1. The current issue and full text archive of this journal is available at
www.emeraldinsight.com/1463-5771.htm
A ROA
Benchmarking with data perspective
envelopment analysis: a return
on asset perspective
529
Seong-Jong Joo
Hasan School of Business, Colorado State University-Pueblo,
Pueblo, Colorado, USA
Don Nixon
College of Business, Central Washington University-Des Moines,
Des Moines, Washington, USA, and
Philipp A. Stoeberl
John Cook School of Business, Saint Louis University, St Louis, Missouri, USA
Abstract
Purpose – Selecting appropriate variables for analytical studies is critical for the validity of analysis.
It is the same with data envelopment analysis (DEA) studies. In this study, for benchmarking using
DEA, the paper seeks to suggest a novel framework based on return on assets (ROA), which is popular
and user-friendly to managers, and demonstrate it by use of an example.
Design/methodology/approach – The paper demonstrates the selection of variables using the
elements of ROA and applies DEA for measuring and benchmarking the comparative efficiency of
companies in the same industry.
Findings – It is frequently impossible to obtain internal data for benchmarking from competitors in
the same industry. In this case, annual reports may be the only source of data for publicly traded
companies. The framework demonstrated with an example is a practical approach for benchmarking
with limited data.
Research limitations/implications – This study employs financial data and is subject to the
limitations of accounting practices.
Originality/value – The approach is applicable to various studies for performance measurement
and benchmarking with minor modifications. Contributions of the study are twofold: first, a framework
for selecting variables for DEA studies is suggested; second, the applicability of the framework with a
real-world example is demonstrated.
Keywords Data envelopment analysis, Benchmarking, Variable selection, Return on assets,
Performance measures
Paper type Research paper
1. Introduction
Selecting pertinent variables is critical for analyzing data and affects the validity of a
study. Choosing variables for data envelopment analysis (DEA) is not an exception.
What variables and why they are selected should be justified and supported by the body
of knowledge in the area of the study. Like statistical analyses, variable selection for DEA Benchmarking: An International
models must be guided by relevant theories and approaches. For example, if researchers Journal
Vol. 18 No. 4, 2011
are interested in measuring the comparative efficiency of organizations using DEA, they pp. 529-542
may try endogenous and exogenous variables from related organization theories. q Emerald Group Publishing Limited
1463-5771
Likewise, if one attempts to measure the financial efficiency of firms, variables can DOI 10.1108/14635771111147623

2. BIJ be extracted from the studies in accounting and finance. Depending on the topic, there are
18,4 various theories that can be used for choosing variables for DEA studies.
We attempt to formalize a way to include related variables derived from the most
popular measure of profitability in finance, return on assets (ROA), which is frequently
defined by net income after tax divided by total assets. ROA is a comparative measure
and does not provide an absolute value. It is recommended for comparing a company’s
530 ROA to its previous ROA or similar companies’ ROA. Because of this feature of ROA,
deriving variables from a ROA framework is a good match to DEA, which also can
provide a comparative measure of firms’ performance. However, unlike ROA, which
employs single numbers for a numerator and a denominator, DEA can incorporate the
array of “vectors” in the numerator and the denominator, and analyze them for
managerial insights, such as potential improvements.
Because DEA provides a comparative measure of efficiency, which is good for
evaluating companies’ performance and for benchmarking, DEA studies are popular
and available in various industries. However, there are not many studies about selecting
variables with a normative approach.
The contributions of this study are twofold: one, by providing an approach to select
appropriate variables; and two, by applying them to a real-world example in the retail
industry. This study is applicable to almost any industry and expandable to similar
research with different theories and frameworks. The remainder of this study consists
of benchmarking and DEA, selecting variables with an ROA perspective, and an
application followed by a discussion and conclusion.
2. Benchmarking and data envelopment analysis
2.1 Benchmarking
Benchmarking is a management approach used to implement the best practices found
in similar industries or even in different industries in order to improve the performance
of an organization. Originally, benchmarking was implemented by the Xerox
Corporation in 1979 to overcome quality and cost problems created by challenges from
Japanese copier machine manufacturers (Horvath and Herter, 1992; Jackson, 2001). The
main goals of benchmarking are summarized by Furey (1987) as follows:
Identify key performance measures for each function of a business operation; Measure one’s
own internal performance levels as well as those of the leading competitors; Compare
performance levels and identify areas of comparative advantages and disadvantages;
Implement programs to close a performance gap between internal operations and the leading
competitors.
