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Evaluating Heuristics Used When Designing Product
Costing Systems
Ramji Balakrishnan, Stephen Hansen, Eva Labro,
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Ramji Balakrishnan, Stephen Hansen, Eva Labro, (2011) Evaluating Heuristics Used When Designing Product
Costing Systems. Management Science 57(3):520-541. https://doi.org/10.1287/mnsc.1100.1293
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MANAGEMENT SCIENCE
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Vol. 57, No. 3, March 2011, pp. 520–541
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doi 10.1287/mnsc.1100.1293
© 2011 INFORMS
Evaluating Heuristics Used When Designing
Product Costing Systems
Ramji Balakrishnan
Tippie College of Business, University of Iowa, Iowa City, Iowa 52242, ramji-balakrishnan@uiowa.edu
Stephen Hansen
School of Business, The George Washington University, Washington, DC 20052, shansen@gwu.edu
Eva Labro
Kenan-Flagler Business School, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599,
eva_labro@unc.edu
T
he academic and practitioner literature justifies firms’ use of product costs in product pricing and capacity
planning decisions as heuristics to address an otherwise intractable problem. However, product costs are the
output of a cost reporting system, which itself is the outcome of heuristic design choices. In particular, because
of informational limitations, when designing cost systems firms use simple rules of thumb to group resources
into cost pools and to select drivers used to allocate the pooled costs to products. Using simulations, we examine
how popular choices in costing system design influence the error in reported costs. Taking information needs
into account, we offer alternative ways to translate the vague guidance in the literature to implementable
methods. Specifically, we compare size-based rules for forming cost pools with more informationally demanding
correlation-based rules and develop a blended method that performs well in terms of accuracy. In addition, our
analysis suggests that significant gains can be made from using a composite driver rather than selecting a driver
based on the consumption pattern for the largest resource only, especially when combined with correlationbased rules to group resources. We vary properties of the underlying cost structure (such as the skewness
in resource costs, the traceability of resources to products, the sharing of resources across products, and the
variance in resource consumption patterns) to address the generalizability of our findings and to show when
different heuristics might be preferred.
Key words: costing; estimation; activity-based costing; cost drivers; cost pools
History: Received September 6, 2009; accepted November 11, 2010, by Stefan Reichelstein, accounting.
Published online in Articles in Advance January 28, 2011.
1.
Introduction
firms therefore employ simple rules of thumb, judgment, and unavoidably incomplete statistical analyses to make choices such as how many cost pools to
have, which resources to group into a given pool, and
how to choose cost drivers. To our knowledge, few
studies systematically evaluate alternative practical
approaches to cost system design and the consequent
implications for decision making. Thus, our objectives
in this paper are threefold. First, we examine how
choices regarding the design of a cost system influence the accuracy of reported product costs. Second,
we provide guidance on the implementation of generally worded (e.g., “group like resources” or “focus
on expensive resources”) prescriptions in the practitioner literature. Third, we provide insights into the
characteristics of economic environments that exert
the greatest influence on the preferences for system
features.
To capture complex interactions among the design
choices embedded in a cost system and to vary the
Long-run product and resource capacity planning
decisions are among the most important issues that
firms face. Because these decisions are computationally complex and informationally demanding, firms
often resort to simple and implementable decision
rules (Cooper and Kaplan 1998b, Govindrajan and
Anthony 1983, Shim and Sudit 1995). Consequently,
a recent stream of literature in management accounting has focused on the efficacy of alternative heuristics, especially those that rely on cost information
generated by product costing systems (Balakrishnan
and Sivaramakrishnan 2002). However, the efficacy
of such decision rules crucially depends on characteristics of the reporting system that provides the
inputs to the heuristic. In practice, organizations offering diverse products that share numerous capacity
resources do not have the granularity of information needed to design a cost reporting system that
reflects the production environment perfectly. Such
520
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Management Science 57(3), pp. 520–541, © 2011 INFORMS
nature of the production environment, we resort to
simulation experiments. Specifically, we simulate a
multiproduct, multiresource manufacturing environment, where we parameterize critical cost structure
dimensions such as heterogeneity in resource costs
and resource consumption patterns of various products in the product portfolio. Through this parameterization, we are able to examine the sensitivity
of design and decision heuristics to a rich array of
manufacturing configurations, thereby lending generalizability to our findings. Within each such configuration, we first construct error-free cost systems
that serve as benchmarks. We then introduce noise
in these benchmark cost systems by using combinations of design choices that are rooted in practice (e.g.,
Cooper and Kaplan 1998a, b; Cokins 2001); we view
each such noisy approximation as an instance of an
observed costing system. We calculate the error in a
noisy system (or “accuracy”) by comparing reported
and benchmark costs, which are obtained from the
observed and benchmark systems, respectively, and
analyze how the error changes across heuristics and
manufacturing configurations. For select heuristics,
we also consider how the coarsening of the information available to implement the design choice affects
system accuracy.
We first focus on heuristics that firms employ to
group resources into cost pools. Virtually all observed
product costing systems group resources into a manageable number of cost pools. Doing so reduces information needs because the firm only has to designate
and measure one allocation basis for each pool rather
than for each resource. To form cost pools, practitioners and academicians advocate the use of two kinds of
heuristics: those that rely on resource size and those
that rely on correlations in resource consumption patterns. Size-based rules segregate the most expensive
resources in separate cost pools, the idea being that
errors related to low-cost resources do not matter as
much in determining system accuracy. Implementing
a size-based rule requires only data on resource costs
(usually available in accounting records). Correlationbased rules, in contrast, combine “like” resources into
one pool under the premise that similarity in how
products consume these resources will reduce the
consequent error. Correlation-based rules are information intensive, as they require information on resource
consumption patterns, information that may be costly
(if not impossible) to collect.
Our experiments reveal the following insights with
respect to the implementation of heuristics related to
forming cost pools:
• For both size- and correlation-based rules, it is
preferable to group “small” resources into one miscellaneous overhead cost pool rather than distribute
them over the large pools (as is done, for example,
521
when labor supervision costs are added to the labor
cost pool or machine maintenance costs are added
to the machining cost pool). Surprisingly, this result
holds even when the set of small resources accounts
for up to 50% of total costs.
• A fairly low number of cost pools, formed using
gross information about consumption patterns, might
be acceptable (trading off the costs of adding more
pools with system accuracy) even for firms with a
large number of resources. Thus, we present the first
research findings in support of intuitive prescriptions
by Turney (1991, p. 51) that “10–20 cost pools might
be enough,” as well as by Cooper and Kaplan (1998a,
p. 99) that “Activity-Based Costing (ABC) systems settle down to between 35–50 activity cost drivers.”
• A blended method, which groups resources into
“tiers” (using gross estimates of correlations in consumption patterns) and then uses a size-based rule
within tiers, performs very well in terms of the accuracy of reported product costs. This blended method
resembles the structure of an ABC system but does
not demand as much information.
• Correlation-based rules perform well even when
the precision of available correlation information is
low. Crude estimates of correlations in consumption
patterns (e.g., merely knowing whether the correlation is greater than 0.4) appear to be sufficient to
implement correlation-based rules effectively.
Overall, our results on cost pools show that simple costing systems that use size-based rules to segregate the largest resources work well when a few
resources account for a majority of the costs. More
complex ABC systems that rely on correlation-based
rules might be preferable when the manufacturing
environment has many resources that are all equally
expensive. Our unique contribution in this regard is
to provide estimates of the required dispersion in
resource costs for size-based rules to be preferred over
correlation-based rules.
We next focus on the heuristics for selecting cost
drivers. The choice of a cost driver is critical because
the use of a single driver forces the costs of all
resources in the pool to be distributed in the same
proportion, potentially introducing specification error
(Datar and Gupta 1994). Moreover, one can either
use simple, easy-to-identify drivers (e.g., number of
setups as the driver for the pool of setup costs) or construct more complex drivers (e.g., intensity-adjusted
setup hours) that might represent consumption patterns better but be informationally more demanding.
We find that when resource costs are disparate, the
common practice of using the consumption pattern
for the largest resource (e.g., labor hours for the pool
of all labor-related resources) as the cost driver is
inefficient. Economically significant gains obtain from
instead considering an indexed or composite driver,
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522
Balakrishnan, Hansen, and Labro: Evaluating Heuristics Used When Designing Product Costing Systems
Management Science 57(3), pp. 520–541, © 2011 INFORMS
particularly when we also employ correlation-based
rules to group resources. Furthermore, data show that
an indexed or composite driver that combines the
largest two to five resources in a given pool into
an index might represent the best trade-off between
accuracy and collecting additional information on the
drivers of every resource in the cost pool. Overall, we
interpret these findings as pointing to potentially considerable gains from using indexed drivers to reduce
specification error (Datar and Gupta 1994), particularly for ABC-type systems that form cost pools by
grouping like resources.
Finally, we consider how characteristics of the production environment (with moderate skewness in
resource costs) affect the error in reported costs.
We find that the extent of resource traceability significantly affects the preferred method for grouping resources. In particular, it becomes increasingly
important to consider correlation-based methods for
pooling resources when the system designer believes
that resource consumption patterns vary considerably.
A practical implication is that a job shop with little sharing of resources across products might need
a more sophisticated system (e.g., more pools) to
accomplish the same level of accuracy as a process
shop in which all products make use of the same
set of resources (even if the pattern of consumption
varies across products).
We organize the remainder of this paper as follows.
In §2, we discuss the firm’s joint product and capacity
planning problem and the role of heuristics in solving
it. We describe our simulation protocol in §3. Section 4
discusses the properties of the generated systems and
also provides descriptive data on the production settings. We consider the performance of the candidate
heuristics in §5. In §6, we examine issues of fit with
the production environment. Finally, we offer additional thoughts concerning future research and conclude in §7. The appendix provides a summary of our
results.
2.
Why Do Firms Use Heuristics?
Our focus is on heuristics used to construct cost
accounting systems that report product costs. In such
an enquiry, it is important to understand the factors
that lead to the use of heuristics. We therefore begin
by examining the underlying product pricing and
capacity planning decisions. We argue that it is not
practically feasible to formulate and solve a general
version of these decisions, forcing the use of decision
rules and heuristics. Although there are many heuristics, surveys show that a popular approach is to use
product costs to decompose the general portfolio-level
planning problem into many product- and resourcelevel problems. However, product costs themselves
are outputs of a cost reporting system, and firms often
do not have the information required to compute
product costs that fully reflect the underlying production environment. Thus, again, firms have no choice
but to resort to simple decision rules to design system features such as the number of cost pools and the
choice of cost drivers. Obviously, these choices (e.g.,
choosing 5 versus 15 cost pools) significantly affect
the product costs reported by the system. Taking
information needs into account, we therefore examine
how alternative design rules for constructing product
costing systems affect the accuracy of reported product costs. We elaborate on these arguments below.
2.1. The Capacity and Product Planning Problem
Capacity planning and product planning are joint
decisions that involve long-term commitment (Balakrishnan and Sivaramakrishnan 2002). This exercise
in constrained stochastic programming is complex
and informationally demanding to formulate, let
alone solve.
Several dimensions contribute to the computational
complexity of this problem. First, once installed,
capacity levels are difficult to adjust in the short
term in response to demand fluctuations. This inability implies that in periods of demand spikes when
installed capacity is not enough, firms may have to
pay premium prices to acquire additional capacity
in the spot market (Banker and Hughes 1994). Consequently, firms have to make capacity and product
planning decisions based on their beliefs about the
demand distribution for its products, demand–price
relations, and production feasibility and technology
constraints, keeping in mind resource interdependencies, the role of inventory, and the costs of buying
additional capacity in the spot market. For instance,
when choosing capacity levels, a firm has to foresee future product prices, which in turn are solutions
to the quadratic program that reflects the allocation
of acquired capacity among products, given demand
realizations for each product. The firm also has to
anticipate future spot prices for acquiring additional
capacity resources on an as-needed basis. Allowing for inventory requires that the firm incorporate
intertemporal considerations; nonlinear demand functions possibly make the problem nonconvex; and
shocks to the demand parameters themselves likely
make the problem intractable. All of these issues
become that much more complex when we recognize that even organizations of manageable size have
numerous capacity resources.
Decentralized decision making contributes to informational complexity. Within a firm, capacity planning and product pricing decisions might be made by
different managers. Production managers, for example, might know the details about resource consumption and costs, whereas marketing has greater
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insight into demand distributions. Moreover, it is
likely impossible to transfer the large amounts of
relevant information possessed by different departments and to implement a centralized solution when
reporting is limited by feasibility and cost constraints
(Jordan 1989).
In sum, because of the dimensions discussed above,
we argue that firms must necessarily resort to some
simplification to overcome the computational and
informational complexity present in the traditional
formulation of the product and capacity planning program (which we refer to as the “grand program”).
2.2. Product-Based Planning
One way to address these informational and computational issues is to decompose the full-fledged
grand program into many smaller, more manageable
problems. Although firms may use many approaches,
we focus on product-based planning because surveys indicate this to be a popular, if not dominant,
approach. Recent research (e.g., Balachandran et al.
1997, Balakrishnan and Sivaramakrishnan 2002) justifies this practice as the use of heuristics helping
firms tackle an otherwise intractable problem. Banker
and Hughes (1994) note that this computationally easier approach also simplifies communication between
departments because product costs, which aggregate
resource consumption patterns and resource costs,
serve as economically sufficient estimates of long-run
marginal costs under certain conditions.
Product-based planning breaks the product and
capacity planning problem into two pieces: setting
product prices and determining resource quantities.
Product costs, which summarize data about the consumption of resources by product and resource costs,
are central in this decomposition. In simple terms,
product-cost-based planning involves calculating the
J
product cost of each product i as PCi = j=1 rij Cj ,
where rij is the quantity of resource j used to make
one unit of product i, and Cj is the cost per unit of
resource j. Then, the pricing problem is to choose Pi
for each product i to maximize Ai − Bi Pi Pi − PCi ,
where A B > 0 are market demand parameters. In
this simple formulation, note that resource constraints
and demand shocks are absent; furthermore, resource
usage and costs only enter the pricing problem indirectly via the calculation of product costs.1 Once the
pricing policy is determined, the implied demand distribution can be derived for resource j from product
demand distributions (see Banker and Hughes 1994
for details). The firm can then determine the quantity
1
In line with Balakrishnan and Sivaramakrishnan (2002), we view
list prices as the prices set in this deterministic setting. Once the
demand shocks for a particular period are known, the firm adjusts
list prices to yield tactical prices.
523
of capacity to install upfront by trading off the costs
of acquiring the resource now versus on an as-needed
basis but at a premium price later.
The focus in extant product-based planning
research has been on the computational difficulty
and/or the difficulty in transferring information
across departments, as both are important rationales
for decomposing the Grand Program. This literature
therefore takes as given the availability of product
cost information (i.e., assumes that the firm can compute PCi ). In contrast, we argue that the computation
of product costs is itself a complex task. Considerable literature suggests that it is not possible for a
firm to calculate error-free product costs (e.g., Datar
and Gupta 1994, Hwang et al. 1993). Rather, firms calculate product costs (we term the collection of these
procedures a costing system) based on imperfect and
incomplete information about resource costs and consumption patterns.2 Furthermore, firms employ rules
of thumb in this process because there are no clear
guidelines on how to construct a costing system. In
other words, the product costs that firms use are themselves the outcomes of heuristically designed systems. Our
focus is on how the use of system-design heuristics
affects the accuracy of reported product costs, and
therefore the efficacy of the capacity planning rules
that use this information.
2.3. Product Costing Systems
We define a benchmark costing system (as implicitly
visualized in extant literature) as comprising two
pieces: a vector of costs (RC) and a matrix of resource
consumption patterns (RES_CONS_PAT) that models resource usage by individual products.3 Each
element of RC is a dollar value, representing the
cost of a particular resource. We interpret each row
of RES_CONS_PAT as an allocation basis, i.e., the
cost driver, for distributing the cost of the associated resource across products. Thus, the elements are
proportions, with each row summing to 100%. The
2
Jordan (1989) also investigates incomplete information as the
motivation for product costs. He derives a set of transfer prices
constructed with limited information as might be found in a financial accounting system. When communicated to marketing and
production managers making independent decisions, the prices
lead to long-run optimum resource capacities, prices, and resource
allocations. We are not aware of work that has followed up on
these insights. Moreover, we assert that system designers might
have more limited information than is assumed available in
Jordan (1989).
3
The calculation of PC for solving the grand program occurs before
resources are bought. However, observed cost systems are mostly
ex post in nature (i.e., they allocate the costs of resources already
in place). We reconcile this potential inconsistency by noting that
firms periodically replenish their capacity resources and thereby
update resource costs.
Balakrishnan, Hansen, and Labro: Evaluating Heuristics Used When Designing Product Costing Systems
524
Management Science 57(3), pp. 520–541, © 2011 INFORMS
output from a benchmark costing system is a vector
of product costs (PCb . Formally,
Downloaded from informs.org by [146.50.140.255] on 07 April 2025, at 12:22 . For personal use only, all rights reserved.

