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Proceedings of the Asia Pacific Industrial Engineering & Management Systems Conference 2012
V. Kachitvichyanukul, H.T. Luong, and R. Pitakaso Eds.
† : Corresponding Author
1949
A Fuzzy Time-Driven Activity-Based Costing Model in an
Uncertain Manufacturing Environment
Annaruemon Phoonsiri Chansaad†
Department of Industrial Engineering, Faculty of Engineering
Prince of Songkla University, Songkhla, Thailand
Tel: (+66)813-884-433 Fax: (+66)74-558-829
Email: [email protected]
Wanida Rattanamanee
Department of Industrial Engineering, Faculty of Engineering
Prince of Songkla University, Songkhla, Thailand
Tel: (+66)74-287-160 Fax: (+66)74-558-829
Email: [email protected]
Supapan Chaiprapat
Department of Industrial Engineering, Faculty of Engineering
Prince of Songkla University, Songkhla, Thailand
Tel: (+66)74-287-159 Fax: (+66)74-558-829
Email: [email protected]
Pisal Yenradee
School of Manufacturing Systems and Mechanical Engineering, Faculty of Engineering
Sirindhorn International Institute of Technology, Thammasat University, Bangkok, Thailand
Tel: (+66)29-869-101 Fax: (+66)29-869-112
Email: [email protected]
Abstract. Due to substantial information required to complete the conventional ABC model, its popularity
faded away while the Time-Driven Activity-Based Costing (TDABC) is introduced. TDABC formulates cost
equations on the basis of time, called a “time equation”. When all consumed resources are converted into a
unit of time, difficulties on large information handling are minimized. However, TDABC is not flawless.
Under uncertain circumstances, TDABC is incapable of accounting for any variation that might occur, leading
to insufficient information to make the right decision. The fuzzy sets theory is widely known as a logical
approach that deals with reasoning to manage uncertainty. In manufacturing cost analysis, uncertainty is
mainly found in annual budget distributed to each support and operating departments. The objective of this
study is to propose a new framework of a fuzzy-TDABC. Using a fuzzification technique, the uncertain
parameters are transformed into fuzzy sets before being bundled together by time equations. The sets are then
defuzzified to a real value which is deemed to be the most accountable representative of product cost. It is
expected that this model will provide more reliable and complete information for managerial and strategic
planning.
Keywords: Time-driven activity-based costing; Fuzzy Set; Uncertainty
Chansaad, et al.
1950
1. INTRODUCTION
Staying competitive in an uncertain business
environment is a real challenge. Rapid changes in
technologies force us to constantly find new manufacturing
solutions. Competitive business strategies nowadays turn to
an ability to produce products with shorter lifespan and
better quality (Qian and Ben-Arieh, 2008). As more
automated technologies, hence less labor, are introduced to
the process, the proportion of overhead cost is growing
notable. When the paradigm of cost structure has shifted as
a result, the traditional cost systems are now inadequate.
Activity-based costing (ABC) has been acknowledged as a
costing system that more accurately allocates costs down to
the products. However, the calculation involves such
detailed information as lists of all related activities and
costs spent by them. This process can really be a burden
especially in large enterprises when substantial information
is required. Cost of data collection and system
maintenance through re-interviews and re-surveys has been
a major barrier to widespread ABC adoption (Kaplan and
Anderson, 2007). Time-driven activity-based costing
(TDABC) was eventually introduced by Kaplan and
Anderson (2007) to overcome this deficiency. Because
TDABC formulates cost equations from each activity on
the basis of time, called a “time equation”, difficulties on
large information handling are minimized and
computational time is notably reduced. In general, TDABC
seems like a magic tool to ease an implementation of the
widely known ABC system. However, when employed
under uncertain circumstances, TDABC is unable to
efficiently incorporate any possible variation. TDABC, as
well as ABC, draws out a representative of the collected
data set by simply averaging them or relying on intuitive
judgment. This approach works fine when variation of the
data set is minimal. But if the variation is large, significant
amount of information will be neglected.