Currently, benchmarking is widely used to achieve a competitive advantage by
implementing best practices in organizations (Elmuti and Kathawala, 1997; Hinton et al.,
2000). In general, benchmarking is a managerial process used by an organization for
evaluating its internal strengths and weaknesses, analysing comparative advantages of
leading competitors, recognizing the best practices of the best performers, and
implementing these findings into its strategic plan for achieving a position of superiority
(Min and Galle, 1996). Recent exemplary studies on benchmarking are available on green
operations initiatives in the automotive industry (Nunes and Bennett, 2010),
sustainability in the pharmaceutical industry (Schneider et al., 2010), and service
quality in the utility industry (Chau, 2009).

3. As an addition to these more traditional studies, we are interested in benchmarking A ROA
using DEA. The selected recent applications of DEA for benchmarking include
evaluating coffee stores ( Joo et al., 2009), third party logistics providers (Min and Joo,
perspective
2009), emergency medical services (Lambert et al., 2009), and telecommunication
companies (Kwon et al., 2008).
2.2 Data envelopment analysis 531
DEA is a special application of linear programming (LP) based on frontier methodology
of Farrell (1957). Since Farrell, a major breakthrough for developing DEA was achieved
by Charnes et al. (1978) and by Banker et al. (1984). DEA is a useful approach for
measuring relative efficiency using multiple inputs and outputs among similar
organizations or objects. An entity that is an object to be measured for efficiency is called
a decision-making unit (DMU). Because DEA can identify relatively efficient DMUs
among a group of given DMUs, it is a promising tool for comparative analysis or
benchmarking.
To explore the mathematical property of DEA, let E0 be an efficiency score for the
base DMU 0 then:
nXR o
r¼1
ur0 yr0
Maximize E 0 ¼ nXI o ð1Þ
i¼1
vi0 xi0
subject to:
nXR o
r¼1
ur0 yrk
nXI o # 1 for all k ð2Þ
i¼1
vi0 xik
ur0 ; vi0 $ d for all r; i; ð3Þ
where:
yrk is the observed quantity of output r generated by unit k ¼ 1, 2, . . . , N.
xik is the observed quantity of input i consumed by unit k ¼ 1, 2, . . . , N.
ur0 is the weight to be computed given to output r by the base unit 0.
vi0 is the weight to be computed given to input i by the base unit 0.
d is a very small positive number.
The fractional programming model can be converted to a common LP model without
much difficulty. First, set the denominator of the objective function of the fractional
model equal to one and move it to the constraint section. Next, transform constraints
into linear forms by multiplying the respective denominator of each constraint,
and the fractional model becomes a LP model. A major assumption of LP is a linear
relationship among variables. Accordingly, an ordinary LP for solving DEA utilizes a
constant returns-to-scale so that all observed production combinations can be scaled up
or down proportionally (Charnes et al., 1978). However, when we use a piecewise LP,
we can model a non-proportional returns-to-scale such as an increasing, decreasing

4. BIJ or variable-returns-to-scale (Banker et al., 1984). Depending on returns-to-scales used,
18,4 and/or various modeling approaches, different types of DEA models are available.
Sherman and Ladino (1995) summarize the capability of DEA in the following
manner:
.
Identifies the best practice DMU that uses the least resources to provide its
products or services at or above the quality standard of other DMUs.
532 .
Compares the less efficient DMUs to the best practice DMU.
.
Identifies the amount of excess resources used by each of the less efficient DMUs.
.
Identifies the amount of excess capacity or ability to increase outputs for less
efficient DMUs, without requiring added resources.
In this study, involving comparative measures of performance for benchmarking,
slack-based (SBM), Charnes-Cooper-Rhodes (CCR) and Banker, Charnes, and Cooper
(BCC) models are employed. First, we measure the efficiency of DMUs using the SBM,
CCR, and BCC models, respectively. Next, we try to identify the sources of inefficiency
by decomposing the results of the three models.
The efficiency scores computed by CCR models are defined as technical efficiency
(TE), which is taken from the economics literature and represents economic efficiency.