RC1
T 
alt11

 
 RC2   
 

 
   
 
RCJ
altJ 1
alt1 I


PC1b
T
 

  PC b 
  2
=
   
 

altJ I
PCIb
The calculations of product costs from detailed data
(as in Banker and Hughes 1994) and in a product costing system are closely related. Both approaches use
information at the level of the individual resource and
consider the consumption pattern of each resource by
a given product. Under suitable conditions, it can be
shown that the two approaches are alternative views
of the solution to the grand program.4
As argued earlier, information limitations bar a firm
from implementing the benchmark system. These
limitations mean that an observed cost system necessarily involves some aggregation relative to the
benchmark system. Consider the information that a
firm is likely to possess regarding resource costs. Generally, we expect that accounting records, vetted by
auditors, provide reliable and detailed resource costs
(i.e., data on RC), albeit after applying some materiality threshold. However, even here some aggregation is inevitable for resources that support multiple
activities. For example, the accounting record likely
reports only the total cost for a purchase office even
though the office might process many different types
of orders; a benchmark system would require that
the costs be separately identified for each activity.
We also argue that firms possess incomplete information about their production environment (i.e., as modeled in RES_CONS_PAT). Although they may know
the number of machine hours consumed by a product, they might not track the number of purchasing
hours devoted to procuring associated raw materials. Practically, we therefore observe that firms group
resources into cost pools; as a result, they use a single
driver to allocate the costs from a cost pool that might
contain many resources with different consumption
patterns. This approach considerably reduces information needs because the firm has to collect data for
fewer cost drivers. For example, we only need data
on total resource costs and labor hours consumed by
each product to implement a one-pool, labor-hourbased cost system.
4
The elements of the resource consumption matrix, altji =
rij Qi / i rij Qi , are the proportions of resource j consumed to make
Qi units of product i. Further, equating the supply and demand
for resources, the capacity bought at time t = 0 is Lj = i rij Qi , and
RCj = Cj × Lj .
We hasten to note that firms are not devoid of information that helps determine product costs. In particular, although incomplete and imperfect, a firm
likely has substantive information that it can bring
to bear when constructing an observed cost system.
First, firms likely have a good sense of resource traceability. For example, indices of component commonality (Fisher et al. 1999) measure the extent of resource
sharing by products. Firms that organize their production around postponing assembly of products
and delaying customization (e.g., those that work
with “vanilla boxes” as described in Swaminathan
and Tayur 1998) are likely to have more sharing of
resources by products than firms that operate in a
make-to-order context. Production systems that make
use of worker rotation within a multiskilled workforce also exhibit less resource traceability relative to
an assembly line that is organized around rigid job
classifications (Hopp and Spearman 2000). Second,
firms likely have coarse estimates of similarity in consumption patterns, allowing for clustering of “like”
resources. For example, a firm would infer high variation in the consumption patterns of volume- and
batch-level resources when its products vary widely
in terms of the volume of production and batch size.
Moreover, the consumption pattern for labor hours is
likely to be more highly correlated with the consumption for machine hours than with the consumption of
design activity. In the language of activity-based costing, the former are volume-based resources, whereas
the latter is a product-level resource. Based on this
clustering into “tiers,” the firm also might be able to
identify the proportion of costs in batch resources.
Finally, the data required for constructing the rows
of RES_CONS_PAT (i.e., the consumption patterns)
might be available for a few large resources (e.g., the
firm might track machine hours, but not marketing
hours, by product).
Formally, we represent an observed costing system
as follows:

T
PC1R
T 


cd11 cd1 I
AC1


R
 
 

 PC2 

    = 

 

 


