4.benchmarking with

Benchmarking with dataenvelopment analysis: a return

on asset perspectiveSeong-Jong Joo

Hasan School of Business, Colorado State University-Pueblo,Pueblo, Colorado, USA

Don NixonCollege of Business, Central Washington University-Des Moines,

Des Moines, Washington, USA, and

Philipp A. StoeberlJohn 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 usingDEA, the paper seeks to suggest a novel framework based on return on assets (ROA), which is popularand user-friendly to managers, and demonstrate it by use of an example.

Design/methodology/approach – The paper demonstrates the selection of variables using theelements of ROA and applies DEA for measuring and benchmarking the comparative efficiency ofcompanies in the same industry.

Findings – It is frequently impossible to obtain internal data for benchmarking from competitors inthe same industry. In this case, annual reports may be the only source of data for publicly tradedcompanies. The framework demonstrated with an example is a practical approach for benchmarkingwith limited data.

Research limitations/implications – This study employs financial data and is subject to thelimitations of accounting practices.

Originality/value – The approach is applicable to various studies for performance measurementand benchmarking with minor modifications. Contributions of the study are twofold: first, a frameworkfor selecting variables for DEA studies is suggested; second, the applicability of the framework with areal-world example is demonstrated.

Keywords Data envelopment analysis, Benchmarking, Variable selection, Return on assets,Performance measures

Paper type Research paper

1. IntroductionSelecting pertinent variables is critical for analyzing data and affects the validity of astudy. 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 bodyof knowledge in the area of the study. Like statistical analyses, variable selection for DEAmodels must be guided by relevant theories and approaches. For example, if researchersare interested in measuring the comparative efficiency of organizations using DEA, theymay try endogenous and exogenous variables from related organization theories.Likewise, if one attempts to measure the financial efficiency of firms, variables can

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Vol. 18 No. 4, 2011pp. 529-542

q Emerald Group Publishing Limited1463-5771

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be extracted from the studies in accounting and finance. Depending on the topic, there arevarious theories that can be used for choosing variables for DEA studies.

We attempt to formalize a way to include related variables derived from the mostpopular measure of profitability in finance, return on assets (ROA), which is frequentlydefined by net income after tax divided by total assets. ROA is a comparative measureand does not provide an absolute value. It is recommended for comparing a company’sROA 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 canprovide a comparative measure of firms’ performance. However, unlike ROA, whichemploys single numbers for a numerator and a denominator, DEA can incorporate thearray of “vectors” in the numerator and the denominator, and analyze them formanagerial insights, such as potential improvements.

Because DEA provides a comparative measure of efficiency, which is good forevaluating companies’ performance and for benchmarking, DEA studies are popularand available in various industries. However, there are not many studies about selectingvariables with a normative approach.

The contributions of this study are twofold: one, by providing an approach to selectappropriate variables; and two, by applying them to a real-world example in the retailindustry. This study is applicable to almost any industry and expandable to similarresearch with different theories and frameworks. The remainder of this study consistsof benchmarking and DEA, selecting variables with an ROA perspective, and anapplication followed by a discussion and conclusion.

2. Benchmarking and data envelopment analysis2.1 BenchmarkingBenchmarking is a management approach used to implement the best practices foundin similar industries or even in different industries in order to improve the performanceof an organization. Originally, benchmarking was implemented by the XeroxCorporation in 1979 to overcome quality and cost problems created by challenges fromJapanese copier machine manufacturers (Horvath and Herter, 1992; Jackson, 2001). Themain goals of benchmarking are summarized by Furey (1987) as follows:

Identify key performance measures for each function of a business operation; Measure one’sown internal performance levels as well as those of the leading competitors; Compareperformance levels and identify areas of comparative advantages and disadvantages;Implement programs to close a performance gap between internal operations and the leadingcompetitors.