We use the term TE to differentiate it from the technological aspects of production. The
efficiency scores by BCC models show pure technical efficiency (PTE). Let scale efficiency
(SE) mean the efficiency due to the scale difference between constant returns-to-scale and
variable returns-to-scale. Then, we can show the relationship between CCR and BCC
models as follows: TE ¼ PTE £ SE, where SE stands for scale efficiency. Finally, the
efficiency scores by the slack-based DEA model (SBM score) are the products of mix
efficiency (MIX), PTE, and SE; that is, SBM score ¼ ½MIXŠ £ ½PTEŠ £ ½SEŠ.
Mix efficiency is originated from the accounting literature and represents efficiency
variance due to the excessive use of resources such as labor, materials etc. When we apply
this decomposition of SBM scores, we can find the source of inefficiency for DMUs. When
SBM scores are low because of MIX and/or PTE, managers should look at projections
generated by the SBM model and take action on variables suggested to increase the SBM
efficiency scores.
3. Selecting variables using ROA
Benchmarking a firm’s performance with the performance of competing companies in
the same industry is sometimes not easy mainly due to the lack of available data. It is
especially true for DEA users. For competing firms, information is limited to publicly
available data, which is filed with the Securities and Exchange Commission. This
guide shows a way to select input and output variables using publicly traded firms’
annual reports (10-K) for DEA studies. It is possible to use quarterly reports (10-Q)
depending on the situation and availability of data.
3.1 ROA defined
ROA is one of popular profitability measures, which is a ratio between earnings after
tax (EAT) and total assets: ROA ¼ (EAT/total assets). Instead of EAT, depending on
the types of profitability measures used, one may use different earnings such as income
before taxes or operating income. The use of operating income will show

5. the profitability that focuses on the operations of a company. Information on earnings A ROA
is available in companies’ income statements. Total assets, which are entries in firms’ perspective
balance sheets, consist of current assets, fixed assets, and other assets. Current assets
include cash and cash equivalent, inventory, accounts receivable, and other current
assets. Current assets tend to be converted to cash, bartered, exchanged, and expensed
within a year for usual business operations. Fixed assets are mainly investment on
buildings, equipment, furniture, machinery, and leasehold improvements. Unlike 533
current assets, fixed assets are not transformed to cash for routine business operations
within a year, yet are subject to amortization and depreciation. Other assets contain
assets not included in either current or fixed assets such as prepaid expenses, patents,
and computer programs. The drawback of total assets in the current balance sheet is
that it cannot incorporate certain assets such as human capital, brand values, and
relationships, which are not easily measurable in monetary units. Overall, all elements
in ROA are candidates for variables in DEA analyses.
3.2 Decomposition of ROA
ROA can be rewritten in a multiplicative form using two elements such as profitability
measured by EAT divided by revenues, and speed (or turns) expressed by revenues
divided by total assets. The following formulas show this relationship:
EAT Revenues
ROA ¼ Profitability £ Speed ðor turnsÞ ¼ £ :
Revenues Total assets
Profitability represents a profit margin, and speed shows an asset turnover ratio. When
competitive pressures hurt profitability, it is possible to maintain or improve ROA by
increasing speed. The decomposition of ROA widens the selection of variables in DEA
analyses. The inclusion of revenues along with earnings will provide additional output
variables to DEA models. In addition, potential improvements, which are by-products
of DEA analyses, will show the types of revenues to be increased for improving
efficiencies.
3.3 Specifying variables
Existing studies in variable selection for DEA studies are similar to variable reduction
in statistical analysis. Wagner and Shimshak (2007) suggested a stepwise approach
that was based on the increase or decrease of efficiency scores by adding and removing
´
a variable in the DEA model. Similar to this study, Fanchon (2003) and Lopez and DuIa ´
(2008) demonstrated variable selection methods for DEA studies. These studies
assume that rich sets of variables are readily available. Meanwhile, Casu et al. (2005)
employed a unique method that utilized a group decision support system with an
expert panel for choosing relevant variables for a DEA study. At the time of this study,
we fail to find literature for selecting variables using a normative approach.
Accordingly, we try to formalize a novel approach for selecting variables for DEA
studies and demonstrate the approach using an example in the retail industry.