ACK
cdK 1 cdK I
R
PCI
where AC is a vector of activity cost pools, and
the elements of the activity consumption matrix
(ACT_CONS_PAT) map activities to products. As
with the benchmark system, each element of AC is
a dollar value and each element of ACT_CONS_PAT
is a proportion, with rows summing to 100%. This
computation yields the vector of reported product
costs, PCR .
How does the benchmark system relate to an
observed system? In the above representation, we
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Management Science 57(3), pp. 520–541, © 2011 INFORMS
map each resource (i.e., elements in RC) to a cost pool
(i.e., an element in AC). Thus, sum(RC) = sum(AC) =
sum(PCb = sum(PCR . The value of any given cost
pool is the sum of the costs of the resources mapped
to that cost pool. Usually, the number of activity
pools is much lower than the number of resources,
dimAC dimRC . Indeed, AC is a scalar in firms
that employ a one-pool system, as found in a large
fraction of firms (Horngren et al. 2003). Similarly, the
matrix of activity consumption patterns summarizes
the information about resource consumption patterns.
Because observed costing systems coarsen information relative to benchmark costing systems, reported
product costs differ from benchmark product costs. In
particular, the grouping of resources into cost pools
results in aggregation error (Datar and Gupta 1994,
Gupta 1993, Hwang et al. 1993). Reducing the cardinality of the consumption matrix results in specification error because different resources in the same pool
might have different consumption patterns. Finally,
aggregation and specification errors interact in subtle
ways (Labro and Vanhoucke 2007). Indeed, as Christensen and Demski (1997) demonstrate, there is no
simple method to select the approach that results in
the lowest error. Thus, when choosing among cost
systems, a firm implicitly chooses among portfolios
of errors. In sum, consistent with intuition, prior
research indicates that the features of the cost system
(e.g., number of pools, process of assigning resources
to pools, choice of cost drivers) exert a significant
influence on the accuracy of reported product costs.
As noted earlier, we focus on the heuristics that
firms employ to construct the vector of activity cost
pools and the matrix of activity consumption patterns. We refer to these choices as assigning resources
to pools and as selecting cost drivers, respectively.
Conceptually, there are numerous options that a firm
might adopt for either decision. We therefore focus on
a few popular choices as documented in surveys and
textbooks. We list the detailed choices we consider
after we describe our simulation protocol.
3.
Simulation Protocol
Our simulation protocol has four major steps. First,
we generate a set of production environments by
varying several dimensions of the economic environment. Second, for each such production environment, we simulate many benchmark systems. Each of
these draws represents a “firm” with a unique vector of resource costs and an associated consumption
matrix. Using these data, which are the most granular
information available to model the consumption of
resources by products, we calculate the benchmark
vector of product costs. Third, for each benchmark
system, we construct many associated “noisy” or
525
observable systems. Each noisy system is a combination of the heuristics for selecting the number of cost
pools, for assigning resources to cost pools, and for
calculating cost driver rates. For each noisy system,
we compute the associated vector of reported product costs. The use of heuristics means that this set
of reported product costs is computed with coarser
information than is used to compute benchmark costs.
Fourth, for each noisy system, we compute an error
metric by comparing the vectors of the benchmark
and reported product costs. We then analyze how
variations in the construction of noisy systems affect
this metric and examine the robustness of specific
heuristics to available information by coarsening the
data used to implement the rule. We detail each of the
above steps in the following paragraphs.5
3.1. Step 1: Model a Production Environment
We parameterize the cost structure of a production
environment along three dimensions. (We defer discussion about the specific values we use for this and
other parameters and the survey evidence that supports the choices.) The parameter RC_VAR (resource
cost variance) determines the variation in the costs of
individual resources, the elements of RC. Low values
of RC_VAR correspond to environments with many
resources with roughly equal monetary importance
(i.e., has low variance in resource costs) such as might
be found in a firm producing a wide and varied product line. High values of RC_VAR indicate an environment with many small resource cost pools and a few
large cost pools such as might be found in a refinery
or a law firm where machine and human resources
account for a majority of costs, respectively.
The parameter DENS (density of consumption
matrix) captures the extent of resource traceability (or,
its counterpart, resource sharing) as measured by the
number of zeros in the resource consumption matrix,
RES_CONS_PAT. When DENS is low, the resource
consumption matrix is sparse, meaning that only a
few products consume any given resource (that is,
we have many zeros in the consumption matrix). As
might occur in a job shop, there is high traceability of costs to products. For instance, we can directly
trace much of a lawyer’s time to individual cases.
In contrast, a dense matrix implies a setting with
many common costs and low traceability. A bottler is
a good example because all products go through the
same line.
The final parameter (COR) models the correlation
between resources whose consumption varies with
production volume (volume-based resources) and
with the number of batches (batch-level resources).
5
A formal description of the simulation protocol is available from
the authors on request.
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Balakrishnan, Hansen, and Labro: Evaluating Heuristics Used When Designing Product Costing Systems
A large positive value induces similarity between the
consumption patterns of batch and volume resources,
across products. This case models a setting in which
most resources are consumed in proportion to volume. A negative value for COR implies significant
disparity between the consumption patterns of batch
and volume resources across products.
3.2. Step 2: Benchmark Costing Systems
For each production environment (i.e., a unique combination of the values for RC_VAR, DENS, and COR),
we simulate 20 benchmark cost systems. For each
such draw, as in Datar and Gupta (1994, p. 571),
we assume that the firm knows the total resource
cost without error and set this value at $1,000,000.6
We distribute this total cost among 50 resources,
with the variance in the distribution governed by
the parameter RC_VAR and a randomly generated
value for PER_BATCH determining the percentage
of costs contained in batch-level resources. This distribution yields a vector of resource costs, RC. We
next simulate the matrix of resource consumption patterns (RES_CONS_PAT) to conform to the parameters DENS and COR, which influence the density of
the consumption matrix and the correlation in consumption patterns respectively. We consider settings
with 50 products. Finally, we compute the vector of
benchmark costs (PCb as the product of resource cost
vector and the resource consumption matrix. Thus,
we have 20 data points (vectors of benchmark costs)
for each combination of the parameters relating to the
production environment.
3.3.
Step 3: Use Heuristics to Construct
“Noisy” Systems
For each benchmark cost system, we construct many
possible observable systems by varying three parameters that reflect potential heuristics that a system
designer could use. First, we vary the number of
activity cost pools. The smaller is the number of activity pools, the greater is the aggregation in the cost
system. Formally, this step specifies the length of AC,
the vector of activity cost pools. Second, we vary
the heuristic to assign resources to activity pools. We
use random size-based and random correlation-based
rules. At the end of this step, we have compressed
the vector of resource costs to generate a set of activity pools and have assigned resources to individual
pools;7 that is, we have generated the vector AC by
aggregating the vector RC. Third, we vary the rule
6
Our tidy allocation scheme maintains comparability across experiments. However, as in Hwang et al. (1993), our method can accommodate partial allocation of resources by interpreting the last cost
object as unused capacity.
7
Consistent with our view that the benchmark system has a row
for each unique activity and the associated resource, we map each
Management Science 57(3), pp. 520–541, © 2011 INFORMS
by which we select a cost driver. For example, as a
baseline, we use as the driver the consumption pattern for the largest resource contained in the cost pool
(the big pool method) to allocate all of the costs in
the pool; we detail later the other methods that we
use. Formally, these rules help construct the activity
driver percentages used to allocate costs in an activity pool to products, and thereby generate the matrix
of activity consumption patterns (ACT_CONS_PAT).8
We compute the vector of reported costs (PCR by
multiplying the activity cost vector and the activity
consumption matrix.
3.4. Step 4: Measuring the Error in Reported Costs
Given our focus on the decision role for product costing systems, ideally, we could study the difference
in decision outcomes with the full-information-based
benchmark costs and the costs reported under heuristically constructed noisy systems. However, even
within the context of decision making, costing systems serve many needs such as setting product prices,
improving production processes, and directing attention. These diverse objectives likely are differentially
sensitive to reported costs, meaning that we need
alternate measures of economic loss for the various
decision contexts. Moreover, we expect that a change
in the decision outcome (e.g., set of prices) would
change the total costs (e.g., change product quantities,
and thus change the costs of resources needed), hindering the comparison of alternate heuristics. Thus,
following the literature, rather than model a specific
context, we attempt to capture the applicability to
many decision contexts by considering a variety of
error measures as the dependent variable.
The main error metric we report in tables and plots
follows Babad and Balachandran (1993), Homburg
(2001), and Labro and Vanhoucke
(2007, 2008). This
I
b
R 2
,
metric is the 2-norm, EUCD =
i=1 PCi − PCi
b
where i indexes products, PCi is the benchmark
cost, and PCiR is the reported cost. This measure,
which resembles the Euclidian distance between the
two vectors, is symmetric and, given we keep total
resource cost constant at $1 million, captures the magnitude of the overall error in the costing system in
resource indivisibly to one activity cost pool. In practice, accounting
records might contain resources that support multiple activities. In
this case, for the purpose of the benchmark system, we can view
each portion as a separate resource.
8
We also varied the extent of measurement error in measuring
driver quantities. Low measurement error corresponds to a setting
with a time clocking system for worker and staff time and where
estimates on driver consumption are regularly revisited. A high
value represents a setting where there is no system to keep track
of staff’s time allocation and the system uses outdated estimates.
We do not focus on the effect of measurement error because the
associated findings are intuitive.
Balakrishnan, Hansen, and Labro: Evaluating Heuristics Used When Designing Product Costing Systems
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Management Science 57(3), pp. 520–541, © 2011 INFORMS
dollar terms. Moreover, the square of this metric (i.e.,
the mean squared error) is a measure of the loss
from incorrect pricing decisions in monopolistic and
oligopolistic markets (Vives 1990, Banker and Potter
1993, Alles and Datar 1998, Datar and Gupta 1994,
Hwang et al. 1993).
We also calculate a “materiality” measure, %ACC,
as the percentage of products whose costs are
reported without substantial error (Labro and Vanhoucke 2007, 2008). Following Kaplan and Atkinson
(1998, p. 111), we define immaterial costing errors as
within a 10% symmetric interval around the benchI
b
R
mark cost; %ACC = 1/I
i=1 1 095 × PCi < PCi <
105 × PCib 0 otherwise}. This metric is valid in decision contexts where small errors are not important,
but large errors are costly (Dopuch 1993).
The final metric we consider is the mean percent
I
b
R
b
error, MPE = 1/I
i=1 PCi − PCi /PCi . This choice
follows Christensen and Demski (1997), who considers percent errors per product and mean percent error
as dependent variables; and Gupta (1993), who uses
percent errors at the product level. In some contexts,
management may be more interested in these relative measures, because a $10 cost difference for a $10
product has a greater chance of inducing an incorrect decision than a $10 cost difference for a $1,000
product.
Not surprisingly, all of our error metrics are highly
correlated. However, it is important to note that all of
our error metrics are “closed” because we impose a
tidy allocation. In the context of EUCD, this restriction means that the dimensions are not independent.
In particular, the error for the last product is entirely
specified by the errors of the other I − 1 products.
Despite this limitation, we use this simple concept of
