D.T College of Engineering,
Davangere 577004 Karnataka, India
e-mail:
S. R. Devadasan
PSG College of Technology,
Coimbatore 641004 Tamil Nadu, India
e-mail:
R. Murugesh
Darshan Institute of Engineering and Technology,
Rajkot 363650 Gujarat, India
e-mail:

of METAL would facilitate the contemporary companies to
systematically infuse AM paradigm and enhance their TAL
values.
Keywords Agile manufacturing . Agility assessment . Air
dryer . Time management . Global optimization

1 Introduction
During past two decades, significant researches on “agile
manufacturing” (AM) have been reported in the literature
arena. AM is a paradigm that makes a company capable of
quickly responding to the customers’ dynamic demands [1,
2]. Today, the manufacturers who successfully implement
AM paradigm are able to thrive in globalized market

environment. Companies belonging to electronic industry,
particularly television and mobile phone manufacturers are
few of such examples [3]. Those AM companies exhibit
their agile capabilities by producing variety of models with
innovative features within a very short period. Hence, those
manufacturers are able to sustain the competition despite
the arrival of many competitors [4]. Despite the dissemination of AM paradigm among researchers and practitioners,
it is applied at slower pace in the manufacturing of
traditional engineering products such as air conditioners,
compressors, air dryers, generators, motors, and refrigerators.
It is high time that the manufacturers of these traditional
products need to acquire AM characteristics at a higher pace to
face the onslaught of competition.
Researchers started to work on AM after the formation
of the institution called AM forum at Iacocca Institute,
Lehigh University, USA in the year 1991 [5–7]. A major
emphasis of these researchers is that technology and
management practices are required to get integrated in


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proportionate form to implement AM paradigm in companies [8]. These researchers have mainly viewed the outcomes of AM from four perspectives namely cost, market,
time, and environment. While viewed from these perspectives, the products produced by an AM company shall
enjoy high sales in the market. Also, these products shall be
ecofriendly. Those products shall require minimum time
and cost to evolve new models [9–13]. These enunciations
suggest that a company shall map the characteristics of the
products produced by it from these four AM perspectives.
The outcome of this mapping exercise would be useful to

identify the potential products about which AM characteristics
shall be infused to enhance the agility level of the company. A
survey conducted in the literature arena revealed the absence
of any model that would enable the modern companies to
enhance their agility levels by conducting such AM mapping
exercise. On identifying this absence, the research being
reported in this paper was undertaken.
During the research being reported in this paper, the way of
enhancing the “total agility level” (TAL) in a company
through assessment and product mapping was explored. This
was accomplished in two stages. In the first stage, a pneumatic
products manufacturing company was identified. Then the
research was focused on the manufacturing of one of the
products produced by this company namely air dryer.
Subsequently, the construction and working of air dryers were
studied. In the second stage, a model for infusing agility by
strengthening the weak AM criteria was designed. This model
basically envisages the assessment of TAL and identifying the
weak AM criteria which shall be strengthened to enhance the
TAL. The working of this model was explored by applying it
on air dryer manufacturing.

2 Literature survey
During the research being reported here, the literature was
surveyed in two directions. In the first direction, the
literature was surveyed to identify agility assessment
models. A search in this direction revealed the appearance
of 11 papers reporting agility assessment models. The
contributions of some of these papers are briefly described
here. Kumar and Motwani [14] identified 23 factors and

subfactors which influence a firm’s agility. These factors
assist in the identification of strengths and weaknesses of
the firms with regard to competing on time. A parameter
named “agility index” has been used for assessment. The
procedure for calculating the agility index has been
explained. However, this agility index has not been tested
and validated. Zhang and Sharifi [15] have proposed a
conceptual model for implementing agility. They have also
contributed an agility assessment model. This model
facilitates the assessment of agility by gathering responses

Int J Adv Manuf Technol (2012) 60:421–436

to the questions contained in a questionnaire. This questionnaire consists of 72 questions for assessing agility needs and
66 questions for determining current agility level of the
organization. These authors have conducted case studies in 12
companies for validating this agility assessment model.
Ramesh and Devadasan [8] have reported their research
on agile assessment using qualification and quantification
tools. The 72 questions for assessing agility needs proposed
by Zhang and Sharifi [15] were used by these authors as
qualification tool. These authors have proposed a quantification tool consisting of 20 AM criteria. The practicality of
this model was explored by these authors by conducting a
case study in an Indian pump manufacturing company. In
line to this research work, Vinodh et al. [16] have
redesigned the 20 AM criteria quantification tool proposed
by Ramesh and Devadasan [8]. These authors have
statistically validated the redesigned 20 AM criteria
quantification tool and carried out a case study in an Indian
electronic switches manufacturing company. An extended

version of this research has been reported in Vinodh et al.
[17]. In this paper, the method of measuring agility index
using multigrade fuzzy logic approach is presented. On
analyzing the characteristics of the agile assessment models
and tools which have surfaced in the literature arena during
the recent years, it was found that the 20 criteria agility
assessment tool proposed by Ramesh and Devadasan [8]
which was further refined by Vinodh et al. [16] was most
simple, exhaustive, and accurate in assessing agility. Yet it
was found necessary to append this tool with the new
criteria of AM reported in literature. This is due to the
reason that the researchers continue to work in the direction
of identifying new criteria of AM [11].
In the second direction of literature survey, the information on the application of AM paradigm on products was
gathered. This direction of literature survey revealed that
few researches have been conducted by applying AM
paradigm on products such as semiconductor, journal
bearing, electronic switches, and pumps. These researches
have been conducted by adopting various technologies and
management models to apply AM paradigm on these
products. Some of these technologies and management
models include rapid prototyping technology (RPT),
computer-aided design (CAD), activity-based costing, and
Tabu-enhanced genetic algorithm. For example, Cheng et
al. [18] have proposed an artificial intelligence and internet
technologies-based system for implementing design and
manufacturing agility in journal bearing. In this system, the
customer shall input the application requirements and then
the system responds quickly to facilitate an optimum
selection and offers design solutions. Likewise, Vinodh et

al. [3] have explored the way of infusing agility in pump
manufacturing company. These authors have considered
CAD and RPT for infusing agility. The Pro/E software


Int J Adv Manuf Technol (2012) 60:421–436

package was used for building the CAD model of the
pump. The GAMBIT and FLUENT software packages were
used for conducting flow analysis. Then, the model was
prototyped using fused deposition modeling technique. Few
qualitative and quantitative techniques were used to gather
the reactions of the practitioners. As a result of this research
experience, the CAD and RPT were found to be practically
feasible for infusing agility in a traditional pump manufacturing company. Thus although a few researchers have
started to explore the way of infusing agility in products, no
research on mapping of the characteristics of products with
AM criteria has not so far been reported.
Altogether, the literature survey conducted during this
research along the two directions has revealed that no model
to enhance the agility of the company by systematically
assessing it and mapping the product characteristics with AM
criteria has been evolved. In order to fill this research and
practice gap, a model named as “model for enhancing total
agility level” (METAL) was evolved during the research being
reported in this paper. The conceptual features of METAL are
briefly described in the next section.