Dealing with uncertainty, Zadeh (1965) introduced the
fuzzy set theory, which was based on the rationality of
uncertainty due to imprecision or vagueness. The theory
was originally employed to imitate human thought. It was
later found that fuzzy applications were extended to a
variety of research areas such as image processing,
automated control or even cost analysis. The objective of
this study is to propose a fuzzy-TDABC to estimate
indirect product costs in an uncertain environment. The
article is structured as follows: the next section provides a
background to the research questions. Section 3 briefly
presents the fuzzy-TDABC implementation on the design
and development of the model. In Section 4, a case study
using fuzzy sets is given. Comparison of results from a
conventional TDABC and the fuzzy-TDABC will be
shown and discussed before the conclusions will be made
in the last section.
2. THEORETICAL BACKGROUND AND PAST STUDIES
2.1 Activity-Based Costing (ABC)
The ABC method was introduced by Kaplan and
Cooper as a better alternative to traditional accounting
methods (Cooper and Kaplan, 1988). In ABC, it is
believed that costs are driven by both administrative and
production activities which consume resources (e.g.
materials and machines). The main questions of the ABC
analysis are how to assign activities down to cost objects
(e.g. products, customers) and more problematically how to
impose a monetary value to such activities. In response to
these questions, cost drivers are defined. They are used to
measure a quantity of activities demanded by a cost object.
In traditional cost-accounting systems, overhead costs are
roughly allocated down by a single cost driver which may
be production volume or production time, leading to cost
distortion. In an organization with a large proportion of
overhead cost, the distortion can be significant. To resolve
this, the ABC model distributes costs through multiple cost
drivers depending on activities being performed. There is a
tradeoff between improving model reliability by using a
variety of cost drivers and difficulties on handling large
information. As a result, despite obvious advantages over
the traditional methods, applications in real practice still are
limited. Because gathering the necessary information to
complete the ABC model is an expensive and time-
consuming process, an analyst relies mainly on cost
estimates (Cooper and Kaplan, 1988; Kaplan and Anderson,
2007). When the actual data is uncertain, reliability of ABC
outputs depends upon the method of estimation which may
be interviews, surveys, intuitive judgment, or averaging out
the historical data. By doing this, the estimates are very
likely to be later found imprecise.
2.2 From ABC to TDABC
According to the drawbacks of the conventional ABC
model, alternative approaches were proposed to lessen the
difficulties of data gathering processes. One approach was
introduced by Kaplan and Anderson (2007) called a time-
driven ABC (TDABC). Instead of defining product costs
through multiple cost drivers, TDABC uses a resource
capacity which in this case is “time” to measure the
demand on any given activities. Each department must
impose a monetary value of a unit of time, called a capacity
cost rate (CCR). A CCR can be calculated by dividing the
total resource cost incurred in the department by the
practical capacity. The practical capacity herein is often
Chansaad, et al.
1951
expressed as 80% or 85% of a theoretical time capacity
(Everaert et al. 2008; Kaplan and Anderson, 2007; Pernot
et al. 2007). Resource costs then are assigned to the cost
object by multiplying the CCR with the total time needed to
perform related activities, as shown in Table 1.
In TDABC, resource costs are allocated to a cost
object using only two sets of estimates: (1) a CCR and (2)
time required to perform a transaction or an activity. With
much less information needed, TDABC simplifies the
costing process by minimizing the need to interview and
survey employees. Because of its simplicity, TDABC was
found recently used in many applications such as in service
industries (Szychta, 2010), logistics (Everaert et al. 2008),
electronics company (Stout and Propri, 2011), managerial
impact in an outpatient clinic (Demeere et al. 2009), a
library acquisition process (Stouthuysen et al. 2010) and
identifying operational improvements (Hooze and
Bruggeman, 2010). Although TDABC can clearly lessen
difficulties of the ABC model, when in lack of information
or under uncertain environment, it; however, still suffers
Table 1: Activity-Based Costing versus Time-Driven
Activity-Based Costing.
ABC
Step 1
Step 2
Step 3
Step 4
Step 5
Identify and classify different overhead
activities to appropriate cost pools.
Estimate and allocate resource costs to the cost
pool using a resource driver.
Identify cost drivers for each pool.