Currently, benchmarking is widely used to achieve a competitive advantage byimplementing best practices in organizations (Elmuti and Kathawala, 1997; Hinton et al.,2000). In general, benchmarking is a managerial process used by an organization forevaluating its internal strengths and weaknesses, analysing comparative advantages ofleading competitors, recognizing the best practices of the best performers, andimplementing these findings into its strategic plan for achieving a position of superiority(Min and Galle, 1996). Recent exemplary studies on benchmarking are available on greenoperations initiatives in the automotive industry (Nunes and Bennett, 2010),sustainability in the pharmaceutical industry (Schneider et al., 2010), and servicequality in the utility industry (Chau, 2009).

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As an addition to these more traditional studies, we are interested in benchmarkingusing DEA. The selected recent applications of DEA for benchmarking includeevaluating coffee stores ( Joo et al., 2009), third party logistics providers (Min and Joo,2009), emergency medical services (Lambert et al., 2009), and telecommunicationcompanies (Kwon et al., 2008).

2.2 Data envelopment analysisDEA is a special application of linear programming (LP) based on frontier methodologyof Farrell (1957). Since Farrell, a major breakthrough for developing DEA was achievedby Charnes et al. (1978) and by Banker et al. (1984). DEA is a useful approach formeasuring relative efficiency using multiple inputs and outputs among similarorganizations or objects. An entity that is an object to be measured for efficiency is calleda decision-making unit (DMU). Because DEA can identify relatively efficient DMUsamong a group of given DMUs, it is a promising tool for comparative analysis orbenchmarking.

To explore the mathematical property of DEA, let E0 be an efficiency score for thebase DMU 0 then:

Maximize E0 ¼

XR

r¼1ur0yr0

n o

XI

i¼1vi0xi0

n o ð1Þ

subject to:

XR

r¼1ur0yrk

n o

XI

i¼1vi0xik

n o # 1 for all k ð2Þ

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 withoutmuch difficulty. First, set the denominator of the objective function of the fractionalmodel equal to one and move it to the constraint section. Next, transform constraintsinto 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 linearrelationship among variables. Accordingly, an ordinary LP for solving DEA utilizes aconstant returns-to-scale so that all observed production combinations can be scaled upor 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

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or variable-returns-to-scale (Banker et al., 1984). Depending on returns-to-scales used,and/or various modeling approaches, different types of DEA models are available.

Sherman and Ladino (1995) summarize the capability of DEA in the followingmanner:

. Identifies the best practice DMU that uses the least resources to provide itsproducts or services at or above the quality standard of other DMUs.

. 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 lessefficient 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 inefficiencyby 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. Theefficiency 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 andvariable returns-to-scale. Then, we can show the relationship between CCR and BCCmodels as follows: TE ¼ PTE £ SE, where SE stands for scale efficiency. Finally, theefficiency scores by the slack-based DEA model (SBM score) are the products of mixefficiency (MIX), PTE, and SE; that is, SBM score ¼ ½MIX� £ ½PTE� £ ½SE�.Mix efficiency is originated from the accounting literature and represents efficiencyvariance due to the excessive use of resources such as labor, materials etc. When we applythis decomposition of SBM scores, we can find the source of inefficiency for DMUs. WhenSBM scores are low because of MIX and/or PTE, managers should look at projectionsgenerated by the SBM model and take action on variables suggested to increase the SBMefficiency scores.

3. Selecting variables using ROABenchmarking a firm’s performance with the performance of competing companies inthe same industry is sometimes not easy mainly due to the lack of available data. It isespecially true for DEA users. For competing firms, information is limited to publiclyavailable data, which is filed with the Securities and Exchange Commission. Thisguide 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 definedROA is one of popular profitability measures, which is a ratio between earnings aftertax (EAT) and total assets: ROA ¼ (EAT/total assets). Instead of EAT, depending onthe types of profitability measures used, one may use different earnings such as incomebefore taxes or operating income. The use of operating income will show

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the profitability that focuses on the operations of a company. Information on earningsis available in companies’ income statements. Total assets, which are entries in firms’balance sheets, consist of current assets, fixed assets, and other assets. Current assetsinclude cash and cash equivalent, inventory, accounts receivable, and other currentassets. Current assets tend to be converted to cash, bartered, exchanged, and expensedwithin a year for usual business operations. Fixed assets are mainly investment onbuildings, equipment, furniture, machinery, and leasehold improvements. Unlikecurrent assets, fixed assets are not transformed to cash for routine business operationswithin a year, yet are subject to amortization and depreciation. Other assets containassets 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 isthat it cannot incorporate certain assets such as human capital, brand values, andrelationships, which are not easily measurable in monetary units. Overall, all elementsin ROA are candidates for variables in DEA analyses.