3 Conceptual features of METAL
The conceptual features of METAL are depicted in Fig. 1.

As shown, the TAL has to be assessed using an agility
assessment tool in a product-manufacturing company. If the
TAL value is less than 50%, then the path of AM journey of
the company is in disarray which cannot be easily corrected
or enhanced. This principle of fixing 50% as the minimum
TAL base value has been drawn from Vinodh et al. [16].
According to this principle, a company scoring less than
500 marks using the agility assessment tool would lack
management commitment. This is due to the reason that, in
the agility assessment tool encompassed in METAL, 50%
of the marks are allotted under management commitment
enabler. Hence, a company lacking management commitment
towards implementing AM will not be scoring more than 50%
marks when agility assessment tool is used. Hence, such a
company will fail to implement AM successfully as it is an
indication that AM pathway of this company is in disarray and
cannot be corrected or improved. The principle behind
choosing 50% marks as the eligibility for implementing AM
is also an impact of the grading system followed in
educational system. Most universities in the world fail the
students who secure less than 50% of the marks [19, 20]. This
would mean that those students securing less than 50% of
the marks would be failing to exhibit the traits of the
education and skill imparted on them.
If the TAL value is greater than 90%, then the AM
journey is correctly carried out on a hurdle-free path and
hence there is no need to correct or accelerate it. This

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inference is drawn by observing the nature of evaluation of
students followed in educational system. It is observed that,
most Universities in the world award highest grade to the
students who secure more than 85% of the marks [19, 20].
This would mean that those students securing more than
85% of the marks would be capable of successfully
executing the knowledge and skill that are imparted on them
during their courses of study. In line to this observation, in
the METAL, it is earmarked that, a company scoring more
than 90% of the marks when agility assessment tool is used
should be already in the AM path and free from facing any
hurdles. Such companies require no further actions to
accelerate AM journey along the right path.
If the TAL value is equal to or greater than 50% but
equal to or lesser than 90%, then there is a scope for
infusing AM in the product/s of the company to enhance
the TAL value. In this case, the base value of TAL is fixed
to declare weak AM criteria which are to be strengthened
by infusing agility in the product/s of the company. For
example, if base value of TAL is fixed as 50%, then the
AM criteria whose TAL values fall below 50% shall have
to be declared as weak criteria. Meanwhile, the product
characteristics are mapped from the AM perspectives. As
the result of this exercise, the products possessing the
propensity for infusing agility are identified. These are
chosen as candidate product/s for infusing agility with the
objective of strengthening the weak AM criteria. The TAL
value is reassessed and compared with earlier TAL value.
Based on the results of this comparison, strategic decisions
are made to remove the hurdles in the pathway so that the

AM journey of the company is accelerated.

4 Practicality of METAL in the manufacturing
of air dryers
The practicality of METAL was investigated in a company by
name Trident Pneumatics Private Limited (hereafter referred
to as Trident). Trident is located in Coimbatore city of India.
Trident was started in the year 1988 with just four employees.
Today, Trident’s employee strength has increased to 51.
Trident is associated with designing and manufacturing of
various pneumatic application supporting products such as air
dryers, drain valves, and filters. Among the broad classification of air dryers, Trident manufactures two types of air dryers
namely refrigeration and regenerative air dryers. Till now,
Trident has designed and manufactured 17 models of the
refrigeration air dryer and 30 models of the regenerative air
dryer. These air dryers are widely applied in the fields like
automobile, textile, medical, and cement manufacturing.
Trident’s air dryers cater to the need of the applications in
these fields. These air dryers are supplied to companies
located within and outside India. Besides designing and


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Int J Adv Manuf Technol (2012) 60:421–436

Fig. 1 Conceptual features
of METAL

Assessment of total agility level (TAL)

< 50%

> 90%

TAL
value

AM pathway is in disarray and cannot
be corrected or improved

AM pathway is free from hurdles; no
need to correct or improve the
company’s AM path

≥ 50% and ≤ 90%

Agility needs to be infused in the product/s to increase TAL value

Fixing of base TAL value

Declaration and identification of
weak AM criteria

Product mapping from AM perspectives

Identification of the product/s possessing
maximum propensity for applying agility

AM infusion in the candidate product/s

with the objective of strengthening weak
AM criteria

Reassessment of TAL value

Comparison of TAL value before and after
the infusion of AM in the candidate
product/s

Strategic decision making

manufacturing of pneumatic products, Trident is involved in
research and development of pneumatic products. The outcomes of Trident’s research and development activities have
resulted in filing three patents. These information indicate that
Trident has been in the AM journey.
4.1 Agility assessment at Trident
The assessment of TAL value was carried out using a 30
criteria agility assessment tool. This assessment tool is the
extension of the 20 criteria agility assessment tool proposed
by Ramesh and Devadasan [8]. As the name implies, this tool
facilitates the assessment of agility level of an organization

from the perspective of 30 AM criteria. These 30 AM criteria
can be viewed in Fig. 2. This tool is incorporated with
questionnaires under each AM criteria. The competent
personnel of Trident were interviewed with these questionnaires. A conversion table encompassed in 30 AM criteria
model was used to convert the responses of respondents into
marks. These marks were subsequently used to compute
TAL of Trident. The TAL value thus determined indicated
that Trident has acquired 68.37% of agility. This value falls

between 50% and 90%. Hence, according to the METAL,
the need of infusing agility in the products manufactured by
Trident was realized. In order to declare the weak AM
criteria, base TAL value was fixed as 50%. Based on this


Int J Adv Manuf Technol (2012) 60:421–436

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Fig. 2 Actual agility levels and
agility gaps at Trident

fixation of base TAL value, the weak AM criteria at Trident
were identified. The weak AM criteria thus identified are
graphically shown in Fig. 2. As shown, three AM criteria
namely “time management” (with agility level of 30.625%),
“global optimization” (with agility level of 37.5%), and
“production methodology” (with agility level of 45%) were
identified as weak AM criteria of Trident. Due to space
limitation, the detailed explanation about the 30 AM criteria
has not fallen within the scope of this paper. However, in
order to facilitate the clarity of presentation, characteristics of

the above three weak AM criteria considered for enhancing
the TAL value of Trident are briefly described in Table 1.
4.2 Mapping AM factors with air dryer characteristics
Theoretically, an AM company may produce all types of
products to meet the customers’ dynamic demands within a
short duration of time without compromising profitability

[1, 2]. This is possible only if the company produces AM
infused products. As appraised in Section 1, an AM-infused


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Table 1 Weak AM criteria identified in Trident and their characteristics
Weak AM criteria identified in
Trident

Characteristics

Time management

A primary capability of a company implementing AM is the ability to respond quickly against the
customers’ dynamic demands. Such quick response is possible if the time of developing the product and
offering the services is totally eliminated. While this task is not possible in all cases, efforts must be
made to eliminate the nonvalue-adding activities in all endeavors that are required to quickly respond
against customers’ dynamic demands. In order to exert these efforts, the company implementing AM is
required to utilize time management tools and techniques [16, 43]

Global optimization

AM is highly enabled through the operations carried out along both internal and external supply chains
[16]. Along these supply chains, the members of them have contradictory objectives [44]. For example, a
supplier prefers to get order for supplying huge quantity. In this case, the supplier may offer discount to
the company implementing AM. On the other hand, this company will be attempting to enhance agility
by applying just-in-time manufacturing principles in which case small quantities are ordered by allowing

least lead times. In this case, the company implementing AM stands to lose profit due to the absence of
price discount offered by the supplier. In this context, global optimization plays an important role in AM
environment by providing optimized solutions to balance the contradictory objectives of the members of
supply chains [31]

Production methodology

In an AM environment, the production methodology shall be efficient enough to meet the quantity and
quality requirements of customers within a short period of time. In order to develop such a capability,
flexible and lean manufacturing principles need to be applied in the shop floor. Application of flexible
manufacturing principles will allow the production of customized and innovative products by fulfilling the
quality requirements. On the other hand, lean manufacturing principles will allow the production of exact
quantity of goods without experiencing wastages [45]

product will indicate its agility from the viewpoint of four
perspectives namely cost, market, time, and environment.
These perspectives will be reflected in the forms of indicators.
For example, the agility of a product from market perspective
will be indicated in the form of high sales. These AM
perspectives with their AM indicators are required to be
mapped with the product characteristics. This exercise carried
out at Trident on air dryers is explained in the next subsection.
4.2.1 Mapping exercise at Trident
The exercise on mapping from the AM perspectives was
carried out at Trident on refrigeration and regenerative air

dryers which are manufactured at Trident. This exercise was
carried out by interviewing the managing director (MD) of
Trident and gathering of relevant information along with his
remarks. Table 2 presents the results of this exercise.