Determine the cost driver rate for each pool by
dividing the total activity costs by a practical
volume of the activity driver.
Assign resource costs to products by
multiplying the activity driver rate with the
activity driver consumption.
TDABC
Step 1
Step 2
Step 3
Step 4
Step 5
Step 6
Identify the departments (groups of resources).
(e.g. maintenance department, production
departments)
Estimate a total resource cost of each
department.
Estimate a practical time capacity of each
department.
Calculate a capacity cost rate (CCR) of each
department by dividing the total resource cost
by the practical time capacity.
Determine the required time for each event of
an activity using a time equation.
Multiply the CCR by time required to perform
the activity.
from imprecise parameter estimates.
2.3 Fuzzy Set Theory Applications in Cost Analysis
Zadeh (1965) introduced the concept of fuzzy sets to
deal with imprecision and vagueness in real life situations.
A set containing elements that have varying degrees of
membership is called “a fuzzy set”. The membership
function µ(x) consists of real numbers in the interval [0 1]
that represent the degree of membership of a fuzzy number
within the set. A triangular fuzzy number (TFN) is a special
type of fuzzy numbers that is defined by a triplet (a1, aM, a2)
(as shown in Figure 1). The triangular fuzzy number
conceptually attempts to deal with real problems by
considering possibility of each fuzzy number. For example,
the triangular fuzzy number A or triangular number with a
membership function µA(x) is defined by:
� ≜ ����� = �� ���� ��� �� ≤ � ≤ �� ,�������� ��� �� ≤ � ≤ ��,0 otherwise
� (1)
where [a1 a2] is the interval of possible fuzzy numbers
and the point (aM, 1) is the peak (see Figure 1). This
parameter (a1, aM, a2) represents the smallest possible value,
the most promising value, and the largest possible value
respectively (Kaufmann and Gupta, 1988, 1991)
Figure1: Triangular fuzzy number.
Triangular fuzzy numbers were used to represent
uncertainty of TDABC parameters in this analysis because
of their simplification to formulate in a fuzzy environment
and they are potentially more intuitive than other
complicated types of fuzzy numbers such as trapezoidal or
bell-shaped fuzzy numbers (Chou and Chang, 2008).
Where fuzzification is a transformation of a precise (crisp)
quantity to a fuzzy quantity, defuzzification is opposed to
that. There may be situations where the output of a fuzzy
process needs to be defuzzified to a single scalar quantity.
Available defuzzification techniques include a max-
membership principle, a centroid method, a weighted
0
1
µ
a1 x* aM a2
(aM,1)
.
Chansaad, et al.
1952
average method, a mean-max membership method, a center
of sums, a center of largest area, the first of maxima or last
of maxima (Ibrahim, 2004; Sivanandam et al. 2010).
Among these, a centroid method (also called center of area,
center of gravity) is the most prevalent and physically
appealing methods (Lee, 1990; Sugeno, 1985). By using a
centroid method, a crisp value (x*) from a membership
function µA(x) can be obtained from:
�∗ = � ���� ���� (2)
Applications of the fuzzy set theory have been
increasingly found in engineering economics such as
evaluating information technology investments (Roztocki
and Weistroffer, 2005), capital budgeting (Kahraman et al.
2002), supply chain planning (Peidro et al. 2009) and
project cash flow analysis (Maravas and Pantouvakis,
2012). In cost analysis, the fuzzy set theory was first used
as a method of parameters estimation in an ABC system by
Nachtmann and Needy (2001). Four models for handling
uncertain input parameter in ABC systems: interval
mathematics, Monte Carlo simulation with triangular
distributed input parameters, Monte Carlo simulation with
normally distributed input parameters and fuzzy set theory
were proposed (Nachtmann and Needy, 2003). From this
study, it was concluded that the fuzzy set theory is
recommended as a viable and efficient method for
incorporating inherent data uncertainty and imprecision
into ABC models. This model has the potential benefits to
provide additional significant information for managerial
decisions making and performs an immediate ABC
sensitivity analysis by providing the best and worst case
results (Nachtmann and Needy, 2003).
