Expert Systems with Applications 24 (2003) 73–77
www.elsevier.com/locate/eswa
Application of a hybrid genetic algorithm and neural network approach
in activity-based costing
Kyoung-jae Kima,*, Ingoo Hanb
a
Department of Management Information Systems, Kyung Hee Cyber University, 1 Hoegi-Dong, Dongdaemon-Gu, Seoul 130-701, South Korea
b
Graduate School of Management, Korea Advanced Institute of Science and Technology, 207-43 Cheongryangri-Dong, Dongdaemun-Gu,
Seoul 130-012, South Korea
Abstract
Activity-based costing (ABC) has received extensive attention since it achieves improved accuracy in estimating costs, by using multiple
cost drivers to trace the cost of activities to the products associated with the resources consumed by those activities. However, it has some
problems. The first problem is that ABC does not have general criteria to select relevant cost drivers. Second, ABC assumes linearity between
the uses of activities and the assigned quantities of indirect cost. When cost behavior shows a nonlinear pattern, conventional ABC may
distort product costs. This paper proposes hybrid artificial intelligence techniques to resolve these two problems. Genetic algorithms are used
to identify optimal or near-optimal cost drivers. In addition, artificial neural networks are employed to allocate indirect costs with nonlinear
behavior to the products. Empirical results show that the proposed model outperforms the conventional model.
q 2002 Elsevier Science Ltd. All rights reserved.
Keywords: Activity-based costing; Genetic algorithms; Artificial neural networks; Cost-driver optimization; Cost estimating relationships
1. Introduction
Cost allocation is a very important task involved in many
engineering and business decisions. In this sense, activitybased costing (ABC) has received extensive attention
during the past decade because it was developed for
overcoming the problems of the traditional costing system
through more a reasonable cost allocation process. Conventional ABC, however, has some problems to be resolved.
The first problem is that ABC does not have general criteria
to select relevant cost drivers. This problem is related to the
cost-drivers optimization (CDO) problem and associated
with the efficiency of costing systems. Second, conventional
ABC generally assumes a linear cost function. The linear
cost function is a function where the graph of total costs
versus a single cost driver forms a straight line within the
relevant range. Horngren, Foster, and Datar (1997) pointed
out that a cost function, in practice, is not always linear, but
sometimes shows nonlinear behavior. They described a
nonlinear function as a cost function where the graph of
total costs versus a single cost driver does not form a straight
line within the relevant range. In this aspect, conventional
* Corresponding author. Tel.: þ 82-2-968-0755; fax: þ82-2-968-0549.
E-mail address: kjaekim@hanmail.net (K. Kim).
ABC may distort product costs when a cost behavior shows
a nonlinear behavior. Thus, the second problem is
associated with cost estimating relationships (CERs), and
it is also related to the effectiveness of costing systems.
Prior researchers have endeavored to overcome these
problems of conventional ABC. Some of these studies
showed that the estimating performance of artificial neural
network (ANN) outperforms that of linear regression for
optimal cost allocation in ABC (Bode, 1998a,b; Creese &
Li, 1995; Garza & Rouhana, 1995; Lee, 1993; Lee & Ahn,
1993; Smith & Mason, 1997). Other studies proved the
efficiency of heuristic search techniques to select optimal
cost drivers (Babad & Balachandran, 1993; Levitan &
Gupta, 1996). However, they did not consider these two
problems simultaneously.
This study proposes a hybrid model composed of genetic
algorithms (GAs) and ANN to resolve the above two
problems of conventional ABC simultaneously. First, GA
portion of the model is proposed as an optimization method
of relevant cost drivers. Second, ANN portion of the model
is used to reflect a nonlinear cost function for the cost
allocation process. In the hybrid model, the GA globally
searches and seeks an optimal or near-optimal ANN
topology.
The paper is organized as follows: Section 2 reviews
0957-4174/03/$ - see front matter q 2002 Elsevier Science Ltd. All rights reserved.
PII: S 0 9 5 7 - 4 1 7 4 ( 0 2 ) 0 0 0 8 4 - 2
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K.-j. Kim, I. Han / Expert Systems with Applications 24 (2003) 73–77
related prior studies. Section 3 presents a description of our
hybrid model of GA and ANN. In addition, Sections 4 and 5
describe the process of experiments and experimental
results. Finally, Section 6 discusses the conclusions and
the limitations of the study and future research issues.