3.2 Decomposition of ROAROA can be rewritten in a multiplicative form using two elements such as profitabilitymeasured by EAT divided by revenues, and speed (or turns) expressed by revenuesdivided by total assets. The following formulas show this relationship:

ROA ¼ Profitability £ Speed ðor turnsÞ ¼EAT

Revenues£

Revenues

Total assets:

Profitability represents a profit margin, and speed shows an asset turnover ratio. Whencompetitive pressures hurt profitability, it is possible to maintain or improve ROA byincreasing speed. The decomposition of ROA widens the selection of variables in DEAanalyses. The inclusion of revenues along with earnings will provide additional outputvariables to DEA models. In addition, potential improvements, which are by-productsof DEA analyses, will show the types of revenues to be increased for improvingefficiencies.

3.3 Specifying variablesExisting studies in variable selection for DEA studies are similar to variable reductionin statistical analysis. Wagner and Shimshak (2007) suggested a stepwise approachthat was based on the increase or decrease of efficiency scores by adding and removinga variable in the DEA model. Similar to this study, Fanchon (2003) and Lopez and DuIa(2008) demonstrated variable selection methods for DEA studies. These studiesassume 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 anexpert 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 DEAstudies 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 mentionedthat the components of a profitability measure, return on equity, could be used for DEAstudies for analyzing the comparative financial performance of companies. We furthershow 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.

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Revenues are generated by the various activities of firms. There are basically two typesof revenues: revenues from operating activities and revenues from non-operatingactivities. 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 haverevenues produced by rooms, food and beverage, and other sources. Additionally, whenwe read descriptive portions of annual reports, we can find valuable information notpresented in income statements or balance sheets. For example, non-financial variablessuch as number of branches, number of memberships, and square footages arefrequently available. Next, input variables can be extracted from resources such asassets and expenses used by companies. In a balance sheet, there are three basic types ofassets: current, fixed, and other assets. Accordingly, one may simply select all three ofthem. Current assets can be further classified into various entries. Among them, cash andcash equivalents, accounts receivable, and merchandise inventory are critical to theefficiency of firms’ working capital. Fixed assets include plants, warehouses, offices,machines, etc. Fixed asset turns are critical to the operating efficiency of firms. Becausefirms increasingly use intangible assets such as computer software, patents, certainrights, etc. “other assets” may be as important as the aforementioned two types of assetswith respect to an individual firm’s efficiency in some industries. Earnings fromoperations are computed by revenues after applicable expenses for operations. Althoughexpenses are not shown in the decomposition of ROA, they are used for computing ROAand can be selected for input variables. In an income statement, one can find differenttypes of expenses. Cost of goods sold (COGS), selling, general and administrativeexpenses (SG&A), depreciation and amortization, and “other expenses” arerepresentative of expenses found in income statements. COGS reflects information onsourcing and purchasing activities of a firm. SG&A includes indirect expenses, whichare necessary to support operating activities. Charging depreciation and amortization asexpenses is required for firms’ reinvestment in fixed assets in the future. Table Isummarizes and exemplifies the combination of input and output variables.

Table I simply illustrates a method for selecting variables. Depending on theindustry, variables might be different. For example, inventory may not be a significantvariable to pure service oriented companies such as financial institutions, transportationcompanies, and communication firms. Likewise, depreciation and amortization may notbe important to non-asset based companies. Thus, one must be cautious and selective infinding relevant variables for a specific industry.