Because manufacturing in emerging economies often
operates in an uncertain environment, evaluating costs
using a conventional TDABC may not always be
practicable. When implemented in uncertain environment
with large amount of information involved, both fuzzy-
ABC and TDABC systems are found inadequate and
deficient to provide reliable outputs. With such attractive
capability of the fuzzy set theory-based model, it is
interesting to also employ the fuzzy concept in parameters
estimation of the TDABC model. The objective of this
study is to develop a parameter estimation methodology
based on fuzzy set theory that will incorporate knowledge
concerning inherent data imprecision and uncertainty into a
TDABC system. Figure 2 shows evolutionary development
of cost analysis models.
Figure 2: Evolutionary development of cost analysis
models.
3. APPROACH AND METHODOLOGY
3.1 Research Setting and Data Gathering Process
To exemplify the implementation of the proposed
fuzzy-TDABC model, the authors used a scenario of a
manufacturing company who exports toy products
worldwide with uncertain resource costs. In this study, all
the data were gathered by interviewing key personnel and
reviewing historical financial and production records. The
TDABC with a fuzzy system was built on triangular fuzzy
resource costs. Each parameter has three values: smallest
possible, most promising, and largest possible. Resource
expenses flow is shown in Figure 3. Support departments
i.e. maintenance, finance and information system do not
directly touch the products. They provide the infrastructure
required for frontline people or equipment to perform their
work. In this article, the maintenance and production
departments are our focus because they offer high resource
Time-Driven Activity-
Based Costing (TDABC)
Kaplan and Anderson
(2004)
Fuzzy-Time-Driven
Activity-Based Costing
(Fuzzy-TDABC)
Fuzzy-Activity-Based
Costing (FABC)
Nachtmann and Needy
(2001)
Traditional Costing
Volume-Based Costing
(VBC)
Activity-Based Costing
(ABC)
Cooper and Kaplan (1988)
Chansaad, et al.
1953
Figure 3: Resource expenses flow of the production and maintenance departments.
costs and incur frequent unexpected transactions. From
the flow, it can be seen that the maintenance department
provides resource support through the production
department who directly fabricates the products.
3.2 TDABC Model Development 3.2.1 Time Equation Formulation
Generally the existing cost systems are fed by the
most recent data that are probably reported at the end of
one, three, or six-month period. In fact, these data are often
suffered by nonsystematic variation, for example, repair
expenses for unexpected machine break-down. If there is
an unusual incident, which is very likely to occur, the costs
assigned to products made in that period would be too high
or low away from the average costs. Besides, variation in
costing data can also be from timing differentials relating to
when bills are paid. Figure 4 shows resource expenses of
the maintenance and production departments throughout
the year 2011. This cost fluctuation is definitely
undesirable for organization executives to establish their
strategic marketing plans. They need more reliable, precise
and decisive information.
Figure 4: Resource expenditures of the maintenance and
production departments in the year 2011.
A pronounced advantage of TDABC is its ability to
capture the resource demands from diverse activities by
simply adding more terms to the equation. Where a basic
activity is mandatory, an optional activity is performed
occasionally when needed, for example, a customer may
ask for an additional packaging layer. Time required for a
given activity therefore can be obtained from a summation
of basic sub-activities and optional sub-activities times. A
time equation of a given activity can be formulated as
follows (Kaplan and Anderson, 2007):
!"=β1+β
2+ ⋯β
m+γ
1X1+γ
2X2+…+γ
nXn (3)
where tj is time needed to perform a given activity j
βm is a standard time for a basic sub-activity m γn is an estimated time for an optional sub-activity n
Xn is a number of times that an optional sub-activity
n is performed.
Before a time equation can be formulated, a flow
process of the maintenance and production departments
needs to be identified. An activity flow of both departments
is as shown in Figure 5.
Considering the process flow in Figure 5,
1) The time equation for the maintenance department
MT =β1+
[γ1×(# of maintenance) + γ2×(# of tool
adjustment)]{if it is a routine maintenance} +
[γ3×(# of initial checking) + γ4×(# of
repair){if special repair is not needed} +
γ5×(# of special repair){if special repair is
Jan
Feb
Mar
Ap
r
M…
Jun
Jul
Au
g
Sep
Oct
No
v
Dec
maintenance production
500,000
400,000
300,000
200,000
100,000
0
Personnel Equipment Utilities Supplies Facilities
Resources Cost
Operating Departments
Production Design Purchasing
Support Departments
Maintenance Information system Finance Selling
Cost Objects
Product A Product B Product C
Chansaad, et al.