2. Prior research
In general, traditional costing systems, volume-based
costing systems usually with a single cost driver, distort the
cost allocation process because they allocate costs by only
one criterion such as direct labor-hour, machine-hour, or
unit of production. Indirect costs, however, do not always
behave in proportion to the single cost driver in practice. In
addition, if cost drivers are not selected appropriately,
traditional approach does not accurately allocate indirect
costs to the products. This may cause distorted decisionmaking.
ABC is the costing method that assigns costs to activities
using multiple cost drivers, then allocates costs to products
based on each product’s use of these activities (Maher &
Deakin, 1994). ABC differs from traditional costing systems
in two ways (Cooper, 1989). Cost pools are defined as
activities rather than as production cost centers. In addition,
the cost drivers are used to assign activity costs to products,
which differs from traditional costing systems. ABC reduces
the risk of distortion because it uses multiple activities as
cost drivers based on CER.
There are two practical issues related to the proper
allocation of indirect cost for ABC systems. The first issue is
how to select proper cost drivers for cost allocation. It
focuses on the efficiency of ABC because optimal cost
drivers save the information-gathering cost without sacrificing major accuracy in cost estimation. It is a task currently
handled by application of human judgment for the purpose
of selecting appropriate cost drivers from the larger set of
available candidate drivers (Schniederjans & Garvin, 1997).
The second issue is how to determine the cost relationship.
It focuses on the accurate estimation of a cost function. It is
related to the effectiveness of ABC systems because
effectiveness can be achieved by the proper cost function
for cost allocation. Incorrect estimation of the cost function
will have repercussions in the areas of cost management and
control (Horngren et al., 1997).
Prior research has tried to resolve these two problems.
For the CDO problem, Maher and Deakin (1994) suggested
the following three criteria to select relevant cost drivers:
causal relation, benefits received, and reasonableness.
However, their criteria were abstract and subjective.
Babad and Balachandran (1993) attempted to optimize
cost drivers in ABC using greedy algorithms. They also
identified a priority order, according to which low-priority
and relatively insignificant activities with their associated
drivers would be combined to save costs without sacrificing
much accuracy in cost estimation. In addition, Levitan and
Gupta (1996) tried to optimize the selection of relevant cost
drivers using the GA in ABC systems. In their study, the GA
and the greedy algorithm are used to solve two cases from
the published literature. They concluded that a GA approach
achieved superior results to the greedy algorithm for both
cases. They found that the GA not only reduces informationgathering costs through fewer drivers, but also produces
more accurate costs even with fewer drivers.
A more recent study of Schniederjans and Garvin (1997)
proposed the combined analytic hierarchy process (AHP)
and zero –one goal programming to select relevant cost
drivers in ABC. They showed how the AHP approach could
bring consistency to the cost driver selection process. They
also illustrated how the AHP weighting can be combined in
the zero –one goal programming model to include resource
limitations in the cost driver selection process.
For the CERs, many researchers have made advances in
the cost allocation process. Several studies reported that
ANN outperforms linear regression for cost estimation
(Creese & Li, 1995; Garza & Rouhana, 1995; Lee, 1993;
Lee & Ahn, 1993). Smith and Mason (1997) suggested that
ANN has advantages when dealing with data for which there
is little a priori knowledge of the appropriate CER to select
for regression modeling. Bode (1998a) reported that ANN
after grouping of data outperforms linear and nonlinear
regression for cost estimation. He suggested that ANN
produces better cost predictions than conventional costing
methods when the following conditions are satisfied: a
sufficient case-base, known cost-driving attributes, few cots
drivers, and no explicit knowledge about cost effects. In
addition, Bode (1998b) suggested that ANN could be used
for R&D management. He carried out the estimation of final
cost of a new product under development, a typical R&D
management application, using ANN.
In this section, we describe prior studies which tried to
resolve the CDO and the CER problems in ABC systems.
However, they did not consider these problems simultaneously. There has been much research interest since these
two problems are interrelated for the estimation of product
costs. This study proposes the hybrid GA and ANN model to
resolve the CDO and the CER problems simultaneously.
Section 3 presents our research model.
3. The hybrid model of GA and ANN
The GA is a search algorithm based on survival of the
fittest among string structures (Goldberg, 1989). Recently,
the GA has been investigated and shown to be effective in
exploring a complex space in an adaptive way, guided by
the biological evolution mechanisms of reproduction,
crossover, and mutation (Adeli & Hung, 1995).