an error metric to avoid the additional specifications
required and complexity involved in calculating the
economic loss from using heuristics. (We discuss this
issue more in the final section.)
We next provide detail on the heuristics we consider in Step 3 of our protocol. As noted earlier, we
focus on two kinds of heuristics: grouping resources
into pools and choosing a driver for the costs in
each pool.
3.5.
Heuristics for Assigning
Resources to Activity Pools
The number of pools formed is a key feature of
observed systems. The desired number of pools is
likely to be affected by the assignment heuristic as
well as the information available about resource consumption patterns. We therefore consider a baseline
experiment in which we fix the number of pools and
focus on the assignment heuristic. Constructing fewer
pools is consistent with the firm using less information when designing the product costing system.
527
Thus, in a baseline experiment, we vary the number
of pools as a design parameter. In a modified experiment, we determine the number of pools endogenously to consider the robustness of the heuristics to
available information.
3.5.1. Baseline Experiment. In this experiment,
we fix the number of pools to form and consider
six heuristics for assigning resources to cost pools.
These heuristics vary in terms of the underlying
rationale and in the information required to implement them. In our baseline (“random”), we randomly
assign resources to activity cost pools. We also view
this assignment as a system that has grown organically over time. This method needs no information
regarding resource costs or consumption patterns.
Next, we consider two size-based methods that
examine the intuitive “Willie Sutton rule” that designers of product costing systems should focus on the
largest resources (Cooper and Kaplan 1998a). We were
unable to find a consistent definition of this rule in the
literature. We thus model two interpretations. Both
of these methods require only information regarding resource costs (available in accounting records)
and do not employ data regarding consumption patterns. First, the “size-random” rule assigns the largest
resources systematically, by size, to activity pools.
To design a system with six pools, we assign the
six largest resources to individual activity pools. We
then randomly assign the remaining resources among
the six pools. This approach reflects the practice of
adding smaller pools like labor supervision to a bigger pool like labor, or machine maintenance to the
pool for machine depreciation. Second, the “sizemisc” method also assigns the largest resources to
individual pools, but differs in its treatment of the
remaining resources. In the above example, we would
form five pools for the five largest resources and
lump the costs of the remaining resources into a residual pool. This approach reflects the use of an aggregate “miscellaneous” cost pool for resources not large
enough to warrant an individual cost driver but that
need to be allocated to products.
The next two methods follow the prescription
to group like resources together. We define “like”
resources by the correlations among consumption patterns. Thus, these methods for grouping resources
into cost pools are information intensive. First, in the
“correlation-random” method, we seed the desired
number of activity pools with a random choice of
resources. We then pick “like” resources to add to
the base resource in an activity pool. “Like” resources
have the greatest positive correlation with the base
resource that seeds the pool. We restrict the number of resources added to a pool so that each activity pool contains approximately the same number of
resources. Second, the “correlation-size” method is
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528
Balakrishnan, Hansen, and Labro: Evaluating Heuristics Used When Designing Product Costing Systems
similar to “correlation-random” except that we seed
the desired number of activity pools with the largest
resources. This method reflects a convex combination of the Willie Sutton rule that focuses on size
and the prescription of using correlations to group
like resources together. This method also follows the
prescriptions to use multiple criteria when grouping
resources into activities (Cokins 2001, Fremgen and
Liao 1981).
Finally, because implementing correlation-based
methods requires data on consumption patterns, we
investigate the performance of a “blended” method
with reduced information needs. We employ a rough
estimate of correlation to group resources into tiers
and use a size-driven method within each tier.
In particular, we group resources into batch- and
volume-based resources. Such grouping of resources
is feasible in practice because these resource groups
are likely to have dissimilar consumption patterns.
We then implement the size-misc assignment within
each tier.
3.5.2. Modified Experiment. In the baseline
experiment, we fix the number of activity cost pools
to isolate the effect of the assignment heuristic on
system accuracy. However, it is reasonable to assert
that information about consumption patterns affects
the number of pools to form. We therefore consider
a modified experiment in which we vary the number
of pools endogenously. Using the “correlation cutoff”
method, we seed the first pool with the largest
resource. We then add to this pool all those resources
whose consumption patterns are correlated (above a
specified cutoff value) with the consumption pattern
for the base resource. We then seed the second pool
with the largest among the remaining resources. We
again consider correlations to decide the resources to
group into the second activity pool. We continue this
process until the number of remaining resources is
less than a specified number of resources, when all
remaining resources are put into a miscellaneous cost
pool. Under this procedure, the number of resources
per pool and the number of pools formed will vary
with the cutoff value and with the correlation in
consumption patterns. Note that a lower cutoff is
consistent with coarser information about consumption patterns. We vary the cutoff correlation value
to determine the effect of reducing the precision of
available information on the number of pools formed
and on system accuracy. We also vary the number
of resources to put into the miscellaneous pool to
determine the effect of aggregation error on these
outcomes.9
9
We would need to model the cognitive and economic costs associated with the number of cost pools to say more about the desired
number of pools with size-based rules. Such an extension is outside
the scope of this study.
Management Science 57(3), pp. 520–541, © 2011 INFORMS
3.6. Heuristics for Calculating Driver Quantities
The other major decision in designing a cost system
is to select cost drivers. Cooper and Kaplan (1988;
1998a, p. 99) describe driver choice as a “central innovation” but also the “most costly aspect of ABC systems” because “reality takes hold” when designers
consider the associated information needs and costs.10
In our context, the choice determines the elements of
the activity consumption pattern, ACT_CONS_PAT,
used to allocate activity costs to products. The choice
is complicated because each resource in a given activity pool would have a distinct consumption pattern,
but we use one pattern to allocate the costs of all
resources in that pool.
The simplest approach in this context is to use the
driver for the largest resource in an activity cost pool
as the driver for all the costs in that pool. For example, a firm can use direct machine hours on the largest
machine as the basis for allocating all costs in the
machining cost pool. This choice ensures that the cost
of the largest resource is allocated without specification error but induces such error when allocating the
costs of the remaining resources in the pool. Whereas
we refer to this as the “big pool” method, Hwang
et al. (1993) refer to it as the “high cost” method.
At the other end, we consider a consumption driver
that is the average of the individual drivers for all
of the resources in the cost pool (“average” method).
This method represents a system in which the time
spent on any machine in a production cell enters the
allocation basis for the costs of that cell. Whereas the
big pool and average methods anchor two ends of a
spectrum, intermediate methods might average only a
subset of the largest resources in a pool. For example,
a firm might use only a combination of labor hours
and machine hours to develop an indexed driver.
Such approaches (which can be viewed as improving
the specification of the cost driver) require more data
to implement than is required by the big pool method
but less than the average method.
Composite drivers are particularly relevant when
the same resource supports multiple activities (equivalently, when multiple resources are pooled). For
concreteness, consider a purchasing department that
processes both domestic and overseas orders. Conceptually (as in a benchmark system), we should have
a separate resource cost and an associated consumption pattern for each activity. However, the accounting system might not record the costs in separate
ledger accounts. Observed systems deal with this
issue by using a composite driver of the activities.
For example, the designer might construct a synthetic
10
Information costs also naturally influence the number of pools to
form. This relation underscores the link between the decisions of
how to form pools and how to pick drivers.
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Management Science 57(3), pp. 520–541, © 2011 INFORMS
driver that defines an overseas order as a multiple
(say, three) of a domestic order. Other applications
include distinguishing between a major and a minor
setup when allocating changeover costs (Cooper and
Kaplan 1998a, p. 98) and weighting loan recalls more
than item returns when allocating the costs in a
library (Ellis-Newman 2003).11 The use of indexed or
composite drivers appears to be widespread. Fremgen
and Liao (1981) report that firms used indexed cost
drivers to allocate about 10% of activity cost pools,
with the proportion being significantly higher in areas
with low cost traceability. They also report that firms
used indexed cost drivers to allocate 44% of selling, general and administrative expense pools, 31%
of research and development pools, and 45% of the
marketing cost pools. In a meta-analysis, Shields et al.
(1991) report a range of 8.9% to 46.3% for the use of
multiple allocation bases in the United States; the rate
in Japan is 18.4%. Finally, Sakurai (1996, pp. 100–101)
discusses the construction and use of both weighted
and unweighted composite cost drivers by Japanese
manufacturers.
4.
Data and Descriptive Statistics
Table 1 provides descriptive statistics concerning our
benchmark cost systems in the baseline experiment.12
We simulate 48 economic environments (comprising
three levels of variance in resource costs and four levels each of the extent of resource sharing and correlation in consumption patterns; 48 = 3 · 4 · 4) and
draw 20 samples for each environment, resulting in
960 benchmark systems. The top section of panel A
shows that as we increase RC_VAR, the ratio of percentage costs in the largest to the smallest resource
cost pool increases monotonically from 3.20 to 11.39.
Furthermore, the percentage cost in the top 20% of
resources increases from 30% to 39%.13
11
In our context, the benchmark system assumes a unique activity
for each resource. Therefore, aggregating resources implies that the
resources in an activity pool support multiple activities. The use
of a composite driver suggests itself. We do not weight drivers
because we do not model the relative intensities of the underlying
activities. In our linear model, weighting drivers by resource cost
recovers the benchmark system.
12
Our main results relate to environments with 50 resources and
50 cost objects. Robustness checks for different combinations yield
identical inferences. Because our interest relates to the ratio of the
number of resources to the number of cost objects, our robustness tests hold the number of cost objects, CO, at 50 and vary
the number of resource cost pools. We do not vary the number of
cost objects because changing CO would systematically affect our
error measures, thereby hindering comparability across simulated
environments.
13
Although some kind of a Pareto rule is likely to apply, we
could not find reliable survey information about the distribution of
resource costs. However, management accountants in a particular
firm should have an intuitive understanding of their own resource
cost distribution.
529
As seen in panel A, as we increase the value of
DENS (the density of the benchmark consumption
matrix), the percentage of zeros in the consumption
matrix decreases from 71% to 6%. The decrease in
the traceability of resources leads to the number of
products sharing any given resource increasing from
14.52 to 46.88 or from 29% to 94% of all products. We
also find more dispersion in consumption of resources
across products as we increase resource sharing. The
average range of consumption (i.e., range in percentage of resource cost consumed by products for a
resource, averaged across resources) decreases from
23% to 5%; that is, the fewer products that consume a resource, the more unequal their relative
consumption.
The third section of panel A shows the impact
of changing COR, the correlation pattern we induce
on the drivers that describe resource usage by products. We find that the average correlation between
the consumption pattern for the largest pool and all
other pools drops from 0.376 to 0.149 as we decrease