1954
needed}]{if repair is requested} + β2 (4)
Figure 5: Flow process of the maintenance and production departments.
2) The time equation for the production department
PT = β1 +
[γ1×(# of lots)]{if it is a daily plan} +
[γ2×(# of batches) + γ3×(# of lots)]{if it is not
a daily plan} + β2 (5)
3.3.2 A Proposed Fuzzy-TDABC Model
As previously mentioned, in real practice variation in
resource consumption is very common. In a conventional
TDABC, if variation exists, the input parameters would
have to be averaged out before being fed into the equation.
By doing this, each value in a resource data set will be
assumed and regarded as equally important. But when
some values are more frequent to appear than others, this
assumption cannot hold true. A fuzzy set is proposed in this
study to represent imprecision and vagueness of resource
data. A degree of membership will be assigned to each
value indicating its likeliness to be found. Figure 6 shows a
procedural scheme of the proposed fuzzy-TDABC in
comparison with a conventional TDABC.
The procedure illustrated in Figure 6 can be explained
in 3 stages as follows:
Stage1. Calculate a CCR
A CCR indicates a monetary value for each minute
spent in an activity. It is a total resource cost (or budget
allocated to the department) divided by a total time at
practical capacity.
1) Identify a fuzzy set of resource costs. In a fuzzy-
TDABC model, resource costs of each
department are represented in a triangular fuzzy
number. The smallest possible (Csi), most
promising (Cmi), and largest possible (Cli)
resource costs for a department i are plotted as
shown in Figure 7. From the figure, the costs
beyond the interval [Csi Cli] has a degree of
membership of 0, meaning that it is very unlikely
that the department will have resource costs
daily plan
Production Flow Process
N
Y production order
receiving
(β1 mins)
production
scheduling
(γ3 mins)
production
planning
(γ2 mins)
product
checking
(γ1 mins)
record taking (β2 mins)
Maintenance Flow Process
Y
N
Y maintenance order
receiving
(β1 mins)
preventive
maintenance
(γ1 mins)
routine tool
adjustment
(γ2 mins)
initial
checking
(γ3 mins)
special
repair
special
repair
(γ5 mins)
repair
(γ4 mins)
N
record taking (β2 mins)
Chansaad, et al.
1955
which are either less than Csi or greater than Cli.
Cmi is a value of resource cost that is the most
frequent to be detected.
Figure 6: The framework of the TDABC model development.
Resource cost fuzzy set (Ci) = (Csi, Cmi , Cli) (6)
2) Compute the practical capacity time of each
department (Tpci).
3) Calculate the smallest possible (Rsi), most
promising (Rmi), and largest possible (Rli) CCR
for a department i.
�Rsi,Rmi,Rli�= $ Csi
Tpci
,Cmi
Tpci
,Cli
Tpci
% (7)
Stage2. Formulate a time equation
1) Use Eq.(3) to determine the activity time equation
of an activity j. A total time equation of a
department i is
!& = ' !" (8)
where ti is the total time of j activities in a
department i
Figure 7: The resource cost fuzzy set.
0
1
µ
Csi Cmi Cli
Stage 3
Stage 2
Fuzzy-TDABC Conventional TDABC
Calculate a cost object
OHsi OHmi OHli
Defuzzify indirect cost
Calculate a cost object
OH
Compute a standard time for a given activity
ti
Formulate a time equation
Compute a total time needed
Stage 1
Calculate a CCR
Determine resource cost fuzzy set
Csi Cmi C li
Rsi Rmi R li
Determine resource cost
Calculate a CCR
C
R
Chansaad, et al.
1956
Stage3. Calculate a cost object
1) Calculate the cost object.
(OHsi
,OHmi,OHli)=�ti×Rsi,ti×Rmi,ti×Rli� (9)
where OHsi , OHmi and OHli are the total smallest
possible, total most promising, and total largest
indirect cost of a cost object from a department i.