The first step of the GA is problem representation. The
problem must be represented in a suitable form to be
handled by the GA. Thus, the problem is described in terms
of genetic code, like DNA chromosomes. The GA often
K.-j. Kim, I. Han / Expert Systems with Applications 24 (2003) 73–77
works with a form of binary coding. If the problems are
coded as chromosomes, the populations are initialized. Each
chromosome within the population gradually evolves
through biological operations. There are no general rules
for determining the population size. But, population sizes of
100 –200 are commonly used in GA research. Once the
population size is chosen, the initial population is randomly
generated (Bauer, 1994). After the initialization step, each
chromosome is evaluated by a fitness function. According to
the value of the fitness function, the chromosome associated
with fittest individuals will be reproduced more often than
those associated with unfit individuals (Davis, 1994).
The GA works with three operators that are iteratively
used. The selection operator determines which individuals
may survive (Hertz & Kobler, 2000). The crossover
operator allows the search to fan out in diverse directions
looking for attractive solutions and permits chromosomal
material from different parents to be combined in a single
child. In addition, the mutation operator arbitrarily alters
one or more components of a selected chromosome.
Mutation randomly changes a gene on a chromosome. It
provides the means for introducing new information into the
population. Finally, the GA tends to converge on a nearoptimal solution through these operators (Wong & Tan,
1994).
The GA is usually employed to improve the performance
of artificial intelligence (AI) techniques. For ANN, the GA
is popularly used to select neural network topology
including optimizing relevant feature subsets, and determining the optimal number of hidden layers and processing
elements. The feature subsets, the number of hidden layers,
and the number of processing elements in hidden layers are
the architectural factors of ANN to be determined in
advance for the modeling process of ANN (Kim & Han,
2000). However, determining these factors is still part of the
art. These factors were usually determined by the trial and
error approach and the subjectivity of designer. This may
lead a locally optimized solution because it cannot
guarantee a global optimum.
In this paper, we propose the hybrid GA and ANN model
to resolve two problems of conventional ABC systems. In
this study, the GA is used for the step of selecting relevant
cost drivers and optimizing the network topology of ANN.
The GA globally searches an optimal or near-optimal ANN
topology in the hybrid model. The estimating process of the
hybrid model consists of the following three stages:
In the first stage, the GA searches (near-)optimal cost
drivers and the number of hidden nodes. The populations,
cost drivers and the number of hidden nodes, are initialized
into random values before the search process. The
parameters for searching must be encoded on chromosomes.
The encoded chromosomes are searched to optimize a
fitness function. The fitness function is specific to
applications. In this study, the fitness function is the average
deviation between expected and predicted values of product
costs. The parameters to be searched use only the
75
information about the training data. In this stage, the GA
operates the process of crossover and mutation on initial
chromosomes and iterates until the stopping conditions are
satisfied.
The second stage is the process of feed-forward
computation in ANN. In this stage, a sigmoid function is
used as an activation function. This function is a popular
activation function for the backpropagation neural network
because it can easily be differentiated. A linear function is
used as a combination function for the feed-forward
computation with selected cost drivers and ANN topology.
In the third stage, selected cost drivers and ANN
topology are applied to the holdout data. This stage is
indispensable to validate the generalizability because ANN
has the eminent ability of learning the known data. If this
stage is not carried out, the model may fall into the problem
of overfitting with the training data.
4. Research data and experiments
This study selects a revised case excerpted from Cooper
and Kaplan (1991) and Lee (1993). This is the case of Destin
Brass Products Co., which produces valves, pumps, and
flow controllers. The initial cost drivers (activities) are
‘Setup labor’, ‘Receiving’, ‘Materials handling’, ‘Engineering’, ‘Packing and shipping’, ‘Maintenance’, and
‘Machine usage’. The description of the research data is
as follows:
The possible production range of valves is 3500 – 10,500
products at intervals of 2000 products, that of pumps is
7500 – 17,500 at intervals of 1500 products, and that of flow
controllers is 2400 –5600 at intervals of 800 products. A
standard production unit for valves, pumps, and flow
controllers are 7500 products, 12,500 products, and 4000
products. If the number of valves is over 10,000 products,
then we put two units to the number of runs, otherwise put
one unit. In case of pumps, the number of runs increases by
one unit as the number of pumps increases by 2500 products
from the standard production. For flow controllers, standard
production runs are 10 units for 4000 products, and the
number of runs increases by two units as the number of
products increases by 800 products from the standard
production. The application rate is summarized in Table 1.
The following rules are applied for simulation of activity
values. For example, the value of the activity Setup labor is
calculated as 8 £ (the number of runs of valves) þ 8 £ (the
number of runs of pumps) þ 12 £ (the number of runs of
flow controllers). The application rate is presented in
Table 2.