3.4 Limitations for using financial dataThe application of generally accepted accounting principles can be changed over timeand across companies/industries. In addition, entries in annual reports are notstandardized 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 ofrevenues

Different types of revenues Different types ofrevenues

Input variables Current assets; fixedassets; other assets

Cash & cash equivalent;accounts receivable; inventory

COGS; SG&A;Depreciation/amortization

Table I.Combination of variablesfor DEA models

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databases such as Compustat and Hoovers can avoid or reduce these problems. However,we are not free from all limits on the comparison of financial data from different firms.

4. An example4.1 Data, variables, and modelsFor the purpose of a demonstration, we utilize fourteen general merchandisers listed byFortune Magazine: Wal-Mart, Target, Sears Holdings, Macy’s, JC Penney, Kohl’s, DollarGeneral, Nordstrom, Dillard’s, Family Dollar, Saks, Bon-Ton Stores, Belk, and RetailVentures. We then construct three models by following the approach summarized inTable I. Revenue is the output variable for all three models. Relevant input variables arechosen in each model. Table II shows the variables in the models and their descriptivestatistics.

4.2 ResultsThe DEA models used in this study are all input oriented. The first model we tested isan 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 modelssuch as SBM, CCR, and BCC models explained in the previous section. Table III showsthe efficiency scores of the Asset Model computed by SBM, CCR, and BCC DEAmodels, 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, SBMefficiency ¼ [MIX efficiency] £ [BCC efficiency] £ [SE], we use this relationship forinterpreting the results of our analyses. The efficiency scores computed by the DEAmodels in Table III are between zero and one inclusively. SBM scores are the mostrestrictive measure of efficiency as shown with averages in Table III. The averageefficiency score of SBM is 59.28 percent and the lowest among the average efficiencyscores 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 themodels. Target, Sears Holding, and Bon-Ton Stores are 100 percent efficient in the BCCmodel. When we consider CCR and BCC models only, their inefficiency is due to thedifferent 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 OutputAsset 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 InputOther 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 InputReceivables 10.5 6,194.0 873.4 1,651.6 InputInventory 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 InputSG&A 769.4 58,542.0 8,019.6 14,551.7 InputD/A 62.9 5,459.0 816.4 1,364.4 Input

Note: Values in million US dollars

Table II.Descriptive statistics

of variables

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which employs proportional increases and decreases of input and output variables forcomputing efficiency scores. Meanwhile, BCC models apply a non-linear scale. Thesethree companies are locally 100 percent efficient and include inefficiency in the CCRmodel, which may be due to different market conditions. Besides, the three companiesexhibit MIX inefficiency in the SBM model, which is due to the undesirable mix ofresources or the use of input variables. To correct this problem, the companies need toadjust the utilization of input variables or assets by looking at the potentialimprovement 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 theutilization of assets than the other companies in the model. They need to seek a way toimprove 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 to100 percent. It shows that their source of inefficiency is MIX, which is about theinefficient combination of input variables or assets in this case. Macy’s and Nordstromneed fine tuning of assets based on the potential improvements suggested by the DEAmodel. Table IV shows potential improvements of variables for DMUs which are lessthan 100 percent efficient in Table III.

The improvements for the asset model shown in Table IV are computed by using aSBM model. Negative numbers mean reductions in input variables: current, fixed, andother assets. The average scores found in the bottom row of the Table IV reveal thatthe largest inefficiency is from other assets. Based on these results, to increaseefficiency scores, Sears Holdings, Macy’s, JC Penney, Saks, Bon-Ton Stores, and Belkshould virtually eliminate their other assets. The next inefficient variable is fixedassets. Six retailers are urged to cut their fixed assets more than half in order to becompetitive with their peers. When we look at current assets, Saks is the least effectivein the reduction of current assets. JC Penney, Nordstrom, and Belk follow Saks in theirinefficiency of current assets. We do not include potential improvements by CCR andBCC models to avoid redundancy. The way to interpret the improvements by differentmodels is similar to one we have discussed.