2) Defuzzified the indirect cost
In this step, the fuzzy set of cost objects is
defuzzified to obtain a crisp value of OHi using
Eq.(2).
4. AN EXPERIMENTAL STUDY AND DISCUSSION
To illustrate an implementation of the proposed
model, the authors used data collected in a year from a
wooden toy manufacturer. Costs are calculated at the end of
a 3-month period or a quarter year. Actual resource costs
were found fluctuating over time in each period due to
timing differentials relating to when bills are paid and other
nonsystematic variation in resource spending. Resource
costs are represented in a triangular fuzzy set. Results from
the proposed model are presented in comparison with those
from a conventional TDABC.
4.1 Calculate a CCR
All possible resource costs are represented in a
triangular fuzzy set: smallest possible (Csi), most promising (Cmi), and largest possible (Cli).
C = (Csi, Cmi, Cli)
For example, at the end of the first quarter (January-
March), resource costs of the maintenance department (CM)
always fall within the following interval.
CM = (681,420.00, 953,760.00, 1,125,000.00)
The CCR can be obtained by dividing these resource
costs by a practical capacity time. The practical capacity
time for the maintenance department is about 36,000
minutes a quarter. According to Eq.(7), a fuzzy set of CCR
(Rsi, Rmi, Rli) is:
Maintenance CCR = (681,420.0036,000
,953,760.00
36,000,1,125,000.00
36,000*
= (18.93, 26.49, 31.25)
Because the maintenance department is a support unit
that does not directly touch the product, total costs billed to
this department will be distributed down to the related
operating departments (see Figure 3). The total cost of the
operating department will therefore be composed of
transactions processed within the department itself and
additional transferred costs from support departments. To
calculate, for example, costs that were actually incurred in
the production department at the end of first quarter, we
need
1) The interval of expenditure within the production
department (CP), which is as well established
from past records.
CP = (393,750.00, 675,050.00, 879,900.00)
2) The transferred costs from the maintenance
department (CT)
CT = (351,877.72, 492,511.07, 580,937.50)
The total resource cost of the production department
is a summation of the above two.
C = (745,627.72, 1,167,561.07, 1,460,837.50)
The CCR of the production department where its
practical capacity time is 90,000 minutes is
Production CCR = (8.28, 12.97, 16.23)
4.2 Formulate Time Equation
If the product cost is calculated quarterly, for
example, at the end of one quarter, in manufacturing one
part, say, a piece of a crocodile body, it was found that
the order receiving std.time is 5 minutes (β1)
the product recording std. time is 10 minutes (β2)
the product checking std. time is 55 minutes (γ1)
the planning std. time is 100 minutes (γ2)
the scheduling std. time is 180 minutes (γ3)
the number of lot is 8 (NL)
the number of batch is 3 (NB).
According to Eq.(5), a time equation of this part is
PT = β1+ γ1NL + γ2NB +γ3NL + β2
= (5×3)+(55×8)+(100×3)+(180×8)+(10×8)
= 2,275 minutes
Chansaad, et al.
1957
Table 2: Unit costs from the fuzzy-TDABC model and the conventional TDABC
Period Fuzzy-TDABC Conventional
TDABC
Difference
OHS OHM OHL OH
1st Quarter 11.56 18.11 22.65 18.19 18.11 0.08
2nd
Quarter 14.48 23.62 31.75 24.43 23.62 0.81
3rd
Quarter 15.49 18.32 20.88 18.38 18.32 0.06
4th
Quarter 9.58 13.36 20.65 14.97 13.36 1.61
4.3 Calculate a Cost Object
Referring to Eq.(9), once the total activity time of the
production department (PT) is determined, it will be
multiplied by a triangular fuzzy set of CCRs to obtain a set
of product overhead costs.
(OHs, OHm, OHl) = 2,275×(8.28, 12.97, 16.23)
= (18,837.00, 29,506.75,
36,923.25)
This total production cost will be divided by the
number of products produced (N) to obtain a unit cost.