An analysis of the information presented in Table 2
would reveal that the refrigeration air dryers possess
propensities for implementing AM from the AM perspectives namely market and environment. However, refrigeration air dryers do not possess propensities to implement
AM from the AM perspectives namely cost and time
requirements. The regenerative air dryers have been found
to possess propensities to implement AM from all AM
perspectives. Thus, the exercise on mapping air dryer

Table 2 Mapping AM perspectives with air dryer characteristics in Trident
Serial
number

AM
perspectives

AM indicators

Refrigeration
air dryer

Regenerative
air dryer

Remarks by the MD of Trident

1

Cost

2

Market

3

Time

Low initial cost
Low operating cost
Low maintenance cost
High demand (high sales volume)
High customization capabilities
Various product models
High performance in long run
Least design time

–
Yes
–
Yes
–
Yes
–
–

Yes
–
Yes
–
Yes

Yes
Yes
–

4

Environment

Least production and assembly time
Ecofriendliness

–
Yes

Yes
Yes

–
–
–
–
–
–
–
All the types of air dryers
are equally design intensive
–
–

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capabilities from AM perspectives has revealed that regenerative air dryers possess maximum propensity for infusing agility.
Hence, the regenerative air dryer was to be considered as the
candidate product for infusing AM with the objective of
strengthening weak AM criteria at Trident. However, the
MD of Trident wanted to consider refrigeration air dryer
as the candidate product. This is due to the reason that,
refrigeration air dryers are more widely used [21] than
regenerative air dryers. In this context, during the research
work being reported here, refrigeration air dryer was
chosen as the candidate product for investigating the
practicality of METAL.
4.3 Strengthening the AM criterion “time management”
As shown in the Fig. 2, the agility level of the AM criterion
“time management” at Trident is 30.625%. The remaining
69.375% of agility gap in time management AM criterion
needs to be filled. In order to strengthen “time management” AM criterion, time compression technologies such as
CAD/Computer-aided manufacturing (CAM), RPT, simulation, mass customization, “removal of non-value adding
activities”, quick response strategies, “configure to produce
according to the order”, and “redesign according to
customers’ perceptions” are required to be employed
[3, 22–28].
While conducting agility assessment and carrying out
subsequent analysis at Trident, two deficiencies were
identified under “time management” AM criterion. The
first deficiency was that there has been no program to train
the employees about the power of time compression in
acquiring the competitiveness. The second deficiency was
that there has been no deployment of time-compression

technologies at Trident. The first deficiency could not be
rectified during the research being reported here as allotting
the time of employees to train them on time management is
not currently affordable at Trident. In this background, the
efforts were made to rectify the second deficiency. To begin
with, the steps of assembling refrigeration air dryer were
closely observed at Trident. This observation indicated that,
out of the several time compression technologies listed in
the previous paragraph, the “removal of non-value adding
activity” has high potential in applying time compression in
the case of manufacturing refrigeration air dryer at Trident.
Hence, efforts were made to identify the nonvalue adding
activities and the methods of removing them.
At Trident, assembly of refrigeration air dryer is carried
out in an assembly cell. In this assembly cell, three
components namely compressor, condenser, and heat
exchanger are assembled. The activities carried out during
this assembly practice are shown in Fig. 3.
The time taken to carry out each of these activities is
indicated in brackets. These activities were studied to

427
Receiving and unpacking the outsourced components (10 minutes)

Placing the unit containing compressor
and condenser away from assembly cell

Dismantling of compressor and
condenser separately (25 minutes)

Placing of compressor
on the pallet

Placing of condenser
on the pallet

Placing of heat
exchanger on the pallet

Assembly of compressor, condenser and heat exchanger (25 minutes)

Brazing of copper tubes (25 minutes)

Leak testing (10 minutes)

Vacuum process (20 minutes)

Gas charging (20 minutes)

No load and full load testing (20 minutes)

Final inspection and packaging (20 minutes)

Fig. 3 Activities carried out in the assembly cell of refrigeration air
dryer at Trident

identify those that add no value while assembling the air
dryer. The nonvalue adding activities thus identified and the
proposals drawn to eliminate them are enumerated in the
following subsections.

4.3.1 Unloading and unpacking of outsourced components
As shown in Fig. 3, the components outsourced are received
and unpacked. Since these components are heavy, this
exercise consumes as much as 10 min while assembling
one refrigeration air dryer. Subsequent to this exercise, these
components are unloaded and moved to a place located at a
distance of 10 ft from the assembly cell. Instead if these
components are unloaded at the assembly cell itself, then the
time of 10 min consumed to move them to the assembly cell
and placing them there can be reduced to 5 min.
4.3.2 Receiving compressor and condenser
as separate units
Currently, Trident receives compressor and condenser as an
integral unit from a manufacturer. Then the compressor and


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Int J Adv Manuf Technol (2012) 60:421–436

condenser are dismantled and made as separate units.
Subsequently, the compressor and condenser are assembled
on the base plate of a component called canopy. This
dismantling and fixing are necessitated as the compressor
and condenser are assembled in the refrigeration air dryer in
different orientation to suit the dimensions of the base plate
of canopy. This exercise consumes as much as 25 min
while assembling one unit of the refrigeration air dryer.
This exercise is pictorially depicted in Fig. 4.
During the research being reported here, this whole

exercise was recognized as a nonvalue adding activity.
After analyzing the steps, the following two proposals were
suggested:
1. Trident may place order for procuring the compressor
and condenser separately from the same or two
different manufactures. These two components may
be assembled on the base plate of the canopy at Trident.
Thus, the nonvalue adding activity shown as steps 1
and 2 in Fig. 4 can be eliminated.
2. Trident may ask the manufactures to manufacture the
base plate of the canopy in accordance with the
dimensions furnished by the Trident. This manufacturer
shall assemble both compressor and condenser on this
base plate of canopy and dispatch the same to the
Trident. In this case, all the three steps shown in Fig. 4
can be eliminated at Trident.
Trident may choose to implement any one of the above
proposals. Here, it is obvious that the nonvalue-adding
activity can be totally eliminated in the case the second
proposal is implemented at Trident.
4.3.3 Centralized inventory management facility
One of the assembly activities is the positioning of the
compressor, condenser, and heat exchanger according to the
Fig. 4 Steps currently followed
to assemble compressor and
condenser

canopy size of refrigeration air dryer at Trident. The time
taken to carry out this activity is 25 min. While carrying out
this activity, the operator is required to collect the inventory

located at two different places. One place is located inside the
assembly cell and the other is located outside the assembly
cell. Further, these inventories are stacked in the rack which
cannot be rotated. These conditions result in unnecessary
motion of operators. Hence, this motion is considered as a
nonvalue-adding activity. In order to remove this nonvalue
adding activity, it is proposed that the inventory may be
centrally maintained within the assembly cell. Furthermore, it
is suggested that the inventory shall be stacked in a rack which
may be rotated. Implementing these proposals may reduce
10 min from the currently consumed time of 25 min in
collecting the inventory.
4.3.4 Reducing the time of carrying out brazing operation
In order to enhance agility level, all the components and
sub-assemblies required to manufacture refrigeration air
dryers are outsourced at Trident. These components and
sub-assemblies are assembled at Trident using few manufacturing processes. One of those manufacturing processes
employed is brazing. Brazing is employed to join the
copper tubes with the compressor, condenser, and heat
exchanger. During this process, the copper tube is bent to
the required dimension and positioned. The time taken for
carrying out this process is 25 min. During this research,
this process was recognized as a nonvalue-adding activity.
In order to remove this nonvalue-adding activity, following
proposals were evolved:
1. Trident may outsource the bending process to bend the
copper tube to the required shape and dimension.
2. A fixture may be designed and manufactured to speed
up the bending process.

Condenser

Condenser
Compressor

Base plate supplied
by the manufacturer
Step 1 : Compressor
and condenser are
supplied by the
manufacturer as an
integral unit.

Condenser
Compressor

Compressor

Base plate of canopy
manufactured at
Trident
Step 2: Compressor and
condenser are dismantled Step 3 : Compressor
and condenser are
separately.
fixed on the base
plate of canopy.