DMU SBM CCR (TE) BCC (PTE) MIX SE

Wal-Mart 100.00 100.00 100.00 100.00 100.00Target 48.98 72.24 100.00 67.80 72.24Sears Holdings 50.02 72.81 100.00 68.70 72.81Macy’s 34.15 53.25 54.67 64.13 97.40JC Penney 42.83 61.37 76.31 69.79 80.42Kohl’s 53.99 81.41 91.22 66.32 89.25Dollar General 100.00 100.00 100.00 100.00 100.00Nordstrom 47.56 63.12 64.95 75.35 97.18Dillard’s 43.83 66.72 75.20 65.69 88.72Family Dollar 100.00 100.00 100.00 100.00 100.00Saks 30.27 42.14 70.99 71.83 59.36Bon-Ton Stores 43.61 65.47 100.00 66.61 65.47Belk 34.63 51.86 79.31 66.78 65.39Retail Ventures 100.00 100.00 100.00 100.00 100.00Average 59.28 73.60 86.62 77.36 84.87

Table III.Efficiency scores (%) forthe asset model

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In the second attempt, we assess efficiency of revenues over current assets. Like theasset model, we name the current asset model after the input variables.

Wal-Mart, Target, Kohl’s, Dollar General, Dillard’s, and Bon-Ton Stores are100 percent efficient in the all DEA models in Table V; that is, they are good atmanaging current assets. The majority of companies that are not 100 percent efficientshow SBM efficiency scores of less than 50 percent. Nordstrom and Retail Ventures arenot globally but locally 100 percent efficient. Nordstrom’s major source of inefficiencyis the different mix of current assets, which requires adjustments by managers.For Retail Ventures, its source of inefficiency is on SE, meaning that its inefficiencyis not from managerial factors but from external ones such as market differences. Inaddition to Retail Ventures, Family Dollar, Saks, and Belk have the same issues withtheir SE. Their low efficiency scores are due to the use of different scales or external

DMU Current assets Fixed assets Other assets

Wal-Mart 0.00 0.00 0.00Target 223.12 262.56 267.40Sears Holdings 234.60 221.70 293.63Macy’s 234.94 268.29 298.32JC Penney 243.10 235.50 292.90Kohl’s 213.13 260.83 264.05Dollar General 0.00 0.00 0.00Nordstrom 240.67 234.29 282.35Dillard’s 227.51 266.64 274.36Family Dollar 0.00 0.00 0.00Saks 255.33 263.93 289.94Bon-Ton Stores 228.20 248.08 292.87Belk 241.52 261.18 293.40Retail Ventures 0.00 0.00 0.00Average 224.44 237.36 260.67

Note: Negative numbers mean reduction on input variables or resources

Table IV.Potential improvement(%) of input variables

in the SBM asset model



Table V.Efficiency scores (%) for

the current asset model

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factors in the DEA models. In fact, these companies demonstrate relatively high BCCscores, which represent pure technical or managerial efficiency. Table VI displayspotential improvements computed by the SBM current asset model.

Cash management is the prime source of inefficiency for the companies not 100 percentefficient 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 morethan 70 percent. Accounts receivable is the next inefficient variable. Nordstrom requiresthe highest reduction of receivables followed by Saks and Sears Holdings. Retailersincreasingly engage in credit card business and, as a result, have ended up with higherlevels of receivables than before. Nonetheless, the companies with high receivables mustcompare themselves with peer retailers for the reduction of receivables. Prolongedaccounts receivable can become bad debt in the future. For the last variable in the currentasset model, Macy’s and Belk need to improve their inventory management by cutting thelevel of inventory more than half. Inventory management can be made more efficient byemploying a better model and/or collaborating with suppliers.

The final analysis includes expenses as input variables. The expense model shownin 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 achieve100 percent efficiency. Saks shows the lowest SBM scores with 74.08 percent. Its sourceof inefficiency is the MIX score of 75.66 percent. To improve efficiency, the managers ofSaks should seek a different mix of expenses. Likewise, Dillard’s and Bon-Ton Storesshould take action on the mix of expenses for their store operations. In the BCC modelwith 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 canconclude that most companies in this study are relatively efficient in managing theirexpenses. 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 costsby 22.06 percent. Dollar General and Bon-Ton Stores should reduce their SG&Aexpenses more than ten percent. Saks is least efficient with respect to

DMU Cash Receivables Inventory



Table VI.Potential improvement(%) for the SBM currentasset model

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depreciation/amortization expenses, followed by Dillard’s. Depreciation/amortizationas related to fixed assets should be managed accordingly.