the value for COR. In addition, a similar correlation
with batch resources by themselves turns negative.
We would expect such a negative correlation when
the ratio of the number of batches to the number
of units varies across products. Such variance occurs
when, for example, a firm makes large-volume products in a few large batches but uses many small
batches to make low-volume products. In either case,
significant differences in consumption patterns exist
between unit-level activities and batch-level activities
in an ABC hierarchy.
Finally, for several other elements of the cost structure, we set bounds and vary them randomly for
each benchmark system, as shown in panel B. For
instance, we simulate the average percentage of costs
devoted to volume resources randomly to be between
50% and 80%.14 Similarly, we generate the unadjusted consumption pattern for volume resources by
randomly inducing a positive correlation with the
baseline resource. The average correlation of the consumption pattern of the largest volume resource with
other volume resources, weighted by the percentage costs in each resource pool, is reliably positive at 29.36%.15
14
This is in line with survey research (Foster and Gupta 1990) and
case-based observations (Ittner et al. 1997, Goddard and Ooi 1998).
We vary the remaining resources between positive (additional volume resources), zero, and negative (batch resources) correlations.
Our data contain an average of approximately 35% batch costs.
15
The accounting literature provides limited insight about the correlation in the consumption patterns of volume-based resources or
on relative product costs. In our data, the ratio of the costs of the
products with the five highest to the five lowest benchmark costs
has a mean of 4.55 with a minimum of 1.5 and a maximum of
16.27. The average ratio of the costs of the highest- and lowest-cost
products is 14.3.
Balakrishnan, Hansen, and Labro: Evaluating Heuristics Used When Designing Product Costing Systems
530
Table 1
Management Science 57(3), pp. 520–541, © 2011 INFORMS
Descriptive Statistics
Panel A: Benchmark cost systems—Characteristics systematically varied
Average values
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Variation in resource
costs (using parameter RC_VAR)
Global
average
Low dispersion
RC_VAR = 025)
Med dispersion
RC_VAR = 050
High dispersion
RC_VAR = 075)
N = 960
N = 320
N = 320
N = 320
Ratio
678
320
575
1139
Percent
34
30
34
39
Global
average
Little sharing of
resources
DENS = −075)
Medium sharing of
resources
DENS = 0
High sharing of
resources
DENS = 075
Very high sharing
of resources
DENS = 150
N = 960
N = 240
N = 240
N = 240
N = 240
3604
3197
7095
1452
4611
2694
2087
3956
622
4688
1143
2322
1108
661
479
Global
average
Similar
consumption
patterns
COR = 033
Intermediate
consumption
patterns
COR = 00
Intermediate
consumption
patterns
COR = −033
Dissimilar
consumption
patterns
COR = −066
N = 960
N = 240
N = 240
N = 240
N = 240
Number
0264
0376
0298
0232
0149
Number
−0029
0300
0000
−0061
−0125
Units
Percentage of cost in largest pool/
percentage of cost in smallest pool
Percentage of costs in top 10 resources
Density of consumption matrix
(using parameter DENS)
Percentage of zero entries in consumption matrix
Percent
Average number of products
Number
consuming a resource
(max. = 50)
Average range in consumption of a resource
Percent
across products (given positive use)
Importance of resources devoted to
batch activities (using parameter COR)
Correlation between largest pool
and all resources
Correlation between largest pool
and batch resources
Panel B: Benchmark cost systems—Characteristics not systematically varied
Characteristic
Percentage of resources in pools devoted to batch activities
Correlation between largest pool and volume resources
Unit
Average
Median
Interquartile range
Percent
Number
3507
2936
3487
2960
1414
1560
Panel C: Error metrics—Univariate statistics (N = 17 280)
EUCD
%ACC
MPE
Mean
Min
Quartile 1
Quartile 2
Quartile 3
Max
28,448
2584
168
2,514
0
147
16,237
14
966
24,882
22
1492
36,919
34
2182
124,155
100
6259
Panel D: Correlation among error metrics (N = 17 280)
EUCD
%ACC
MPE
EUCD
%ACC
MPE
100
−0745
1000
0955
−0769
1000
Notes. Size-random method used for assigning resources to activity pools: largest resources were assigned to a number of activity pools chosen by the system
designer (ACP ). The costs of the remaining resources are assigned randomly to the activity pools. Average method for selecting driver used to allocate costs
from activity pools to cost objects: driver percentages were calculated as the average of the driver percentages for all resources in the activity cost pool.
Inferences in panels C and D were unaltered with other methods for assigning resources to activity pools or selection of driver pattern. The average method
for selecting driver was used to allocate costs from activity pools to cost objects. Consumption percentages are calculated as the average of the consumption
percentages for every resource in the activity pool. Inferences are unaltered with other choices for drivers. RC_VAR , dispersion in the size of resource cost
pools. Higher values correspond to greater dispersion. COR , magnitude of the (average) correlation in resource consumption patterns between the baseline
volume resource and batch resources. DENS , measure of the extent of resource sharing by products. Greater values correspond to a greater degree of resource
sharing and lower traceability of resources to cost objects. EUCD , metric of error between benchmark and reported costs, calculated as the 2-norm between
the vectors of benchmark and reported costs. %ACC , percent of products whose reported cost is within 10% of their benchmark costs. MPE , mean percentage
error, which is the average of the relative error in reported costs.
Balakrishnan, Hansen, and Labro: Evaluating Heuristics Used When Designing Product Costing Systems
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Management Science 57(3), pp. 520–541, © 2011 INFORMS
We next turn to the noisy systems associated
with the benchmark systems. For clarity, we present
descriptive data for the baseline experiment, for one
method for assigning resources to activity pools (sizerandom), and for one method for choosing drivers
(average). (As we see later, the value of the error
metric changes considerably based on the methods
chosen.) We aggregate data over three levels for measurement error (10%, 30%, and 50% error in measuring driver percentages)16 and over six values for the
number of activity pools (1, 2, 4, 6, 8, and 10).17 Thus,
we have 18 associated observations for each of the 960
benchmark systems, giving us 17,280 observations.
In panel C, we report univariate statistics concerning the error metrics we consider. The percentage accurate metric, %ACC, shows that, on average,
25.84% of products have reported costs that are within
10% of their benchmark costs; the average mean percentage error (MPE) is 16.8%. However, there is wide
variation across different environments and noisy systems. The percent of products with accurate costs
(%ACC) ranges from 0 to 100%, and the mean percentage error (MPE) goes from 1.47% to 62.59%; thus,
system design exerts considerable influence on the
error relative to benchmark costs. The data also show
that for all error metrics the mean value exceeds
the median; that is, all of the error distributions are
skewed.
Data reported in panel D show that the metrics are
highly correlated (note that the percentage of products with accurate costs is inversely related to error).
This correlation also is robust to the choice of methods and untabulated checks indicate that our results
are robust to changing the dependent variable. Thus,
in what follows we only report results with EUCD as
dependent variable.
5.
Results: Performance of Heuristics
for Assignment of Resources to
Cost Pools
Result P1. Correlation-based methods for assigning resources to pools (i.e., pooling “like” resources)
lead to lower overall error relative to size-based
assignment rules when the distribution of resources
costs is moderately skewed (i.e., when top 20% of
resources trigger less than 50% of cost). Size-based
531
assignment rules only start to dominate correlationbased assignments in an economically significant way
when the top 20% of resources account for more than
∼75% of total cost.
Figure 1 reports on the baseline experiment in
which we fix the number of cost pools. Panel A
indicates that when resource costs are moderately
skewed, correlation-based methods dominate other
approaches in terms of reducing the error in reported
costs (Result P1). More surprising, the baseline random allocation is indistinguishable from one sizebased method (size-random) and beats the other
size-based method (size-misc) handily. Furthermore,
within correlation-based methods, a size-based seeding shows limited improvement over a random seeding. Intuitively, a correlation-based method leads
to most costs being allocated with low specification error because this method pools resources with
similar resource consumption patterns. Size-based
methods suffer either because they pool smaller
costs with larger resources (size-random) or group
a large amount of costs into a miscellaneous pool
(size-misc).18
Panel B reports results obtained when we progressively increase the concentration of total costs into the
top 20% of resources to find the point at which the
system designer might prefer a size-based assignment
rule (Result P1).19 We find that the size-misc rule is
preferred over random assignment when the top 20%
of resources account for 50% or more of the costs.
The method also is preferred over the best correlationbased assignment when the top 20% of resources
account for more than 65% of total costs. However,
the difference is not very large until the top 20% are
70–75% of total costs. Overall, as expected, size-based
rules do well when resource costs are focused on a
handful of resources; our contribution in this regard
is providing insight into the cross-over percentages.
Note that unlike the correlation-based rules, sizebased rules require no information about how products consume resources. Furthermore, driver selection
is much simpler when each of the largest resources
forms its own pool (as in the size-misc method). Thus,
18
16
Cardinaels and Labro (2008) find in a lab experiment that people
overestimate the time they spend on all activities that constitute
their job description (a form of measurement error) by 37%, on
average.
Our results stand in a system in which we measured correctly
the driver pattern for the largest cost pools, which could be an
alternative way to interpret the Willie Sutton rule. We also note
that the number of resources per activity pool is similar between
the size-random method and the correlation-random method. Thus,
the difference is not driven by this possible source of variation. We
thank Romana Autrey for suggesting this test.
17
19
The range for the number of activity pools is consistent with
the Drury and Tayles (2005) survey of 187 firms about their management accounting systems. Their Table 3 shows that the median
number of cost pools was between 6 and 10. The minimum was
one, and 85% of the organizations had 50 or fewer cost pools.
For this comparison, we calculated driver percentages using the
methods that worked best with a given assignment rule to present
each method advantageously. Specifically, we used the average
method for correlation-based assignments and the big pool method
for size-based assignments.
Balakrishnan, Hansen, and Labro: Evaluating Heuristics Used When Designing Product Costing Systems
532
Management Science 57(3), pp. 520–541, © 2011 INFORMS
Figure 1
Effect of the Method for Assigning Resources to Activity Pools
Panel B: Comparison of assignment methods with
skewed resource costs
40,000
80,000
35,000
70,000
Error in reported costs (EUCD)
Error in reported costs (EUCD)
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Panel A: Comparison of assignment methods:
Baseline experiment
30,000
25,000
20,000
15,000
10,000
1
2
4
6
8
60,000
50,000
40,000
30,000
20,000
10,000
10
Number of activity cost pools
0
40–45 45–50 50–55 55–60 60–65 65–70 70–75 75–80
Random
Size-random
Correl-random
Size-misc
Percentage of cost in top 20% of resources (%)
Correl-size
Correl (avg)
Random (BP)
Size-random (BP)
Size-misc (BP)
Notes. Panel A uses the average method for selecting the driver used for allocating costs from activity pools to cost objects whereby consumption percentages
are calculated as the average of the consumption percentage for all resources in the activity pool. Inferences are unaltered with other choices for calculating
consumption percentages. Random, resources are assigned randomly to activity pools. Size-random, largest ACP resources assigned to number of activity
pools chosen by the system designer (i.e., ACP ). The costs of remaining resources are assigned randomly to the activity pools. Size-misc, largest ACP-1
resources assigned to number of activity pools chosen by the system designer, with one pool left open. The costs of remaining resources are assigned to the
last open pool (miscellaneous costs). Correlation-size, largest ACP resources assigned to the number of activity pools chosen by the system designer (ACP ).
For the first activity pool, select those resources with the highest correlation with the resource in the pool. Assign a total of INT(RCP/ACP ) resources to this
pool. Repeat for the second activity pool and so on. Correlation-random, pick ACP resources randomly and allocate one each to the number of activity pools
chosen by the system designer (ACP ). For the first activity pool, select those resources with the highest correlation with the resource in the pool. Assign a