Int J Adv Manuf Technol (2012) 60:421–436

Implementing either one of the above proposals would
reduce 10 min out of the currently consumed time of
25 min in bending the copper tubes.
4.3.5 Time reduction through the removal of nonvalue
adding activities
An estimation indicated that, on implementing the proposals evolved during this research being reported here to
strengthen the AM criterion “time management”, the time
of manufacturing a refrigeration air dryer may reduce from
a minimum of 45 min to maximum of 65 min at Trident.
4.4 Strengthening the AM criterion “global optimization”
As shown in Fig. 2, the agility level of the AM criterion
“global optimization” at Trident is 37.5%. Hence, the AM
criterion “global optimization” needs to be strengthened to
fill 62.5% of agility gap prevailing in Trident. The efforts
made to fill this agility gap are described in the following
two subsections.
4.4.1 Strengthening through information technology
infrastructure
While conducting agility assessment and carrying out
subsequent analysis at Trident, two deficiencies were identified under the AM criterion “global optimization”. The first
deficiency is that there has been no deployment of information
technology (IT) infrastructure to handle conflicting objectives
prevailing in global supply chain. In order to overcome this
deficiency, the necessary IT infrastructure is required to be
employed at Trident. The IT infrastructure such as enterprise
resource planning, electronic data interchange, internet protocols, local area network, database management systems,
groupware, intranets, extranets, decision support systems,
multimedia, e-commerce, expert system, modeling, and
simulation are required to be employed [7, 29, 30]. In this

background, the IT infrastructure at Trident was closely
observed.
Presently at Trident, the information among the customers, suppliers, and employees are managed over telephonic
and postal communications. A study in this direction
revealed that, out of the several IT infrastructure listed
above, internet technology possesses high potential for
application in the case of manufacturing refrigeration air
dryer at Trident. The internet technology allows people to
interact with each other. If internet technology is used in
Trident, then their employees, suppliers, and customers can
interact with each other. In this context, a web portal was
designed to facilitate the Trident to overcome the aforementioned first deficiency. This web portal is named as
“Trident Global Optimization Platform” (Trident-GOP).

429

The “Trident-GOP” has been designed using the PHP
version 5.2.3 as front end, MySQL client version: 5.0.45 as
back end and XAMPP 1.6.3a software as editor. The
Trident-GOP can be accessed by three categories of users.
The first category of users of the Trident-GOP is named as
“Trident group”. These users are the top management and
employees of Trident. The other two categories of TridentGOP are suppliers and customers, Trident-GOP allow the
customers to place the order online. The web page of
Trident-GOP enabling this process is shown in Fig. 5.
Trident-GOP allows the Trident group users to record the
components to be supplied by the suppliers and the due
date of supplying them. The web page of Trident-GOP
enabling this process is shown in Fig. 6. On the other hand,
Trident-GOP allows the supplier to submit a request to

revise the due date. The web page enabling this process is
shown in Fig. 7. Now the Trident group user can view the
orders placed by the customers and the request made by the
suppliers to revise the due date. The web page displaying
these information is shown in Figs. 8 and 9. Thus TridentGOP has been designed and developed to meet rudimentary
requirements of globally optimizing the supply chain of the
Trident. More facilities can be added in the future to
Trident-GOP for meeting many other globalized optimization requirements of Trident.
4.4.2 Strengthening through the use of optimization
techniques
The second deficiency identified under the AM criterion
“global optimization” at Trident was that there has been no
deployment of techniques to optimize the contradictory
objectives of supply chain management activities. In order
to overcome this deficiency, appropriate optimization
techniques are required to be employed. Several optimization techniques and mathematical models are available in
the literature to optimize the contradictory objectives of
supply chain. For example, optimal policy models for
handling temporary price reduction and price increase
situations are presented in [31]. Besides these kinds of
mathematical models, other optimization techniques namely
genetic algorithm and artificial neural network are required to
be employed to enhance the efficiency and performance of
supply chains [32–37]. In this background, the contradictory
objectives of the supply chain of Trident were closely
observed.
Presently at Trident, the components are procured from
their suppliers based on monthly forecasting. As mentioned
earlier in Section 4, Trident has been in the AM journey. A
company practicing AM principles is required to follow the

just-in-time (JIT) philosophy [13]. However, this company
often has to confront the business dynamics such as
temporary price discount and price increase. During the


430

Int J Adv Manuf Technol (2012) 60:421–436

Fig. 5 Web page allowing the customer to place an order with Trident

temporary price discount period, the company is tempted to
procure large quantities of components from their suppliers.
Also, when the price increase is expected shortly, the
company is tempted to procure large quantities of components before their price increase becomes effective. The
company will be financially benefited by utilizing these
situations wisely. In these types of situations, the procurement cost is reduced when compared to that is incurred in
JIT scenario. Hence out of the optimization techniques
listed above, the optimal policy models proposed by [31,
38, 39] to handle the temporary price discount and price
increase situations were found to be the most potential
models that can be applied at Trident. The method of
adopting these models in practice is illustrated in the
following parts of this section.
When price discount is offered by the suppliers temporarily,
the following mathematical models may be used.
rffiffiffiffiffiffiffiffiffiffi
2DO
ðModel 1Þ
EOQ ¼

PH

dD
1
Qd ¼
þ
ðP À d ÞH ðP À d Þ

rffiffiffiffiffiffiffiffiffiffiffiffiffi
2POD
Àq
H

ðModel 2Þ

Sd ¼

ðP À d ÞHQd 2
ÀO
2D

ðModel 3Þ

where,
EOQ
Qd
Sd
D
O
P

H
d
q

economic order quantity
optimal discount order quantity in case of
temporary price discount
optimal cost saving in case of temporary price
discount
annual demand
ordering cost
purchasing cost per unit
annual holding cost fraction
reduction in the price per unit in case of temporary
price discount
stock position when optimal discount order quantity
is procured

Model 1 is used when no price discount is offered. In
this case, economic-ordering quantity is computed. An
order may be placed for supplying this quantity of goods. In
case price discount is offered by the supplier, model2 can
be used to determine optimal discount order quantity. When


Int J Adv Manuf Technol (2012) 60:421–436

431

Fig. 6 Web page enabling the Trident group to record the order placed with supplier

this calculated optimal discount order quantity is ordered,
the cost saved is computed using the model3.
When there is price increase, Trident may use the
following mathematical models 4, 5, and 6.
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2DO
EOQr ¼
ðP þ iÞH

iD 1
þ
Qr ¼
PH P

Sr ¼

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2ODðP þ iÞ
Àq
H

PHQr 2
ÀO
2D

ðModel 4Þ

ðModel 5Þ

ðModel 6Þ

where,
EOQr
Qr
Sr
D
O

economic order quantity during price increase
optimal price rise order quantity in case of price
increase
optimal cost saving in case of price increase
annual demand
ordering cost

P
H
d
i
q

purchasing cost per unit
annual holding cost fraction
reduction in the price per unit
anticipated increase in price per unit
stock position when optimal price rise order
quantity is procured

Model 4 is used to calculate the order quantity after the

price increase is announced. There are circumstances in
which Trident may anticipate price increase ahead of time.
In this situation, Trident can increase the order quantity and
escape from the adverse effect of price increase to a
maximum possible extent. This quantity to be ordered
ahead of the price increase can be calculated using the
model 5. The cost saving achieved in this case may be
calculated using the model 6. During these situations, the
company may procure the exact quantities required and
thus save the cost.
4.5 Strengthening the AM criterion “production
methodology”
As shown in Fig. 2, the agility level of the AM criterion
“production methodology” at Trident is 45%. Hence, this