We summarize the comparative efficiency of the companies in the SBM models withdifferent 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. SearsHoldings and Saks do not show 100 percent efficiency in any model in this study. Theremaining companies are 100 percent efficient in at least one model. Finally, efficiencyscores computed by DEA models are relative to DMUs and variables. Accordingly,the different combination of companies and/or variables will yield different scores.



Table VII.Efficiency scores (%)

for the expense model

DMU COGS SG&A Depreciation/amortization



Table VIII.Potential improvement

(%) for the SBMexpense model

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5. ConclusionSince the introduction by Charnes et al. (1978), numerous studies using DEA have beenpublished in various areas. Although DEA is based on estimating the efficiency ofcompanies using the production function concept proposed by Farrell (1957), itsapplications are not limited to the production area. Most published DEA studies areeither developing algorithms or applying DEA in different areas. Although a limitednumber of studies that propose mathematical and procedural approaches for selectingvariables for DEA (Wagner and Shimshak, 2007; Fanchon, 2003) are available, at thetime of this study we fail to find one concerning the selection of variables within atheoretical framework, which is available in the domain of application. Wedemonstrate a framework based on a widely used profitability measure for selectingvariables for DEA and apply it to measuring the efficiency of general merchandisers.

Return on assets or ROA and its components are popular among managers anduser-friendly to managers. ROA is calculated by earnings, which are revenues afterapplicable expenses, divided by total assets. We include components in ROA such asrevenues, expenses, and assets for specifying variables. ROA is a comparative measureof profitability and is not bound by a specific value. Accordingly, users may need tocompare their ROA to the previous values of their ROA and/or those of similarcompanies. In this context, ROA is a good fit with DEA for selecting variables.

We suggest and demonstrate a framework using an example that includes generalmerchandisers. Three models with different input variables are selected and tested:total assets, current assets, and expenses. We find Wal-Mart is the best performeramong the retailers in all models. The second tier group includes Kohl’s, DollarGeneral, and Retail Ventures. In addition to overall efficiency, DEA models provide forpotential improvements in terms of ROA components to the companies that are not100 percent efficient. We confirm that the framework is useful for selecting variablesfor performance measurement and benchmarking.

Finally, our approach is applicable to various studies for performance measurementand benchmarking with minor modifications. Contributions of our study are twofold:first, we suggest a framework for selecting variables for DEA studies; second,

DMU Asset model Current asset model Expense model

Wal-Mart O O OTarget X O XSears Holdings X X XMacy’s X X OJC Penney X X OKohl’s X O ODollar General O O XNordstrom X X ODillard’s X O XFamily Dollar O X XSaks X X XBon-Ton Stores X O XBelk X X ORetail Ventures O X OTotal 4 6 7

Table IX.100 Percent efficientDMUs in the SBM modelswith different inputvariables

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we demonstrate the applicability of the framework using a real world example. Wehope that there will be similar studies with different perspectives and theories forselecting variables in the future.

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About the authorsSeong-Jong Joo is an Associate Professor of Production and Operations Management in HasanSchool of Business, Colorado State University-Pueblo in Pueblo, Colorado. He teaches graduateand undergraduate courses in Operations and Supply Chain Management. His research interestsinclude sourcing/purchasing, supply chain collaboration, inventory management, andperformance measurement/benchmarking. Seong-Jong Joo is the corresponding author and canbe contacted at: [email protected]

Don Nixon is a Professor of Management in the College of Business, Central WashingtonUniversity, Des Moines, Washington. He teaches Strategic Management. His research interestsare developing strategies and measuring the performance of firms.

Philipp A. Stoeberl is the Mary Louis Murray Professor of Management at the John CookSchool of Business, Saint Louis University. He teaches both graduate and undergraduate coursesin Strategy and Current Issues in Management. His current research interests includeperformance measures and benchmarking.

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