Backpropagation algorithm and a sigmoid function are
used in ANN. The learning rate and momentum is 0.1, and
initial connection weight is 0.3 in ANN. Among the data,
60% of the data is training, 20% is testing, and 20% is
holdout data in order to avoid overfitting. The training and
testing data is used to search the optimal or near-optimal
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K.-j. Kim, I. Han / Expert Systems with Applications 24 (2003) 73–77
Table 1
Product summary and application rate (adapted from Cooper and Kaplan (1991) and Lee (1993))
Standard production (number of run)
Application rate
Valves
Pumps
Flow controllers
7500 products (1 run)
If products . 10,000,
then run ¼ 2, else, run ¼ 1
12,500 products (5 runs)
If products þ 2500 (or 22500),
then run þ 1 (or 21)
4000 products (10 runs)
If products þ 800 (or 2800),
then run þ 2 (or 22)
Table 2
Indirect cost activity analysis and application rate (adapted from Cooper and Kaplan (1991) and Lee (1993))
Activity
Application rate for valves
Application rate for pumps
Application rate for flow controllers
Setup labor
Receiving
Materials handling
Engineering
Packing and shipping
Maintenance
Machine usage
Number of runs £ 8
Number of runs £ 4
Number of runs £ 4
2
1
Number of products/2
Number of products/2
Number of runs £ 8
Number of runs £ 5
Number of runs £ 5
3
7
Number of products/2
Number of products/2
Number of runs £ 12
Number of runs £ 10
Number of runs £ 10
5
22
Number of products/5
Number of products/5
Table 3
Accuracy for cost allocation (MAPE)
No. of hidden nodes
3
3
7
7
No. of training patterns
presented since minimum
average error of the
test data is recorded
50,000
100,000
50,000
100,000
Training data
Holdout data
Conventional ANN
(7 drivers)
Hybrid model
(4 drivers)
Conventional ANN
(7 drivers)
Hybrid model
(4 drivers)
0.881
0.871
0.866
0.809
0.905
0.848
0.855
0.809
1.426
1.492
1.317
1.400
1.358
1.295
1.271
1.246
parameters and is employed to evaluate the fitness function.
The holdout data is used to test the results with the data that
is not utilized to develop the model. Using 125 data items,
we train and validate the hybrid model of GA and ANN and
the conventional ANN model. In addition, 50,000 and
100,000 training patterns are presented to ANN since
minimum average error of the test data is recorded. For the
controlling parameters of the GA search, the crossover and
mutation rates vary to prevent ANN from falling into a local
minimum. The crossover probabilities and probability of
mutation are 0.7 and 0.1.
5. Experimental results
For validating the proposed model, 25 holdout data items
are used. After experiments, the GA selects four cost drivers
including Receiving, Materials handling, Maintenance, and
Machine usage from all seven drivers. In addition, the GA
recommends three hidden nodes in ANN. Table 3 presents
mean-absolute-percent-error (MAPE) by different experimental conditions.
The results show that the proposed hybrid model
consistently outperforms conventional ANN, regardless of
changes in the number of hidden nodes and the number of
learning patterns. Although the hybrid model uses fewer
cost drivers than conventional ANN, it produces higher
accuracy in allocating indirect costs.
6. Concluding remarks
This study has proposed the hybrid AI model to resolve
the problems of designing ABC systems. In this study, the
GA was used for the step of selecting relevant cost drivers
and optimizing the network topology of ANN. The GA
globally searched an optimal or near-optimal ANN topology
in the hybrid model. The proposed model outperformed the
conventional model. From the experimental results, we
concluded that the proposed model has advantages when the
model analyzes the data with complex and nonlinear CER.
K.-j. Kim, I. Han / Expert Systems with Applications 24 (2003) 73–77
The major advantage of the proposed model was simultaneous consideration of efficiency and effectiveness issues
for designing ABC systems.
However, this study had some limitations. In this study, a
simulated data based on a real-world case was used for
testing the proposed model. This study cautiously managed
the simulation process, but the results on simulated data
might not guarantee consistency in the real world. Thus, it is
necessary to test the proposed model with the real-world
data. In addition, while ANN performed well with the GAbased optimization, other learning algorithms might also
prove effective in place of ANN. We believe that there is
great potential for further research with the optimization
using the GA for other AI techniques including case-based
reasoning and support vector machines. For future work, we
intend to apply the proposed model to more complicated
areas in accounting including cost estimation, cost allocation to specific departments, and the mitigation of the
linear assumption in cost-volume-profit (CVP) analysis.
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