432

Int J Adv Manuf Technol (2012) 60:421–436

Fig. 7 Web page enabling the supplier to make due date revision

AM criterion needs to be strengthened to fill 55% of agility
gap prevailing in Trident. While conducting agility assessment and carrying out subsequent analysis at Trident, two
deficiencies were identified under the AM criterion “production methodology”. The first deficiency is that there has been
no deployment of automated/computerized inspection at
Trident. The infrastructure such as vision-based automated
inspection system [40], X-ray oblique computed tomography
[41], and reconfigurable automated inspection systems are
required to be employed to enhance agility. In this

background, the infrastructure utilized to inspect the refrigeration air dryer at Trident was closely observed. This
observation indicated that leak testing was carried out
manually. This manual inspection is carried out to check
whether any leak prevails in the joints of the assembly. This
manual inspection was carried out by reading the values in
pressure gauge in regular intervals. Here, the entire refrigeration air dryer was filled with nitrogen gas and the pressure
variation if any was checked in the gauge at the specified
interval of time. Drawbacks such as excessive time consumption, difficulty in pinpointing the leak joint, and need
for removing the nitrogen after leak testing were observed at
Trident due to the adoption of this manual inspection.
Presently at Trident, this manual leak inspection has
been replaced by semi-automated leak inspection. This

semi-automated leak inspection is carried out using a
helium leak detector. Here, the air dryer under inspection
is vacuumed to 0.5 mille bar and then the helium gas is
supplied. If there is any leak in the joints of the assembly,
then this is indicated through an alarm signal. This helium
leak detector overcomes the drawback of the manual
inspection carried out at Trident earlier.
The second deficiency is the adoption of lot-by-lot
acceptance sampling practice at Trident. This acceptance
sampling was carried out by quality control department
personnel. The lot considered for sampling was one refrigeration air dryer per day. Apart from this, the quality control
department personnel used to inspect a particular attribute
based on the customer complaints. Presently at Trident, 100%
inspection is followed. This 100% inspection is executed by
infusing quality control check sheet at all inspection stages
during the manufacturing of refrigeration air dryer. Thus, the
AM criterion “production methodology” has now been

strengthened by overcoming the above two deficiencies.

5 Reassessment of TAL value
According to the METAL, the TAL value has to be
reassessed after strengthening the weak AM criteria. This


Int J Adv Manuf Technol (2012) 60:421–436

433

Fig. 8 Web page enabling the Trident group to view the order placed by the customer

task was carried out by explaining the proposals and
solutions derived to strengthen the weak AM criteria to
the competent personnel of Trident. After clarifying their
doubts, the questionnaires contained under the weak AM
criteria were given to them. As mentioned in the previous
section, Trident has strengthened “production methodology”
AM criterion. However, Trident is yet to implement the
proposals evolved during the research being reported here to
strengthen the two AM criteria namely “time management”
and “global optimization”. Hence, these personnel were
requested to assume that these proposals were implemented
to strengthen weak AM criteria and respond to these
questionnaires. The responses of these personnel were
quantified. Thus, the agility levels of weak AM criteria and
TAL value were reassessed at Trident.
5.1 Comparison of TAL before and after strengthening
weak AM criteria

The agility level and TAL value determined at Trident
before and after reassessment are summarized in Table 3.
As shown, the reassessed TAL value at Trident was found
to be 69.43%. The TAL value has enhanced by 1.06%. The
reason for this meager enhancement is that only three weak

AM criteria were identified and strengthened at Trident. As
shown in Table 3, the reassessed agility level of AM criterion
“time management” is 46.875%. This AM criterion has
enhanced its agility level by 16.25%. However, the agility
gap of 53.125% still prevails in this AM criterion at Trident.
The existence of this large gap is attributed to two reasons.
The first reason is that the proposals for removing nonvalue
adding activities for strengthening this AM criterion are only
partially accepted by the Trident. Second reason is that no
training programs on time management concepts are
conducted at Trident. The reassessed agility level of weak
AM criterion “global optimization” is 66.667%. This AM
criterion has enhanced its agility level by 29.167%.
However, the agility gap of 33.333% prevails in Trident
against this criterion. This is due to the same reason that the
suggestions proposed to strengthen this AM criterion are
only partially accepted by the Trident. The reassessed agility
level of weak AM criterion “production methodology” is
75%. This AM criterion has enhanced its agility level
by 30%. However, the agility gap of 25% prevails in
this AM criterion. This is due to the reason that, the
inspection system adopted is semi-automated and hence,
Trident has to consider adopting fully automated inspection
system.

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Int J Adv Manuf Technol (2012) 60:421–436

Fig. 9 Web page enabling the Trident group to view the request made by the supplier

6 Conclusion
Numerous research papers on AM are found in the literature
arena [11, 42]. An overview of these research papers indicate
that researchers have explored the way of infusing agility in
the companies and products in a scattered manner. However,
there has been no effort made to enhance the TAL of
companies by infusing agility through the mapping of
product characteristics from AM perspectives. In order to
meet this research requirement, the model METAL is
contributed in this paper. METAL facilitates the modern
companies to enhance their TAL value. The practicality of
METAL was examined at Trident. The METAL is initiated
by assessing of the TAL value of the company. In this paper,
the adoption of an agility assessment tool consisting of

30 AM criteria is recommended to assess the TAL value of
the company. On applying this 30 AM criteria assessment
tool, the TAL value of Trident was found to be 68.37%.
Simultaneously, the AM characteristics-enabled products
were identified by mapping refrigeration and regenerative
air dryer characteristics designed and manufactured at
Trident from four AM perspectives. At the end of this

exercise, the refrigeration air dryer was chosen for infusing
agility by strengthening the AM criteria. The weak AM
criteria were identified by fixing the agility base level as
50%. The weak AM criteria identified were studied.
Subsequently, proposals were evolved to strengthen them.
After that, the agility levels were reassessed. It was found
that two weak AM criteria namely “global optimization” and
“production methodology” have been strengthened by 30%.

Table 3 Comparison of TAL and agility levels before and after strengthening the weak AM criteria
Agility level of AM criterion
Time management
Before

After

30.625%

46.875%

Overall TAL value
Global optimization

Production methodology

Enhanced

Before

After

Enhanced

Before

After

Enhanced

Before

After

16.25%

37.5%

66.667%

29.167%

45%

75%

30%

68.37%

69.43%

Enhanced
1.06%


Int J Adv Manuf Technol (2012) 60:421–436

The weak AM criterion “time management” has been
strengthened by 16%. The TAL value was reassessed and
found to be 69.43%. The overall TAL value of Trident has
enhanced by 1.06%.
The research reported in this paper has suffered from few
limitations. One of the limitations is that the proposals
derived to strengthen the weak AM criteria have been only
partially accepted by the Trident management. This is due
to the reason that the effectiveness of implementing the
suggestions proposed is required to be examined and
validated. Another reason is that Trident needs to financially invest for implementing these proposals. This factor
prevents the immediate implementation of the suggestions
at Trident. On the whole, the experience of carrying out the
research reported in this paper has revealed that the
deployment of METAL would facilitate the contemporary
companies to systematically infuse agile characteristics and
enable to enhance their TAL values. This research may be
further continued by implementing METAL in many more
companies. The results of these case studies may be used to
refine METAL and enhance its practical compatibility.
Acknowledgment The authors are thankful for the cooperation and
support rendered by the management and employees of Trident
Pneumatics Private Limited, Coimbatore, 641 004, India towards the

conduct of the research work reported in this paper. The authors are
thankful to an anonymous referee whose two suggestions have been
used to improve the description of the research reported in this paper.