total of INT(RCP/ACP ) resources to this pool. Repeat for the second activity pool and so on. EUCD , metric of error between benchmark and reported costs,
calculated as the 2-norm between the vectors of benchmark and reported costs. In panel B, ACP is fixed at 10. We used the method indicated in parentheses
as the best method for the associated assignment rule.
one way to interpret our results is that simple systems might suffice when resource costs are concentrated and that ABC like systems are likely to have
the greatest benefit when resource costs are diffused
across categories.
The remainder of this section examines how reducing the information available to implement an assignment heuristic affects its efficacy. We first consider
the effects of blending size- and correlation-based
heuristics. We next investigate reducing the precision
of information about correlations. Third, recognizing
that system designers might want to limit the number
of cost pools, we study alternate ways to deal with
the costs of small resources. Finally, we further investigate the trade-offs relating to how many cost pools
to form.
5.1. Blended Method
Recall that the blended method uses gross estimates
of correlations to group costs into tiers and uses
size-based methods inside each tier. In this way,
it combines aspects of size- and correlation-based
assignments even as it reduces information needs.
In particular, we need relatively coarse information
about consumption patterns to implement this heuristic. Figure 2 presents the results.
Result P2. The blended method performs well in
all production environments. In particular, an ABClike system that employs rough estimates of correlations to group resources into tiers and then uses a
size-based rule within each tier results in error magnitudes similar to that obtained with the more informationally demanding correlation-based rules.
We find that the performance of the blended
method is often superior to the performance of the
correlation-based allocation methods even though it
uses less information.20 Untabulated results show that
the gain from the blended method increases as the
distinction in the consumption patterns of volumeand batch-level resources increases (as captured in the
value of the parameter COR).21 Even using a gross
20
The gain tapers off as we increase the number of activity pools.
This finding obtains because the separation of resources into volume and batch resources occurs naturally as the number of activity
pools approaches the number of resources to be assigned.
21
A large negative value for COR is consistent with batch resources
being consumed in patterns that differ from the patterns for
volume-based resources.
Balakrishnan, Hansen, and Labro: Evaluating Heuristics Used When Designing Product Costing Systems
Management Science 57(3), pp. 520–541, © 2011 INFORMS
Figure 2
Result P3. Correlation-based rules can be implemented with relatively coarse information. The
increase in error is small even if we decrease the cutoff correlation used to define “like” resources to 0.40.
Performance of the Blended Method for Assigning
Resources to Activity Pools
40,000
Error in reported costs (EUCD)
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35,000
30,000
25,000
20,000
15,000
10,000
Blended method
Size-random
5,000
Correlation-random
1
2
4
6
8
10
Number of activity pools
Notes. Individual series relate to various methods for assigning resources
to activity pools. Blended, resources are first separated as per whether they
are batch or volume resources. The size-random method is used for each
group, with each category having half the number of available cost pools.
Size-random, largest ACP resources assigned to number of activity pools
chosen by the system designer (i.e., ACP ). The costs of remaining resources
are assigned randomly to the activity pools. Correlation-random, pick ACP
resources randomly and allocate one each to the number of activity pools
chosen by the system designer (ACP ). For the first activity pool, select those
resources with the highest correlation with the resource in the pool. Assign
a total of INT(RCP/ACP ) resources to this pool. Repeat for the second activity pool and so on. EUCD , metric of error between benchmark and reported
costs, calculated as the 2-norm between the vectors of benchmark and
reported costs. The average method was used for selecting the driver used
for allocating costs from activity pools to cost objects. Under this method,
consumption percentages are calculated as the average of the consumption
percentage for all resources in the activity pool. Inferences are unaltered with
other choices for calculating consumption percentages.
guess about correlation structure is useful in reducing error when assigning resources to activities, particularly when we have an ex ante reason to suspect
dissimilar consumption patterns. To our knowledge,
these are the first research findings that support the
ABC prescription of classifying resources as per the
activity hierarchy and constructing separate pools for
each tier of resources. The results also support the use
of multiple criteria for assigning resources to pools
and suggest that size might be a good candidate for
a secondary criterion for grouping resources.
5.2.
533
Modified Experiment: Reducing the Precision
of Available Information
With correlation-based rules, the precision of available
information about consumption patterns might affect
the desired number of pools. We therefore consider a
“correlation cutoff” method in which we determine
the number of pools endogenously. We also view this
experiment as providing guidance on the robustness
of correlation-based assignment heuristics to available
information.
In Table 2, consider the row that reports data
for the setting in which we group as many as 15
resources (30% of all resources) into the miscellaneous cost pool. Even a value of 0.4 for the cutoff
correlation leads to system accuracy that is comparable to the information-intensive method (correlation
with size-based seeding) we employed in the baseline
experiment (see Figure 1). As we increase the cutoff
correlation value we find a steady increase in system
accuracy as well as a steeper increase in the number
of cost pools formed. The trade-off is between the perceived benefits of increased accuracy versus the costs
of adding more pools. Correlation-based methods that
employ crude measures of the underlying correlation
might be a practical way for grouping resources into
activity pools.
5.3. Dealing with the Low-Cost Resources
Costs connected with creating and maintaining a large
number of cost pools as well as the expectation of
diminishing returns to system detail suggest that it
might be worthwhile to deal with low-cost resources
in an ad hoc fashion. We consider two alternatives:
pool all such costs into a miscellaneous cost pool
or distribute the costs for these low-cost resources
among the pools for the high-cost resources. We note
that pooling small resources into one pool requires
less information about resource costs relative to distributing these costs over all cost pools.
Result P4. Firms can group a large portion of their
costs into a “miscellaneous” pool without significantly degrading system accuracy.
Panel A of Figure 1 (related to the baseline experiment) shows little difference across alternate correlation-based assignments, the preferred choice. However, data in panel B show that when size-based
assignments are preferred, we obtain lower error
when we group “small” resources into a single miscellaneous cost pool than when we distribute them
over the larger pools. The size-misc heuristic outperforms the size-random heuristic over the entire range
in which the firm prefers a size-based assignment
rule. The data in Table 2 (relating to the modified
experiment) provide another indication of this finding. Consider the column for the cutoff correlation
of 0.4. Here, our measure of the error in reported
costs (EUCD) has a value of 17,018 when we allow
only five of the 50 resources to be in the miscellaneous cost pool. At this level, the average system has
19 activity pools. When 50% of the available resources
(25 of 50 resources, containing as much as 31% of total
Balakrishnan, Hansen, and Labro: Evaluating Heuristics Used When Designing Product Costing Systems
534
Management Science 57(3), pp. 520–541, © 2011 INFORMS
Table 2
Endogenously Determined Number of Activity Pools
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Number of resources
in miscellaneous cost pool
(% of resources)
Average of cost
in the miscellaneous
cost pool (%)
5 (10)
524
10 (20)
953
15 (30)
1581
20 (40)
2304
25 (50)
3108
Cutoff correlation value for grouping
resources into the same activity pool
0.2
0.4
0.6
22,823
713
2 16
22,742
547
1 12
22,842
439
1 10
23,216
358
1 8
17,018
1917
3 25
17,408
1579
3 25
17,761
1225
2 23
18,176
933
2 19
12,173
2911
14 30 12,263
2693
7 30 12,620
2296
7 30 13,647
1833
5 29
Min no.
ACP
reached
19,610
635
2 16
15,041
1389
4 24
0.8
Max no.
ACP
reached
10,508
2565
16 30 12,089
2068
9 26
Notes. Reported are the average value for EUCD, [average number of activity cost pools], and (range for the number
of activity pools formed). Values in italics indicate that the value is at the exogenously specified maximum for the
number of activity pools (30). The grey shaded areas indicate experiments where the number of endogenously
created ACP hits the maximum number of ACP possible (the number of RCP minus the number of resources in
miscellaneous cost pool) or the number of pools is very small (e.g., 2). The first pool is seeded with the largest
resource. Additional resources that satisfy the correlation cutoff (relative to the first resource in the pool) are
added to pool. The second pool is seeded with largest among remaining resources. Additional resources satisfying
correlation cutoff are added. Continue process until the number of remaining resources is less than specified (all
remaining resources put into miscellaneous cost pool). We also grouped all remaining resources into the last pool
if the number of activity pools became 30 (the maximum number of possible activity pools). We used the average
method for calculating driver percentages for an activity cost pool.
costs) are grouped as miscellaneous costs (last row
of Table 2), the error metric only registers a marginal
increase to 19,610, whereas the number of activity
pools drops to 6. Data reported in the other columns
show a similar pattern.
5.4. Determining the Number of Pools
Result P5. Regardless of the method for assigning
resources to pools, although increasing the number
of cost pools leads to statistical gains in accuracy,
the economic gains are small after we reach ∼12 cost
pools. In practice, a relatively small number of pools
seem adequate.
Panel A of Figure 1 suggests that the number
of activity pools matters greatly. The average error
(EUCD value) reduces from 37,657 for one pool to
23,675 with 10 pools when we use the size-random
method; the decline is from 37,929 to 16,603 with the
correlation-random method. The error is decreasing
and concave in the number of pools.22 Untabulated
data show that we continue to obtain statistically
significant (but economically small) gains of adding
activity cost pools even when the ratio of the number
of activity pools to the number of resources is as high
as 80% (40 pools for 50 resources). Untabulated results
confirm a similar inference when resource cost dispersion is high (size-based rules dominate) and when we
increase the number of resources we consider.
Data in Table 2 provide additional support. For the
modified experiment and for a given correlation cutoff, when five additional resources are taken out of
the miscellaneous pool, the optimal number of pools
formed increases at a lower rate. We conclude that a
firm might be able to devise a “good enough” system
with a relatively small number of activity pools. Thus,
we provide the first research findings in support of
intuitive prescriptions by Turney (1991, p. 51) as well
as by Cooper and Kaplan (1998a, p. 98) that a system
in which the ratio of the number of pools to the number of resources is small might be enough in terms of
delivering desired system accuracy cost effectively.
22
For additional insight, consider the correlation method with sizebased seeding and the average method for selecting a driver. In this
case, analysis of the percentage error shows that with 8–10 pools,
slightly more than 50% of products have reported costs that lie
within 10% of the true cost. Furthermore, there are few products
with more than 50% error in reported costs. This accuracy rate
decreases rapidly as the number of pools decreases. We also find
instances of extremely large (both positive and negative) errors.
Data from other methods lead to qualitatively similar conclusions.
Balakrishnan, Hansen, and Labro: Evaluating Heuristics Used When Designing Product Costing Systems
535
Management Science 57(3), pp. 520–541, © 2011 INFORMS
We parameterize the heuristic for selecting cost
drivers by the number of resources within an activity pool whose consumption patterns we average to
obtain the allocation rate. At one end, the big pool
method considers only the pattern for the largest
resource in the pool. At the other extreme, the average method equally weights all the resources in an
activity pool. Intermediate indexing methods consider
the two, three, four, or five largest resources in a pool
to calculate the allocation base at a cost pool. Such
indexing is consistent with a system designer seeking
more information to refine cost drivers and reducing
specification error.
Figure 3
Effect of Method for Selecting Cost Driver (Indexing)