Although it was not the purpose of their study, Feroz et al. (2003) briefly mentioned
that the components of a profitability measure, return on equity, could be used for DEA
studies for analyzing the comparative financial performance of companies. We further
show that the elements of ROA can be used for selecting variables for DEA studies. First,
output variables can be selected from the different types of earnings and revenues.

6. BIJ Revenues are generated by the various activities of firms. There are basically two types
18,4 of revenues: revenues from operating activities and revenues from non-operating
activities. Operating revenues can be further classified into different types, for example,
revenues from domestic operations and revenues from international operations.
Hospitals have revenues generated from inpatient and outpatient services. Hotels have
revenues produced by rooms, food and beverage, and other sources. Additionally, when
534 we read descriptive portions of annual reports, we can find valuable information not
presented in income statements or balance sheets. For example, non-financial variables
such as number of branches, number of memberships, and square footages are
frequently available. Next, input variables can be extracted from resources such as
assets and expenses used by companies. In a balance sheet, there are three basic types of
assets: current, fixed, and other assets. Accordingly, one may simply select all three of
them. Current assets can be further classified into various entries. Among them, cash and
cash equivalents, accounts receivable, and merchandise inventory are critical to the
efficiency of firms’ working capital. Fixed assets include plants, warehouses, offices,
machines, etc. Fixed asset turns are critical to the operating efficiency of firms. Because
firms increasingly use intangible assets such as computer software, patents, certain
rights, etc. “other assets” may be as important as the aforementioned two types of assets
with respect to an individual firm’s efficiency in some industries. Earnings from
operations are computed by revenues after applicable expenses for operations. Although
expenses are not shown in the decomposition of ROA, they are used for computing ROA
and can be selected for input variables. In an income statement, one can find different
types of expenses. Cost of goods sold (COGS), selling, general and administrative
expenses (SG&A), depreciation and amortization, and “other expenses” are
representative of expenses found in income statements. COGS reflects information on
sourcing and purchasing activities of a firm. SG&A includes indirect expenses, which
are necessary to support operating activities. Charging depreciation and amortization as
expenses is required for firms’ reinvestment in fixed assets in the future. Table I
summarizes and exemplifies the combination of input and output variables.
Table I simply illustrates a method for selecting variables. Depending on the
industry, variables might be different. For example, inventory may not be a significant
variable to pure service oriented companies such as financial institutions, transportation
companies, and communication firms. Likewise, depreciation and amortization may not
be important to non-asset based companies. Thus, one must be cautious and selective in
finding relevant variables for a specific industry.
3.4 Limitations for using financial data
The application of generally accepted accounting principles can be changed over time
and across companies/industries. In addition, entries in annual reports are not
standardized even if we have data directly from individual firms. The use of standard
Total asset model Current asset model Expense model
Output variables Different types of Different types of revenues Different types of
Table I. revenues revenues
Combination of variables Input variables Current assets; fixed Cash & cash equivalent; COGS; SG&A;
for DEA models assets; other assets accounts receivable; inventory Depreciation/amortization

7. databases such as Compustat and Hoovers can avoid or reduce these problems. However, A ROA
we are not free from all limits on the comparison of financial data from different firms. perspective
4. An example
4.1 Data, variables, and models
For the purpose of a demonstration, we utilize fourteen general merchandisers listed by
Fortune Magazine: Wal-Mart, Target, Sears Holdings, Macy’s, JC Penney, Kohl’s, Dollar 535
General, Nordstrom, Dillard’s, Family Dollar, Saks, Bon-Ton Stores, Belk, and Retail
Ventures. We then construct three models by following the approach summarized in
Table I. Revenue is the output variable for all three models. Relevant input variables are
chosen in each model. Table II shows the variables in the models and their descriptive
statistics.
4.2 Results
The DEA models used in this study are all input oriented. The first model we tested is
an asset model. We name the model after the input variables, which are current assets,
fixed assets, and other assets. For computing efficiency, we employ three DEA models
such as SBM, CCR, and BCC models explained in the previous section. Table III shows
the efficiency scores of the Asset Model computed by SBM, CCR, and BCC DEA
models, respectively.
As noted in the earlier section, SBM efficiency ¼ [MIX efficiency] £ [CCR efficiency].