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Int J Adv Manuf Technol (2012) 60:437–451
DOI 10.1007/s00170-011-3620-z

ORIGINAL ARTICLE

Adaptation of the simulated annealing optimization
algorithm to achieve improved near-optimum objective
function values and computation times for multiple
component manufacture
Atef Afifi Afifi & Wasim Ahmed Khan &
David R. Hayhurst

Received: 4 March 2011 / Accepted: 31 August 2011 / Published online: 13 October 2011
# Springer-Verlag London Limited 2011

Abstract The paper concerns the development of the
Simulated Annealing Algorithm (SAA) for the sequencing
of cutter tool movement in machine tools capable of
manufacturing many components, located on a box-like
jig/pallet, in a single setting using a multiple tool magazine.
The objective of the SAA is to minimise the total machine
tool residence time. The general SAA has been enhanced,
to achieve lower values of the objective function during the
iterative scheme, and hence improve solution accuracy;
and, to reduce computation time by cessation of the
iterative scheme when no further improvement in the
objective function occurs. The reconfigured SAA has been
evaluated using a number of case studies. The results show
that a reduction in the objective function value can be
achieved in up to 6%, with far less computational effort. In
addition, it is shown that the computation time can be
reduced by a factor of between 20% and 72%. The
improvement in the objective function value and the

A. A. Afifi
German University in Cairo,
Main entrance Al Tagamoa Al Khames, Al Khames,
New Cairo, Egypt
W. A. Khan
Institute of Business Administration,
City Campus, Garden Road,
Karachi 74400, Pakistan
D. R. Hayhurst (*)
School of Mechanical, Aerospace and Civil Engineering, The
University of Manchester,

George Begg Building C-004, Sackville Street,
Manchester M13 19PL, UK
e-mail:

computational speed depends on the complexity of the
problem posed to the SAA software.
Keywords Simulated annealing algorithm .
Computationally efficient . Optimization .
Multi-component manufacture
Nomenclature
X, Y and Z Three global machine axes, Z is normal to
pallet
B
Fourth pallet rotational axis with range
of 0–360°
b
Random number between 1 and 0
r and s
Operational nodes on different pallet faces
p
Tool number
q
Number of tools utilised
g
Number of operational segments
i–j
Two operational nodes that define a segment
ACF
Acceptance check factor
e

T
Temperature in algorithm of Metropolis
et al. [6]
E
Energy level in algorithm of Metropolis
et al. [6]
Θ
Non-productive machine time objective
functional units (s), c.f. Eq. 2
C
Control parameter used in the optimization
process
Co and Ci Initial/original and general value of
optimization control parameter
Final value of optimization control parameter
Cf
ΔC
Increment of C between optimization steps
Tij
Time of non-productive motion in the X–Y
plane parallel to a single pallet face


438

Int J Adv Manuf Technol (2012) 60:437–451

Tz
p
Tch

p
Ttpwf
Tpr
bB
K
K
K*
Kwi

Q
ξo
ξi and ξi+1
ξp
ξBest
Figures
A
E
S
F
PA
PE
α, β, γ

Time of non-productive motion in the Z
direction
Time to change tool p
Tool path weight factor for tool p
Total pallet rotation time
Boltzmann’s constant
Counter for iteration number

Freezing parameter counter
Number of iterations performed without
improvement of Θ
Pre-determined value of the total number of
iterations
Initial solution
Current solution at the ith and i+1th steps
Potential candidate solution
Best solution in iteration

2–7
Approach to node
Exit from node
Start from node
Finish node
Pre-approach
Post-exit
Origins of respective coordinate systems

1 Introduction
The numerical solution of large combinatorial optimization
problems associated with machining/manufacture of multiple components with multiple tools, and sometimes using
several machine tools, is challenging because of the large
number of variables involved. Many different techniques/
algorithms are available for the optimization of the
associated path planning, and some of these are briefly
addressed. Yue-Jaw et al. [1] used a generic algorithm to
obtain optimal probe travel paths for coordinate measurement machine operation; Saravan et al. [2] optimised
cutting conditions during profile machining using a nontraditional optimization techniques; and, Zamani [3] used a
parallel constrained anytime procedure for manufacturing

project scheduling. Whilst such non-traditional techniques
can be tailored to specific problems, and give acceptably
good results; it is the Simulated Annealing Algorithm
(SAA) that is often preferred due to its adaptability,
robustness in coping with huge numbers of variables, and
its ability to avoid the numerical difficulties associated with
local minima. The SAA has been used successful in
conjunction with other techniques; for example, Wang et
al. [4] have combined it with a genetic algorithm in the
optimization of multi-pass milling; and Bachlaus et al. [5],
have enhanced it using chaos embedded techniques to

sequence the machining of components on multi-functional
machining systems. Although all of these techniques have
their own merits, particularly when tailored to specific
problems, this paper addresses the use of the classical SAA
approach, and seeks to identify those conditions that
improve both accuracy and computational speed.
The SAA is comprised of a stochastic search procedure
which seeks the minimum of a pre-defined deterministic
objective function. The method systematically applies small
perturbations to the current solution whilst seeking to
minimise the overall objective function. The technique
always accepts objective function decreases, but can be
made to accept objective function increases with apparent
benefits. This feature is examined in this paper. For very
large combinatorial problems associated with manufacturing scheduling, the speed of computation can be a limiting
feature; this aspect is also addressed here.
The simulated annealing technique was first developed
by Metropolis et al. [6] to analyse the physical annealing

process associated with condensed matter. Thereafter, it has
been applied to combinatorial problems by a number of
researchers and has been shown experimentally by Kirkpatrick et al. [7] and Cerny [8] to provide near-optimal
solutions. It has also been applied to the formation and
scheduling of manufacturing cells with encouraging results
by Jahangirian et al. [9], Varadharajan and Rajendran [10],
Liu and Wu [11], Vakharia and Change [12] and Tam [13].
In addition, Laarhoven et al. [14] have employed the SAA
to solve the job shop scheduling problem, and they proved
that it converges in probability to a global minimal solution.
The scheduling problem of a semiconductor circuit fabrication plant has been tackled by Peyrol et al. [15] using the
SAA method; and, Ben-Arieh and Maimon [16] have
successfully applied the SAA to the printed circuit board
assembly. Timetabling problems have been addressed by
Zhang et al. [17]; and, constrained optimisation problems
have been studied by Pendamallu and Ozdamar [18] using
hybrid and local search techniques. In this way, it has been
clearly demonstrated that the simulated annealing approach
yields global optimal solutions for large combinatorial
optimization problem.
In the computer-aided manufacture of component laden
pallets in machining centres with multiple tool magazines
(Fig. 1), components can be bolted to four faces of the
box-like pallet which can rotate about a symmetrical
vertical axis, B motion; tools, selected from a magazine,
are driven in the plane of a pallet face, X–Y motion, and
perpendicular to a pallet face, Z motion. In this way, fouraxis tool motion is achieved. When the implication of
large numbers of components and tools are taken into
account, it is found that non-optimal job sequences and
tool selections can have a significant impact on overall

profit margins, and hence on the competitive position of


Int J Adv Manuf Technol (2012) 60:437–451

Fig. 1 Machining on a Bridgeport 320H machining centre

the firm. However, finding the optimum sequence/solution
has proved quite difficult for manufacturing engineers due
to the large number of cutting paths, and tool combinations that may be selected c.f. Bard and Feo [19]. In this
paper, the problem will be addressed of performing
optimization computations for the minimization of the
manufacturing times of pallets that contain multiple
components, located on several pallet faces, and manufactured with multiple tools. The emphasis will be on the
minimization of the related objective function, and the
associated accuracy of solution, whilst keeping computation time to a minimum.
The problem of minimization of pallet residence time for
multiple component, multiple tool manufacturing under
imposed constrains has been formulated as a Euclidian
Travelling Salesman Problem. The constraints are, for
example, associated with the need to manufacture particular
features with individual tools at the required speeds, and
with the need to execute traverses between different
machining operations at maximum speed. In addition,
optimisation constrains are imposed by component geometry, clamps and fixtures and have to be taken account of;
these aspects have been addressed in detail by Afifi et al.
[20] in Section 6 of their paper. The SAA technique has
been used by Khan and Hayhurst [21] and Afifi and
Hayhurst [22] and further developed by Afifi et al. [20, 23]
to achieve optimum tool movement between different

productive contours around the pallet faces. In the work
reported by Khan and Hayhurst [21], the SAA algorithm
achieved optimum solutions for most of the cases examined
due to simplicity of the problem. In the work reported by
Afifi et al. [20, 23] the size of the problems were increased,
and a number of new parameters were included, such as a
cost function for tool changes and a penalty function for
pallet rotations. In the previous work by Afifi et al. [23],
and during the evaluation of the operation of the simulated
annealing method for some complex case studies, it was
found that the SAA reaches a solution which is typically a
few percent from the optimal one, and that it takes a
considerable computational time to do so. It is therefore