For example, if N = 1,630, a unit cost will be (11.56, 18.11,
22.65). This interval is a range of possible costs estimated
based on past records and transactions processed in a
current month. Organization executives can use this critical
information to establish their strategic plans. However, if a
precise data is needed, it can be drawn out from the interval
by a defuzzification technique discussed in Section 2 as
shown in Figure 8.
Figure 8: A fuzzy-TDABC unit cost
+, = � �0.15x�xdx + � �0.22���.���./0�1.���1.����.0/� �0.15x�dx + � �0.22��.���./0�1.���1.����.0/ = 18.19
Results from the fuzzy-TDABC model in comparison
with the conventional TDABC model are shown in Table 2.
The ranges of possible overhead costs calculated from the
fuzzy-TDABC model provide additional information on the
worst and best case results. Organization executives can
use this information for decision making on profitability
analysis and strategic planning. It can be seen that unit
costs released from the conventional TDABC model are
identical with OHM. This is because the conventional
TDABC model uses only the most promising values as an
input parameter, leaving alone all other possible data. Such
incomplete information could lead an organization to
uncompetitive decision making. When a crisp value of
the fuzzy set is needed, defuzzification will be performed.
The last column under the fuzzy-TDABC of Table 2
contains the defuzzified outputs, OH, of the fuzzy sets in
the columns to the left. Although there are slightly
differences between outputs from both models, once these
differences are accumulated by the number of products in a
lot size, the discrepancy may be notable.
5. CONCLUSIONS
This study proposed a new framework of a costing
system on the principle of TDABC and the fuzzy set theory.
It is suitable in the following environment.
1) An uncertain environment. When data variation
exists, a conventional TDABC system relies only
on averaged information. A fuzzy-TDABC
system takes into account all possible extreme
cases of costs by distributing weights to the cases
through a membership function.
2) In lack of data or an ability to establish reasonable
cost estimates.
It is important to note that no significant information
is lost when expanding a TDABC system to a fuzzy-
TDABC system. Moreover, resultant costs released from a
fuzzy-TDABC system are more supportive for managerial
decision making such as product pricing, profitability
assessment, and strategic planning. Future research can be
extended to other variant input parameters such as activity
times. Different types of fuzzy number representations
should also be explored.
0
1
11.56 18.11 18.19 22.65
.µ
Chansaad, et al.
1958
ACKNOWLEDGMENT
This study is financially supported by National
Science and Technology Development Agency (NSTDA) in
NSTDA-University-Industry Research Collaboration (NUI-
RC) (contract number NUI-RC01-54-004).
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1959
AUTHOR BIOGRAPHIES
Annaruemon Phoonsiri Chansaad is a doctoral student in
Industrial and Systems Engineering, Faculty of Engineering,
Prince of Songkhla University, Songkhla, Thailand. Her
email address is <[email protected]>
Wanida Rattanamanee is an associate professor in the
Department of Industrial Engineering, Faculty of
Engineering, Prince of Songkhla University, Songkhla,
Thailand. She received a M.Sc. in Industrial Engineering,
from Iowa State University in 1995. Her research
interests include Production Process, Productivity,
Logistics, Material Handling System and Manufacturing
System. Her email address is <[email protected] >
Supapan Chaiprapat is an assistant professor in the
Department of Industrial Engineering, Faculty of
Engineering, Prince of Songkhla University, Songkhla,
Thailand. She received a Ph.D. in Industrial Engineering
from Iowa State University in 2002.Her research interests
include Computational Geometry, Computer aided design
and manufacturing (CAD/CAM), Computer aided process
planning (CAPP) and Geometric dimensioning and
tolerancing (GD&T). Her email address is
Pisal Yenradee is an associate professor in School of
Manufacturing Systems and Mechanical Engineering,
Faculty of Engineering, Sirindhorn International Institute of
Technology, Thammasat University, Bangkok, Thailand.
He received a D.Eng. in Industrial Engineering and
Management from Asian Institute of Technology (AIT),
Thailand. His research interests include Production and
Inventory control (P&IC) systems, JIT, MRP, and TOC;
P&IC systems for Thai industries; P&IC in supply chain
and Applied operations research and Systems simulation.
His email address is <[email protected]>