Since CCR efficiency ¼ [BCC efficiency] £ [Scale Efficiency or SE] and, SBM
efficiency ¼ [MIX efficiency] £ [BCC efficiency] £ [SE], we use this relationship for
interpreting the results of our analyses. The efficiency scores computed by the DEA
models in Table III are between zero and one inclusively. SBM scores are the most
restrictive measure of efficiency as shown with averages in Table III. The average
efficiency score of SBM is 59.28 percent and the lowest among the average efficiency
scores for the models shown in Table III. Four DMUs, namely, Wal-Mart, Dollar General,
Family Dollar, and Retail Ventures show 100 percent efficiency in all DEA models.
They maintain the highest level of comparative efficiency among the DMUs in the
models. Target, Sears Holding, and Bon-Ton Stores are 100 percent efficient in the BCC
model. When we consider CCR and BCC models only, their inefficiency is due to the
different scales used by the two DEA models. CCR models use constant returns-to-scale,
Model Variable Minimum Maximum Mean SD Type
All models Revenue 2,940.0 348,650.0 40,640.5 87,197.1 Output
Asset model Current assets 888.0 46,588.0 7,606.6 11,791.6 Input
Fixed assets 279.9 66,440.0 10,768.7 22,261.2 Input
Other assets 26.2 16,165.0 2,664.9 4,716.5 Input
Current asset model Cash 24.7 7,373.0 1,356.7 1,989.7 Input
Receivables 10.5 6,194.0 873.4 1,651.6 Input
Inventory 545.6 33,685.0 4,980.0 8,382.5 Input
Expense model COGS 1,804.3 264,152.0 29,247.4 66,239.3 Input
SG&A 769.4 58,542.0 8,019.6 14,551.7 Input
D/A 62.9 5,459.0 816.4 1,364.4 Input Table II.
Descriptive statistics
Note: Values in million US dollars of variables

8. BIJ DMU SBM CCR (TE) BCC (PTE) MIX SE
18,4
Wal-Mart 100.00 100.00 100.00 100.00 100.00
Target 48.98 72.24 100.00 67.80 72.24
Sears Holdings 50.02 72.81 100.00 68.70 72.81
Macy’s 34.15 53.25 54.67 64.13 97.40
JC Penney 42.83 61.37 76.31 69.79 80.42
536 Kohl’s 53.99 81.41 91.22 66.32 89.25
Dollar General 100.00 100.00 100.00 100.00 100.00
Nordstrom 47.56 63.12 64.95 75.35 97.18
Dillard’s 43.83 66.72 75.20 65.69 88.72
Family Dollar 100.00 100.00 100.00 100.00 100.00
Saks 30.27 42.14 70.99 71.83 59.36
Bon-Ton Stores 43.61 65.47 100.00 66.61 65.47
Table III. Belk 34.63 51.86 79.31 66.78 65.39
Efficiency scores (%) for Retail Ventures 100.00 100.00 100.00 100.00 100.00
the asset model Average 59.28 73.60 86.62 77.36 84.87
which employs proportional increases and decreases of input and output variables for
computing efficiency scores. Meanwhile, BCC models apply a non-linear scale. These
three companies are locally 100 percent efficient and include inefficiency in the CCR
model, which may be due to different market conditions. Besides, the three companies
exhibit MIX inefficiency in the SBM model, which is due to the undesirable mix of
resources or the use of input variables. To correct this problem, the companies need to
adjust the utilization of input variables or assets by looking at the potential
improvement of DEA results, which will be discussed later. Macy’s, JC Penny, Kohl’s,
Nordstrom, Dillard’s, Saks, and Belk maintain relatively lower efficiency on the
utilization of assets than the other companies in the model. They need to seek a way to
improve their efficiency by reviewing areas for potential improvement. Particularly,
when we look at the SE scores of Macy’s and Nordstrom, the scores are close to
100 percent. It shows that their source of inefficiency is MIX, which is about the
inefficient combination of input variables or assets in this case. Macy’s and Nordstrom
need fine tuning of assets based on the potential improvements suggested by the DEA
model. Table IV shows potential improvements of variables for DMUs which are less
than 100 percent efficient in Table III.