Panel A: Use size-random method to assign resources
to activity pools
80,000
70,000
Error in reported costs (EUCD)
Results: Performance of Heuristics
for Selecting Cost Drivers
60,000
50,000
40,000
30,000
20,000
10,000
0
Result D1. Using an indexed (composite) driver
leads to lower error than obtained from using a driver
that considers only the consumption pattern for the
largest resource (the “big pool” method).
As Figure 3 shows, there is a significant gain to
using the average method relative to the big pool
method, with the change eliminating about 50% of the
error resulting from use of the big pool method. Thus,
not surprisingly, an improvement in specification
(by considering the consumption patterns for several
resources) has a large effect on system accuracy.23
Although effective, the average method is information
intensive because it requires data on the consumption pattern for all of a firm’s resources. Thus, we
consider intermediate composite rates that consider
fewer resources. Consider the data for NUM = 3 (i.e.,
we consider the top three resources in a pool to calculate driver percentages) in panel A of Table 3. Relative to the big pool method, the gain is only 5.71%
when we have a one-pool system. However, the gain
rapidly increases and reaches 52% when we consider
a 10-pool system, because the number of resources per
pool declines as we increase the number of activity
pools, whereas the number of resources averaged is
the same. Nevertheless, we find a gain of 30.7% even
with six activity pools, meaning that each pool has
8.33 resources, on average.
Result D2. With 8–12 cost pools, using an indexed
(composite) driver that considers the consumption
patterns of the largest four or five resources in a
cost pool could lead to lower error than obtained
from using a driver that considers only the consumption pattern for all resources (the “average method”
method) when using size-based assignment methods.
23
This set of results focuses on the case of moderately skewed
resource costs. Driver selection is a straight forward issue when
costs are concentrated in a few resources and each large resource
forms its own pool.
1
2
4
6
8
10
Number of activity pools
Panel B: Use correlation-random to assign resources
to activity pools
80,000
70,000
Error in reported costs (EUCD)
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6.
Big pool
Num =5
Num= 2
Average
Num= 4
60,000
50,000
40,000
30,000
20,000
10,000
0
1
2
4
6
8
10
Number of activity pools
Notes. Individual series relate to various methods for calculating driver percentages used to allocate costs from activity pools to cost objects. Data pertain to 50 resources. BIG POOL, the allocation percentages are those of the
largest resource in the activity cost pool. NUM , calculated driver percentages
as the average of the largest NUM resources in the activity cost pool. AVG,
calculated driver percentages as the average of the driver percentages for all
resources in the activity cost pool. EUCD , metric of error between benchmark and reported costs, calculated as the 2-norm between the vectors of
benchmark and reported costs.
The data in panel A also show that a system
designer might be better off with an index of a limited
number of resources in the pool relative to a simple
averaging of all resources when selecting an allocation
base. In particular, a driver that considers only four or
five resources beats the average method (in terms of
errors in reported costs) when the number of activity
pools is at a medium level (8–10 pools). Intuitively,
with 7 to 10 resources pooled into an activity pool, the
average method starts to weigh the consumption pattern of the smaller resources in the pool too heavily,
moving away from the weighted average that is the
Balakrishnan, Hansen, and Labro: Evaluating Heuristics Used When Designing Product Costing Systems
536
Management Science 57(3), pp. 520–541, © 2011 INFORMS
Table 3
Gain from Using an Indexed Cost Driver
Percentage of gain relative to error from using the big pool method for selecting driver pattern
ACP
NUM = 2 (%)
1
2
4
6
8
10
628
161
1023
1685
2246
3081
NUM = 3 (%)
NUM = 4 (%)
NUM = 5 (%)
Average of all resources
in activity pool (AVG) (%)
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Panel A: Resources assigned to activity pools using the size-random method
1
2
4
6
8
10
571
521
1884
3069
4209
5282
791
1030
2814
4446
5820
6385
853
1386
3623
5608
6472
6326
4799
5138
5596
5709
5599
5549
Panel B: Resources assigned to activity pools using correlation among resource consumption patterns (random seeding)
634
578
782
1003
4820
1440
2408
3206
3745
6568
2420
3725
4630
5331
6724
2949
4451
5384
6008
6612
3420
5034
5919
6468
6633
3776
5417
6207
6520
6545
Notes. Data pertain to 50 resources. BIG POOL, the allocation percentages are those of the largest resource in the activity cost pool.
NUM , calculated driver percentages as the average of the largest NUM resources in the activity cost pool. AVG, calculated driver
percentages as the average of the driver percentages for all resources in the activity cost pool.
benchmark system’s consumption pattern given our
linear setup.
As shown in Table 3, panel B, we find that our
general conclusion holds if we use a correlationbased method to assign resources to activity pools.
The potential gains from averaging are larger (about
65% relative to 55% for the size-random method)
because the assignment method reduces the probability that we will average dissimilar consumption
patterns. However, although indexing continues to
yield significant gains, the performance never beats
that with the average method. Overall, we conclude
that refining drivers has the potential to significantly
improve system accuracy, particularly if the current system uses correlation-based methods to assign
resources to pools.
7.
Results: Fit with Production
Environment
Our analyses thus far can be construed as examining the efficacy of alternative heuristics for an average production environment. In particular, although
we examined how variation in the dispersion of
resource costs affects the ranking of the heuristics
(with resource cost variation increasing error in the
system and favoring size-based rules), we did not
consider the effects of variations in other dimensions
of the production environment. However, the precision of available information about these dimensions
obviously affects the choice of heuristics for assigning
resources and for selecting cost drivers. In this section, we provide some insight into the cost structure
factors that affect the performance of different heuristics because in the long run, it might be possible for
a firm to partially manage features of its production
environment (e.g., organizing for production in work
cells potentially increases resource traceability relative
to a single assembly line).
7.1. Heuristics for Pooling Resources
Table 4 provides insight into how characteristics of
the production environment (with moderate skewness in resource costs) affect the error in reported
costs in the baseline experiment for two assignment
methods: size-random and correlation-random. Not
surprisingly, the extent of correlations in consumption patterns matters a great deal in determining
the absolute and relative performance of the assignment rules. At an absolute level, the accuracy of any
assignment method worsens as consumption patterns
become increasingly dissimilar (COR moves from 0.33
to −0.66). The relative decline with the correlationbased method is only 20%, whereas the performance
of the size-based assignment method worsens considerably by about 55%.
Result P6. It becomes increasingly important to
consider correlation-based methods for pooling
resources when the system designer has grounds
to believe that resource consumption patterns vary
considerably.
Intuitively, we expect that a greater degree of
resource sharing by products would make it harder
for an allocation to capture true resource consumption. However, we find that a greater degree of
Balakrishnan, Hansen, and Labro: Evaluating Heuristics Used When Designing Product Costing Systems
537
Management Science 57(3), pp. 520–541, © 2011 INFORMS
Table 4
Effect of Environmental Parameters on Assignment Heuristics
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Panel A: ANOVA of percent gain in EUCD of using the correlation-random versus
size-random assignment
Source of variation
d.f.
F
p>F
Number of activity pools (ACP)
Measurement error (MSMT_ERR)
Variance in resource cost (RC_VAR)
Extent of resource sharing (DENS)
Correlation between batch and volume driven
resources (COR)
Residual
Adjusted R2 (%)
5
3
2
3
3
19381
47026
1235
1149
18302
<0.0001
<0.0001
<0.0001
<0.0001
<0.0001
<0.0001
74.80
Panel B: Effect of environmental parameters on the reduction in the error in reported
costs (correlation-random versus size-random assignment)
Variance in resource cost
Value of construct
RC _VAR = 025
RC _VAR = 05
RC _VAR = 075
EUCD (size-rand)
EUCD (corr-rand)
Percentage gain (%)
27,381
22,044
19.49
28 860
22 275
22.82
29 101
23 616
18.85
Correlation in consumption pattern between volume and batch resources
Value of construct
COR = −066
COR = −033
COR = 0
COR = 033
EUCD (size-rand)
EUCD (corr-rand)
Percentage gain (%)
35,162
25,050
28.76
29 837
22 701
23.92
26 201
22 004
16.02
22 591
20 824
7.82
Extent of resource sharing by products
Value of construct
DENS = −075
DENS = 00
DENS = 075
DENS = 150
EUCD (size-rand)
EUCD (corr-rand)
Percentage gain (%)
41,610
32,014
23.06
29 549
23 176
21.56
23 029
18 767
18.51
19 602
16 622
15.20
Notes. Average method for selecting driver was used to allocate costs from activity pools to
cost objects. RC_VAR , variance in the size of resource cost pools. COR , magnitude of the (average) correlation in resource consumption patterns between the baseline volume resource and
batch resources. DENS , measure of the extent of resource sharing by products. Greater values
correspond to a greater degree of resource sharing and lower traceability of resources to cost
objects. EUCD , metric of error between benchmark and reported costs, calculated as the 2-norm
between the vectors of benchmark and reported costs. d.f., Degrees of freedom.
resource sharing reduces error in reported costs. We
observe this effect regardless of the method used to
assign resources to pools. One explanation is that
when we pool resources with a sparse matrix, we
increase the probability that the costs of an unrelated resource are allocated to a product. This error
reduces as resource sharing increases and seems to
offset the greater error in specification.24 A practical
implication is that a job shop with little sharing of
resources across products might need a more sophisticated system (e.g., more pools) to accomplish the
24
This comparison rests crucially on the fact that we fix the number of pools. Firms with high traceability might also find it costefficient to create more cost pools than firms whose products share
resources, thereby leading to systems with lower overall error.
same level of accuracy as a process shop where all
products make use of the same set of resources (even
if the pattern of consumption varies across products).
However, the relative effect of resource sharing on the
difference between the effectiveness of the correlationbased method and the size-based method is not large.
The change in the gain from using the correlationbased method over the size-random method is small
(the percent gain decreases from 23% to 15%) over the
range we consider.
Result P7. Holding the number of pools constant,
increasing the extent of resource sharing reduces the
overall error in the system. However, this environmental factor does not significantly favor one method
for grouping resources into cost pools over another.
Balakrishnan, Hansen, and Labro: Evaluating Heuristics Used When Designing Product Costing Systems
538
Management Science 57(3), pp. 520–541, © 2011 INFORMS
Table 5
Determining the Number of Activity Pools Endogenously: Interaction with Environmental Parameters
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Variance in resource cost
Value of construct
RC _VAR = 025
RC _VAR = 05
RC _VAR = 075
EUCD
Average no. of ACP
17,088
1223
17,557
1231
18,636
1221
Correlation in consumption pattern between volume and batch resources
Value of construct
COR = −066
COR = −033
COR = 0
COR = 033
EUCD
Average no. of ACP
18,171
775
17,303
1462
16,999
1569
18,570
1095
Extent of resource sharing by products
Value of construct
DENS = −075
DENS = 0
DENS = 075
DENS = 150
EUCD
Average no. of ACP
21,841
1310
18,294
1254
16,069
1174
14,838
1163
Notes. The first pool is seeded with the largest resource. Additional resources that satisfy the correlation cutoff (relative to the first resource in the pool) are added to the pool. The second pool is seeded with largest among remaining resources. Additional resources satisfying correlation cutoff are added. Continue the process until the number of
remaining resources is less than the specified number (all remaining resources are put into miscellaneous cost pool).
We also grouped all remaining resources into the last pool if the number of activity pools became 30 (the maximum
number of possible activity pools). We used the average method for calculating driver percentages for an activity cost
pool. Data pertain to a setting with a cutoff correlation of 0.4 and with as many as 15 resources in the miscellaneous
cost pool. RC_VAR , dispersion in the size of resource cost pools. Higher values correspond to greater dispersion.
COR , magnitude of the (average) correlation in resource consumption patterns between the baseline volume resource
and batch resources. DENS, measure of the extent of resource sharing by products. Greater values correspond to a