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apparent that there is a need to improve accuracy and
computational speed of the SAA algorithm when applied to
this class of manufacturing problems.
Because of the enormity of the combinatorial problem,
speed of computation is a prime concern, whilst preserving
computational accuracy, and techniques for the reduction in
computational time are a key part of this paper. Two particular
aspects are thought to offer significant benefits and are
examined in detail. The first relates to the improvement of
solution accuracy, and the second to reduced computer
solution times. Regarding the latter, the solutions due to Afifi
et al. [20, 23] indicate that the SAA iterative scheme can be
operated non-productively for many iterations without
significant reduction in the value of the objective function

or increase in the accuracy of solution. Hence, judicial
truncation of the iterative scheme is thought to be capable of
increasing computational speed.
The paper therefore focused on: (1) improvement of the
accuracy of solution of SAA algorithm by reduction of the
objective function, and (2) reduced computer solution times
by elimination of redundant SAA iterations. In the next
section, descriptions are given of the general SAA and of
the physical problem to be addressed.

2 Description of physical problem
2.1 The general annealing algorithm
Metropolis et al. [6], in the earliest days of scientific
computing, introduced a simple algorithm that can be used
to provide an efficient simulation of a collection of atoms in
equilibrium at a given temperature. In each step of this
algorithm, an atom is given a small random displacement,
and the resulting change in the energy of the system, ΔE, is
computed. If ΔE≤0, then the displacement is accepted and
the configuration with the displaced atom is used as the
starting point for the next step. The case ΔE>0 is treated
probabilistically, and the probability for acceptance of the
configuration is:

.

b BT
e ;
Pð$E Þ ¼ exp À$E K
ð1Þ

e is temperature.
bB is Boltzmann’s constant, and T
where K
Random numbers uniformly distributed in the interval (0–1)
provide a convenient means of implementing the random part
of the algorithm. One such number is selected and compared
with the acceptance probability P(ΔE). If it is less than P(ΔE),
the new configuration is retained; if not, the original
configuration is used to start the next step. By repeating
the basic step many times, the thermal motion of atoms in
thermal contact with a heat sink is simulated at the temperature
e . This choice of the acceptance probability P(ΔE) has the
T


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consequence that the system evolves into a Boltzmann
distribution.
The physical terminology used by Metropolis et al. [6],
e have
atomic configuration, energy E and the temperature T
been replaced in the current problem by the sequence of the
segments in the tool motion that are not associated with
manufacturing/metal cutting; the non-productive machining
objective function value, Θ, to be minimised; and, the
algorithm control parameter Ci. Two types of nodes are
used to define the non-productive tool segments: operational and non-operational nodes. Operational nodes are

points where there is either a need to move to a new
component or to change tool; and, non-operational nodes
are points such as those associated with machining the
same component with the same tool. It is the operational
nodes that are used to define different machining scenarios
and to enact the optimization phase. Entire part programmes are automatically segmented into discrete elements as defined by these nodes, and the sequencing of the
elements is varied until Θ is minimised. Then a new part
programme, that can drive the machine tool, is created from
the optimised sequence.
The objective function Θ defined in Eq. 2 is computed,
principally, as the sum of the following: (1) the time of
travel between non-operational nodes associated with nonproductive manufacturing/metal cutting, expressed by the
first and second terms on the right hand side; (2) the time
for tool changes involving q tools, given by the third term
on the right hand side; and, (3) the time for rotation of the
pallet that holds the multi-components under manufacture,
quantified by the last term on the right hand side. Afifi et al.
[23] used these quantities to define an objective function,
Θ, given by Eq. 4 of their paper, which for convenience, is
reproduced here:
D¼

1Àg
X
iÀj

Tij þ

1Àg
X

Tz þ

p¼q n
o X
X
p
p
Tch
þ Ttpwf
Tpr ;
þ
p¼1

ð2Þ

rÀs

where Tij is the non-productive motion in the X–Y plane
parallel to a single pallet face, Tz is the non-productive
p
motion in the Z direction normal to the pallet face, Tch
is the
p
time to change tool p, Ttpwf is the tool path weight factor for
tool p, and Tpr is the pallet rotation time defined as the time
to move the spindle from operational node r on one pallet
face to operational node s on another pallet face and given
by Eq. 3 of Afifi et al. [23]. The summations in Eq. 2 are
carried out with respect to the two operational nodes i–j

defined in the segmentation phase, which are also used to
execute the optimization phase, and the summation is
carried out over g operational segments, denoted as 1-g.
An efficient tool path is one that minimises the nonproductive motion between all non-operational nodes, and

hence achieves an absolute minimum in Θ. For a more
detailed statement on the definition and use of these terms,
the reader is directed to the work of Khan and Hayhurst
[21] and Afifi et al. [23].
The annealing idea was applied to the travelling
salesman problem by Kirkpatrick et al. [7]. Lundy [24]
has also used the simulated annealing algorithm to solve the
evolutionary tree problem. The general annealing algorithm
is as follows: start with an initial solution ξo that is selected
randomly and select a suitable high initial value of the
control parameter Co, and a suitable final value of Cf. At the
ith step the current solution is termed ξii. The control
parameter is Ci and the objective function is Θi =Θ(ξi). The
algorithm will repeat the following sequence until Ci ≤Cf:
1. Perturb ξi to form ξp as a candidate solution c.f. Khan
and Hayhurst, [21]. The state ξp is a potential candidate
for the next state ξi+1.
2. If Θp ≤Θi (downhill move), set ξi+1 to ξp.
3. If Θp >Θi (uphill move), calculate the acceptance
probability APi =exp [−(Θp −Θi)/Ci].
4. Generate a random number b from the uniform
distribution between 0 and 1.
5. If b≤APi then set ξi+1 to ξp. Otherwise ξi+1 =ξi.
6. Update Ci to Ci −ΔC, and update i to i+1.
7. If Ci

The uniqueness of the annealing method is that it allows
occasional uphill moves (i.e. it accepts inferior solutions) in
an attempt to reduce the probability of becoming stuck in a
poor local minimum solution. However, as noted by
Metropolis et al. [6], the value of the acceptance probability, APi, should approach zero as the iteration limit is
reached. That means the probability decreases as a function
of the number of iterations.
2.2 Description of the problem
Although the simulated annealing procedure is guaranteed to
converge to optimality if the increment in control parameter,
ΔC, is sufficiently small, this usually requires a large number
of iterations, and thus a high computational requirement c.f.
Afifi et al. [20, 23]. Hence, some applications have tried to
restrict the number of iterations. Lundy and Mees [25]
suggest a careful sequence of control parameters which
terminates the SAA arbitrarily close to the global optimum,
with probability arbitrarily near to one. The time to
termination cannot be shown to be polynomially bounded
for a general NP-hard problem. Lundy and Mees [25] gave
examples where the time is exponentially long, and the
annealing method may actually take longer than a deterministic algorithm that simply examines all the solutions.
However, as discussed in Section 1, the SAA will
converge to within a few percent of the optimal solution


Int J Adv Manuf Technol (2012) 60:437–451

for complex combinatorial optimization problems with
appropriate controls. The convergence theorems developed
in the context of simulated annealing suggested that the

choice of an initial solution does not affect the probability
of attaining a global optimum solution after an infinite
number of iterations. Therefore, conventional applications
of the simulated annealing algorithm use a randomly
selected initial solution. Matsuo et al. [26] mentioned that
the previous approach often requires a large amount of
computer time to eliminate the initial solution. They
defined a new approach of using a good initial solution
instead of using a random initial solution, and showed that
this approach yields better results; and, Johnson et al. [27]
have endorsed this approach. Also, the same technique has
been used by Sridhar and Rajendran [28] to achieve better
results. The drawback of the approach is the need for a
good initial solution. As pointed out by Sridhar and
Rajendran [28], and by Matsuo et al. [26], this means the
use of another algorithm to obtain a good initial solution for
the SAA. This will result in a reduction of computation
time for the simulated annealing algorithm but, will add
more time to the overall computation time of the optimization process, and alternative approaches are therefore
required to reduce computation time.
During the course of this research, two techniques have
been used to improve the performance of the simulated
annealing algorithm for large combinatorial problems. The
first technique allows the algorithm to accept increases in
the objective function Θ, and hence permits a wider SAA
solution search to achieve a near-optimal solution without
increase of computational effort. The second technique is
directed to reducing the computational time, without
reducing the accuracy of the output, by control of the
number of iterations made without improvement in the

objective function, Θ.
In the next two sections, the techniques used to improve
the accuracy of the SAA and to reduce the computation
time will be explained with the aid of some case studies.