The improvements for the asset model shown in Table IV are computed by using a
SBM model. Negative numbers mean reductions in input variables: current, fixed, and
other assets. The average scores found in the bottom row of the Table IV reveal that
the largest inefficiency is from other assets. Based on these results, to increase
efficiency scores, Sears Holdings, Macy’s, JC Penney, Saks, Bon-Ton Stores, and Belk
should virtually eliminate their other assets. The next inefficient variable is fixed
assets. Six retailers are urged to cut their fixed assets more than half in order to be
competitive with their peers. When we look at current assets, Saks is the least effective
in the reduction of current assets. JC Penney, Nordstrom, and Belk follow Saks in their
inefficiency of current assets. We do not include potential improvements by CCR and
BCC models to avoid redundancy. The way to interpret the improvements by different
models is similar to one we have discussed.

9. A ROA
DMU Current assets Fixed assets Other assets
perspective
Wal-Mart 0.00 0.00 0.00
Target 223.12 262.56 2 67.40
Sears Holdings 234.60 221.70 2 93.63
Macy’s 234.94 268.29 2 98.32
JC Penney 243.10 235.50 2 92.90 537
Kohl’s 213.13 260.83 2 64.05
Dollar General 0.00 0.00 0.00
Nordstrom 240.67 234.29 2 82.35
Dillard’s 227.51 266.64 2 74.36
Family Dollar 0.00 0.00 0.00
Saks 255.33 263.93 2 89.94
Bon-Ton Stores 228.20 248.08 2 92.87
Belk 241.52 261.18 2 93.40
Retail Ventures 0.00 0.00 0.00 Table IV.
Average 224.44 237.36 2 60.67 Potential improvement
(%) of input variables
Note: Negative numbers mean reduction on input variables or resources in the SBM asset model
In the second attempt, we assess efficiency of revenues over current assets. Like the
asset model, we name the current asset model after the input variables.
Wal-Mart, Target, Kohl’s, Dollar General, Dillard’s, and Bon-Ton Stores are
100 percent efficient in the all DEA models in Table V; that is, they are good at
managing current assets. The majority of companies that are not 100 percent efficient
show SBM efficiency scores of less than 50 percent. Nordstrom and Retail Ventures are
not globally but locally 100 percent efficient. Nordstrom’s major source of inefficiency
is the different mix of current assets, which requires adjustments by managers.
For Retail Ventures, its source of inefficiency is on SE, meaning that its inefficiency
is not from managerial factors but from external ones such as market differences. In
addition to Retail Ventures, Family Dollar, Saks, and Belk have the same issues with
their SE. Their low efficiency scores are due to the use of different scales or external
DMU SBM CCR (TE) BCC (PTE) MIX SE
Wal-Mart 100.00 100.00 100.00 100.00 100.00
Target 100.00 100.00 100.00 100.00 100.00
Sears Holdings 39.07 51.70 53.68 75.57 96.31
Macy’s 45.46 46.91 52.66 96.91 89.08
JC Penney 44.51 59.06 65.13 75.36 90.68
Kohl’s 100.00 100.00 100.00 100.00 100.00
Dollar General 100.00 100.00 100.00 100.00 100.00
Nordstrom 37.63 82.93 100.00 45.38 82.93
Dillard’s 100.00 100.00 100.00 100.00 100.00
Family Dollar 51.42 61.95 91.05 83.00 68.04
Saks 36.88 45.07 90.77 81.83 49.65
Bon-Ton Stores 100.00 100.00 100.00 100.00 100.00
Belk 44.20 44.90 77.49 98.44 57.94 Table V.
Retail Ventures 44.43 54.32 100.00 81.79 54.32 Efficiency scores (%) for
Average 67.40 74.78 87.91 88.45 84.93 the current asset model

10. BIJ factors in the DEA models. In fact, these companies demonstrate relatively high BCC
18,4 scores, which represent pure technical or managerial efficiency. Table VI displays
potential improvements computed by the SBM current asset model.