greater degree of resource sharing and lower traceability of resources to cost objects. EUCD , metric of error between
benchmark and reported costs, calculated as the 2-norm between the vectors of benchmark and reported costs.
We next consider the effect of environmental
parameters when we let the number of cost pools be
determined endogenously in Table 5. Here, recall that
we seed each new pool with the largest remaining
resource and added additional resources as dictated
by a correlation cutoff. Results are generally consistent with the findings reported for the baseline experiment. Consistent with Result P6, we find that the correlation pattern between batch and volume resources
matters greatly. The correlation cutoff method performs well when these two groups of resources have
distinct resource consumption patterns. Intuitively,
with dissimilar consumption patterns, batch and volume resources form separate activity pools, each of
which is allocated well to products. However, a movement toward zero in the correlation in consumption patterns reduces the ability of the heuristic to
separate out batch and volume resources, degrading performance and generating systems with many
cost pools.25
Finally, consistent with Result P7, we find a monotonic decline in error in reported costs as the extent
of sharing of resources by products increases. This
25
Not surprisingly, the method also does well when all resources
are highly correlated, as might happen when all products have similar batch sizes.
pattern obtains even though we find an accompanying reduction in the number of activity pools as the
density of consumption matrix increases. Overall, our
findings indicate that, next to resource cost dispersion, the density of consumption matrix is perhaps
the most important feature of the production environment to consider when making choices about parameters of the cost system.
7.2. Heuristics for Selecting Cost Drivers
Table 6 reports data that examine the influence of
environmental parameters on the performance of
heuristics for selecting cost drivers. For parsimony, we
focus on the gain from one case of indexing (NUM = 3
versus the big pool method) in different production
environments. The descriptive data in panel A and
the results from an analysis of variance (ANOVA)
in panel B both indicate that the gain is general in
nature. We continue to average about a 30% gain
from indexing, relative to the big pool method, across
a wide range of environmental parameters. We note
that the less resource sharing there is in the production environment (low density of the consumption matrix), the higher the gain is from indexing.
Of course, consistent with the data in Table 4, the
ANOVA in panel B indicates a significant effect due to
Balakrishnan, Hansen, and Labro: Evaluating Heuristics Used When Designing Product Costing Systems
539
Management Science 57(3), pp. 520–541, © 2011 INFORMS
Table 6
Interaction Between the Method for Choosing the Driver and Environmental Parameters
Panel A: Effect of environmental parameters and other system design choices on the reduction
in the error in reported costs (big pool versus using index of top three resources)
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Variance in resource cost
Value of construct
RC _VAR = 025
RC _VAR = 05
RC _VAR = 075
Difference in EUCD
Percentage gain (%)
21,084
3353
20,112
3365
19,408
3305
Correlation in consumption pattern between volume and batch resources
Value of construct
COR = −066
COR = −033
COR = 0
COR = 033
Difference in EUCD
Percentage gain (%)
22,860
3532
17,719
3097
18,200
3127
22,027
3577
Extent of resource sharing by products
Value of construct
DENS = −075
DENS = 0
DENS = 075
DENS = 150
Difference in EUCD
Percentage gain (%)
36,332
3393
22,755
3601
12,344
3071
9,376
2988
Panel B: ANOVA of percentage difference in EUCD (EUCD with the
big pool method minus EUCD with index of largest three resources)
Source of variation
d.f.
F
p>F
Number of activity pools (ACP )
Measurement error (MSMT_ERR )
Variance in resource cost (RC_VAR )
Extent of resource sharing (DENS )
Correlation between batch and
volume driven resources (COR )
Residual
Adjusted R2 (%)
5
3
2
3
3
86739
20529
022
2119
2552
<0.0001
<0.0001
0.8050
<0.0001
<0.0001
8521
<0.0001
Notes. Correlation with random initial seeding was used for assigning resources to activity cost pools. RC_VAR , dispersion in the size of resource cost pools. Higher values correspond to greater dispersion. COR , magnitude of the
(average) correlation in resource consumption patterns between the baseline volume resource and batch resources.
DENS, measure of the extent of resource sharing by products. Greater values correspond to a greater degree of resource
sharing and lower traceability of resources to cost objects. EUCD , metric of error between benchmark and reported
costs, calculated as the 2-norm between the vectors of benchmark and reported costs. d.f., Degrees of freedom.
the number of activity pools (mechanically, the number of resources per pool declines, leading to greater
accuracy for indexing). This result suggests that such
indexing or use of composite drivers for the same
activity pool may be particularly important in job
shop environments. Overall, our findings indicate that
although it is useful to consider the consumption patterns of all resources in an activity pool, it might be
economically enough to calculate drivers using only
the largest few resources in a pool. This finding can
be restated as follows:
Result D3. Even marginal improvements in specification have the potential to reduce error considerably in a wide range of environments.
8.
Discussion
Our paper uses simulation data to rank heuristics for
grouping resources into cost pools and for generating
cost drivers for the resulting cost pools. To our knowledge, this paper is the first to compare the alternate
heuristics employed by system designers. Although it
offers important insights into the design of product
costing systems, we believe that the area is ripe for
further enquiry. Four avenues look promising. First,
the grand program is a multiperiod program, whereas
we consider a single-shot framework and assume that
capacity is fully utilized. Thus, it is of particular interest to model a setting that can accommodate the identification of unused capacity. Such a dynamic setting
could then be useful when considering alternate uses
for ABC systems such as cost control and process
analysis.
Second, within limits, managers can modify the
production environment to affect resource cost dispersion and traceability. We could investigate the robustness of the cost system to potential changes in the
production processes. For instance, the use of cellular
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540
Balakrishnan, Hansen, and Labro: Evaluating Heuristics Used When Designing Product Costing Systems
manufacturing techniques provides greater traceability of costs than provided under a regular assembly
line system. Although we have provided some preliminary analyses in §6, it is of considerable interest to
examine how the granularity of the data from the cost
system affects product and process-design decisions.
We believe that such extensions are of considerable
interest because product planning is but one decision
context in which firms use data from product costing
systems.
Third, consistent with prior works that examine
cost system design, we employ an error metric that
compares benchmark and reported costs. Although
we verify robustness with other measures such as
mean absolute percentage error, all of our error metrics employ benchmark costs as the goal. Thus, as
discussed earlier, these comparisons arithmetically
induce correlations among errors in reported product costs. Abandoning error metrics to judge the performance of heuristics requires that we revert to the
grand program and examine changes in the value of
its objective function as the ranking criterion. In a multiperiod setting, such an extension could also allow
us to endogenously determine the error metric as the
difference between an actual and a predicted cost.
Such approaches obviously involve considerably more
structure and add a great deal of complexity. However, the broader view also allows for an examination of heuristics other than product-based planning.
For example, we can investigate whether resourcebased planning dominates product-based planning
in certain production environments. Under resourcebased planning, we estimate opportunity costs at the
resource level, obviating the need for heuristically
designed product costing systems. Furthermore, such
an enquiry does not require the assumption that the
benchmark product cost is the best possible estimate
of opportunity costs at the product level.
Last, this stream of research is also of interest to
researchers who examine the antecedents and/or consequences of the provision in organizations of more
(or less precise) information. For example, accounting literature links the precision of information to
properties of disclosure (see Verrecchia 1990, Dye
and Sridhar 2007, Langberg and Sivaramakrishnan
2008). Empirical testing of these theoretical hypotheses requires that we understand how information precision might translate into properties of observable
data such as the properties of costing systems studied
here. Further research could combine these observable properties into a composite index that might
serve as an empirical proxy of the theoretical construct of precision. Our hope is that such translation
will help ground the often normative literature on
product costing in information economics, providing
it with a solid theoretical base.
Management Science 57(3), pp. 520–541, © 2011 INFORMS
Acknowledgments
The authors appreciate comments from Anil Arya, Romana
Autrey, Dennis Campbell, John Christensen, J. Harry Evans,
Thomas Hemmer, Susan Kulp, Karen Sedatole, Naomi
Soderstrom, K. Sivaramakrishnan, Jeroen Suijs, and directors of the Foundation for Applied Research at the Institute of Management Accountants (IMA). Two anonymous
referees, the associate editor, and the departmental editor
(Stefan Reichelstein) provided invaluable help in improving this paper. They also thank workshop participants at
the following universities and conferences: the Accounting Research Workshop, Bern; Carnegie Mellon University;
Florida International University; the George Washington
University; Global Management Accounting Research Symposium Conference, Copenhagen; Management Accounting
Section midyear meetings; Stanford University; Tilburg University; University of Houston; University of Iowa; University of North Carolina at Chapel Hill; and University
of Southern Denmark. Fang Yang, Saurav Pandit, and
Vasu Balakrishnan provided programming assistance. The
authors gratefully acknowledge funding from the IMA
Foundation for Applied Research. An earlier version of this
paper was titled “Heuristics for Evaluating and Refining
Product Costing Systems.”
Appendix. Select Results
Forming Cost Pools
• When the distribution of resource costs is moderately skewed (top 20% of costs account for less than 40%
of total costs), correlation-based methods dominate sizebased methods. When the distribution of resource costs is
highly skewed (top 20% account for greater than 75% of
total costs), size-based methods dominate correlation-based
methods (Result P1; Figure 1).
• A blended method that groups resources into tiers and
uses a size-based rule within each tier results in error that is
comparable to the error obtained with more informationintensive methods (Result P2; Figure 2)
• Correlation-based methods are robust to reductions in
the precision of information available information regarding correlation patterns (Result P3; Table 2). This finding is
robust to the variance in resource costs and to the similarity in consumption patterns. The effect of coarsening information is more acute when many products share the same
resource (Table 5).
• For all methods for assigning resources to cost pools,
it is generally preferable to group the costs of low-cost
resources into one pool rather than distribute them over the
other pools (Result P4; Figure 1, Table 3). Such a miscellaneous cost pool could contain up to 50% of total costs.
• A moderate number of cost pools (10–20) seem
enough, regardless of the method used to group resources
into cost pools (Result P5; Figure 1, Table 2). For both sizeand correlation-based methods, the gain from adding more
pools is concave in the number of pools formed.
Balakrishnan, Hansen, and Labro: Evaluating Heuristics Used When Designing Product Costing Systems
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Management Science 57(3), pp. 520–541, © 2011 INFORMS
Selecting Cost Drivers
• In every environment and method for grouping
resources into cost pools, an indexed driver is preferred to
the “big pool” method of using the consumption pattern for
the largest resource (Result D1).
• Indexed drivers (using four or five resources) might
even do better than the more information-intensive average
driver with a moderate (8–12) number of cost pools (Figure 3 and Result D2).
Influence of Cost Structure of Production Environment
(Other Than Variance in Resource Costs)
• The firm prefers correlation-based method when consumption patterns become more dissimilar (Result P6).
• The distribution of resource costs exerts the largest
influence on the choice of the method for grouping
resources into cost pools, followed by the density of the
consumption matrix (Result P7; Tables 4 and 5).
• Even marginal improvements in specification have the
potential to reduce error considerably in a wide range of
environments (Result D3).
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