3 Improved solution optimality by acceptance
of objective function increase
3.1 Problem definition and solution strategy
The acceptance of an objective function increase with non
zero probability avoids local minimum traps, and makes
the SAA converge to a near-optimum solution. The
acceptance of the objective function increase is usually
carried out (in the general SAA) by calculating the
acceptance probability, and comparing it with a random
number generated from the uniform distribution between 0
and 1.

441

In this research, this number is termed the Acceptance
Check Factor (ACF). The use of a random number gives
complete freedom of the SAA to find the near-optimal
solution, but it may result in acceptance of a new solution
with very high objective function value relative to the
current one. The acceptance of such a solution often
requires a large amount of computation time to eliminate
its effect. In this case, the approach of reducing the
computational time by restricting the total number of
iterations will result in a solution far from the optimal one
(particularly for complex combinatorial problems). Hence,

there is a need to modify the SAA to give a solution very
close to the optimal one, without increasing the computational time.
In this paper, a new approach is utilised of comparing
the acceptance probability with a constant value of ACF in
the range 0≤ACF≤1.0. The aim was to investigate the
existence of a range of values of ACF for which the
simulated annealing output will be improved. This approach has been employed and examined for three different
case studies with different degrees of complexity.
3.2 Case studies
The first case study concerns the manufacture using a fouraxis machining centre of six components of Afifi et al. [20]
and is presented as Figs. 1, 2 and 3 of this paper. The
components, c.f. Fig. 1, are located on one pallet face and
are machined using nine tools taken from an auto-selection
multi-tool magazine. Figures 2 and 3 respectively define the
un-optimised and optimised problem configurations, and in
addition illustrate the complexity of the problem. The
broken lines and arrows show the direction of tool
movement, the horizontal line at the top of the figure
denotes tool changes, with the associated numbers defining
the tool number. The machine tool is software driven: a tool
is automatically selected and moves in four-dimensional
space (X, Y, Z and pallet rotation B) over a sequence of
machining contours. Each contour is characterized by start
and end nodes. The number of nodes involved in this case
study is 69.
In the second case study the machining of eight
components, around the four pallet faces with a single tool,
has been chosen from Afifi et al. [23]. The case study is
presented in Figs. 4 and 5, and involves 96 nodes. In this
case study, the components are fixed to a box-like pallet

which has four vertical faces. The axis of rotation of the
pallet, or fourth machine axis, is symmetrically located
between the faces. Figure 4 depicts the un-optimised tool
path, and Fig. 5 shows the optimised tool path.
The third case study involves the machining of 10
components around the four pallet faces, using seven
different tools, as shown in Figs. 6 and 7. This case


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Fig. 2 Un-optimised tool path
for six components (case
study no. 1)

study has been taken from Afifi et al. [23], and involves
194 nodes. In this case study, additional nodes correspond
to the extra motions of the tool spindle associated with
tool changes. Figure 6 depicts the un-optimised, or
extracted, tool path, and Fig. 7 shows the optimised tool
path.
3.3 Discussion of results
Comparison between the results obtained by using constant
values for the ACF and the result obtained from using a
random number generator have been made and are shown
in Figs. 8, 9 and 10 where the objective function value, Θ
(s), is plotted against ACF. All three figures show results
for constant values of ACF presented as the solid diamond

symbols connected by a solid line; the computations were

carried out for increments in ACF of 0.01. Results for the
other three cases with random starting values of ACF,
selected between 0 and 1, have objective function values
shown as constant values for maximum, minimum and
mean values of Θ (s). To determine the maximum,
minimum and mean values of Θ (s) for each case study,
11 different runs have been carried out in which the random
number generator has been used to dynamically select the
value of the ACF. In Figs. 8, 9 and 10 for case studies 1, 2
and 3, respectively, the solid line represents the mean value
of these readings. The second and third broken lines
represent the lower and upper bound for the range of
values of Θ.
When the SAA is used to compare the acceptance
probability with constant values of the ACF instead of
using random numbers between 0 and 1, better results have


Int J Adv Manuf Technol (2012) 60:437–451

443

Fig. 3 Optimised tool path for
six components (case study
no. 1)

been obtained for all case studies, as shown by the solid
lines connecting diamond-shaped symbols, typically when

0.4≤ACF≤1.0.
The values of the objective function, obtained by
comparing the acceptance probability with randomly
selected ACF, have been reduced by factors in the range
from 1% to 6% by using constant values of ACF. Figure 8
shows ΔΘ ¼ 1%f¼ ð321:8 À 318:5Þ Â 100=321:8g relative to Θ mean for ACF=0.92; Fig. 9 shows ΔΘ ¼
5:5%f¼ ð167:4 À 158:1Þ Â 100=167:4g relative to Θ mean
for ACF = 0.78 and, Fig. 10 shows ΔΘ ¼ 6%f¼
ð661:8 À 622:0Þ Â 100=661:8g relative to Θ mean for
ACF=0.98. However, to achieve this reduction in Θ, it is
necessary to perform some experimentation with 0.75≤
ACF{Constant starting value}≤1.0. It is suggested that
calculation be performed initially with ACF=1 decreas-

ing with ΔACF=0.02 until no further improvement is
achieved. The reduction in the objective function value
has been achieved in the same computational time as
that for the case of using random numbers between 0
and 1.
The reduction in Θ, depends on the complexity of the
problem, namely the number of nodes in the cases study, i.e.,
69, 96 and 194 for case studies 1, 2 and 3; to demonstrate this
more clearly, an additional problem has been solved with 29
nodes, and the results are presented in Fig. 11, ΔΘ=0.43%.
The figure shows that the percentage reduction in the
objective function value, ΔΘ, increases as the number of
nodes is increased. This clearly shows that the methods are
appropriate for complex problems, particularly those possessing symmetries which may be used to judge, at a glance,
the degree of optimality of the solution.

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Int J Adv Manuf Technol (2012) 60:437–451

Fig. 4 Un-optimised tool path
for eight components (case
study no. 2)

It is important to emphasise that with the limited number
of cases presented in this paper, it is only possible to show
trends, and for more complex problems with the same, and
with larger numbers of nodes, it will be necessary to perform
sensitivity studies to confirm improved performance.

4 Reduction of computation time by control of number
of iterations without improvement of objective function
4.1 Problem definition and solution strategy
In the application of the simulated annealing algorithm to
the tool path re-sequencing problem, one has to take into

account that the number of nodes is unpredictable c.f. Khan
and Hayhurst [21]. By the use of a careful sequence of
control parameters, as suggested by Lundy and Mees [25],
the application of the general SAA to the tool path resequencing problem has been made for the three case
studies used here; and, near-optimal solutions have been
obtained. However, as indicated in Section 3, the SAA
takes a considerable computation time before termination of
the process, and it does so without improvement of the
objective function value.

Although it is known that the output from the SAA is not
optimal, attempts were made to improve the objective
function values in two different ways during the course of
the research reported by Afifi and Hayhurst [23]. The first