Cash management is the prime source of inefficiency for the companies not 100 percent
efficient in the current asset model. It is recommended that Sears Holdings, JC Penney,
Nordstrom, Saks, and Retail Ventures reduce their cash and cash equivalent assets more
538 than 70 percent. Accounts receivable is the next inefficient variable. Nordstrom requires
the highest reduction of receivables followed by Saks and Sears Holdings. Retailers
increasingly engage in credit card business and, as a result, have ended up with higher
levels of receivables than before. Nonetheless, the companies with high receivables must
compare themselves with peer retailers for the reduction of receivables. Prolonged
accounts receivable can become bad debt in the future. For the last variable in the current
asset model, Macy’s and Belk need to improve their inventory management by cutting the
level of inventory more than half. Inventory management can be made more efficient by
employing a better model and/or collaborating with suppliers.
The final analysis includes expenses as input variables. The expense model shown
in Table VII provides the efficiency scores calculated by DEA models with expenses.
In the most restrictive SBM model of this analysis, half of the companies achieve
100 percent efficiency. Saks shows the lowest SBM scores with 74.08 percent. Its source
of inefficiency is the MIX score of 75.66 percent. To improve efficiency, the managers of
Saks should seek a different mix of expenses. Likewise, Dillard’s and Bon-Ton Stores
should take action on the mix of expenses for their store operations. In the BCC model
with expenses, only three companies show efficiency scores of less than 100 percent.
However, these three companies hold their BCC scores higher than 90 percent. One can
conclude that most companies in this study are relatively efficient in managing their
expenses. Table VIII exhibits potential improvements with regard to expenses.
There is no company with a need to improve COGS. Saks needs to cut SG&A costs
by 22.06 percent. Dollar General and Bon-Ton Stores should reduce their SG&A
expenses more than ten percent. Saks is least efficient with respect to
DMU Cash Receivables Inventory
Wal-Mart 0.00 0.00 0.00
Target 0.00 0.00 0.00
Sears Holdings 271.75 2 62.74 248.30
Macy’s 252.90 2 57.51 253.20
JC Penney 284.68 2 38.36 243.44
Kohl’s 0.00 0.00 0.00
Dollar General 0.00 0.00 0.00
Nordstrom 278.21 2 91.83 217.07
Dillard’s 0.00 0.00 0.00
Family Dollar 249.24 2 58.46 238.05
Saks 274.71 2 73.12 241.52
Bon-Ton Stores 0.00 0.00 0.00
Belk 254.48 2 51.12 261.80
Table VI. Retail Ventures 274.99 2 46.03 245.68
Potential improvement Average 238.64 2 34.23 224.93
(%) for the SBM current
asset model Note: Negative numbers mean reduction on input variables or resources

11. A ROA
DMU SBM CCR (TE) BCC (PTE) MIX SE
perspective
Wal-Mart 100.00 100.00 100.00 100.00 100.00
Target 93.04 96.94 100.00 95.98 96.94
Sears Holdings 89.99 95.45 96.74 94.28 98.67
Macy’s 100.00 100.00 100.00 100.00 100.00
JC Penney 100.00 100.00 100.00 100.00 100.00 539
Kohl’s 100.00 100.00 100.00 100.00 100.00
Dollar General 86.40 93.66 99.38 92.25 94.24
Nordstrom 100.00 100.00 100.00 100.00 100.00
Dillard’s 79.81 95.33 95.82 83.72 99.49
Family Dollar 92.44 95.88 100.00 96.41 95.88
Saks 74.08 97.91 100.00 75.66 97.91
Bon-Ton Stores 83.41 98.43 100.00 84.74 98.43
Belk 100.00 100.00 100.00 100.00 100.00 Table VII.
Retail Ventures 100.00 100.00 100.00 100.00 100.00 Efficiency scores (%)
Average 92.80 98.11 99.42 94.50 98.68 for the expense model
DMU COGS SG&A Depreciation/amortization
Wal-Mart 0.00 0.00 0.00
Target 0.00 0.00 2 20.87
Sears Holdings 0.00 2 8.01 2 22.03
Macy’s 0.00 0.00 0.00
JC Penney 0.00 0.00 0.00
Kohl’s 0.00 0.00 0.00
Dollar General 0.00 2 14.26 2 26.55
Nordstrom 0.00 0.00 0.00
Dillard’s 0.00 2 8.40 2 52.16
Family Dollar 0.00 2 8.86 2 13.83
Saks 0.00 2 22.06 2 55.69
Bon-Ton Stores 0.00 2 10.45 2 39.33
Belk 0.00 0.00 0.00
Retail Ventures 0.00 0.00 0.00 Table VIII.
Average 0.00 2 5.15 2 16.46 Potential improvement
(%) for the SBM
Note: Negative numbers mean reduction on input variables or resources expense model
depreciation/amortization expenses, followed by Dillard’s. Depreciation/amortization
as related to fixed assets should be managed accordingly.
We summarize the comparative efficiency of the companies in the SBM models with
different input variables in Table IX.
The best performer is Wal-Mart. It is relatively 100 percent efficient across the models.
Kohl’s, Dollar General, and Retail Ventures are 100 percent efficient in two models. Sears
Holdings and Saks do not show 100 percent efficiency in any model in this study. The
remaining companies are 100 percent efficient in at least one model. Finally, efficiency
scores computed by DEA models are relative to DMUs and variables. Accordingly,
the different combination of companies and/or variables will yield different scores.

12. BIJ
DMU Asset model Current asset model Expense model
18,4
Wal-Mart O O O
Target X O X
Sears Holdings X X X
Macy’s X X O
540 JC Penney X X O
Kohl’s X O O
Dollar General O O X
Nordstrom X X O
Dillard’s X O X
Family Dollar O X X
Table IX. Saks X X X
100 Percent efficient Bon-Ton Stores X O X
DMUs in the SBM models Belk X X O
with different input Retail Ventures O X O
variables Total 4 6 7
5. Conclusion
Since the introduction by Charnes et al. (1978), numerous studies using DEA have been
published in various areas. Although DEA is based on estimating the efficiency of
companies using the production function concept proposed by Farrell (1957), its
applications are not limited to the production area. Most published DEA studies are
either developing algorithms or applying DEA in different areas. Although a limited
number of studies that propose mathematical and procedural approaches for selecting
variables for DEA (Wagner and Shimshak, 2007; Fanchon, 2003) are available, at the
time of this study we fail to find one concerning the selection of variables within a
theoretical framework, which is available in the domain of application. We
demonstrate a framework based on a widely used profitability measure for selecting
variables for DEA and apply it to measuring the efficiency of general merchandisers.
Return on assets or ROA and its components are popular among managers and
user-friendly to managers. ROA is calculated by earnings, which are revenues after
applicable expenses, divided by total assets. We include components in ROA such as
revenues, expenses, and assets for specifying variables. ROA is a comparative measure
of profitability and is not bound by a specific value. Accordingly, users may need to
compare their ROA to the previous values of their ROA and/or those of similar
companies. In this context, ROA is a good fit with DEA for selecting variables.
We suggest and demonstrate a framework using an example that includes general
merchandisers. Three models with different input variables are selected and tested:
total assets, current assets, and expenses. We find Wal-Mart is the best performer
among the retailers in all models. The second tier group includes Kohl’s, Dollar
General, and Retail Ventures. In addition to overall efficiency, DEA models provide for
potential improvements in terms of ROA components to the companies that are not
100 percent efficient. We confirm that the framework is useful for selecting variables
for performance measurement and benchmarking.
Finally, our approach is applicable to various studies for performance measurement
and benchmarking with minor modifications. Contributions of our study are twofold:
first, we suggest a framework for selecting variables for DEA studies; second,

13. we demonstrate the applicability of the framework using a real world example. We A ROA
hope that there will be similar studies with different perspectives and theories for perspective
selecting variables in the future.
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About the authors
Seong-Jong Joo is an Associate Professor of Production and Operations Management in Hasan
School of Business, Colorado State University-Pueblo in Pueblo, Colorado. He teaches graduate
and undergraduate courses in Operations and Supply Chain Management. His research interests
include sourcing/purchasing, supply chain collaboration, inventory management, and
performance measurement/benchmarking. Seong-Jong Joo is the corresponding author and can
be contacted at: seongjong.joo@colostate-pueblo.edu
Don Nixon is a Professor of Management in the College of Business, Central Washington
University, Des Moines, Washington. He teaches Strategic Management. His research interests
are developing strategies and measuring the performance of firms.
Philipp A. Stoeberl is the Mary Louis Murray Professor of Management at the John Cook
School of Business, Saint Louis University. He teaches both graduate and undergraduate courses
in Strategy and Current Issues in Management. His current research interests include
performance measures and benchmarking.
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