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. StoeberlJohn Cook School of Business, Saint Louis University, St Louis, Missouri, USAAbstractPurpose – 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 measuresPaper type Research paper1. 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 DEA Benchmarking: An Internationalmodels must be guided by relevant theories and approaches. For example, if researchers Journal Vol. 18 No. 4, 2011are interested in measuring the comparative efﬁciency of organizations using DEA, they pp. 529-542may try endogenous and exogenous variables from related organization theories. q Emerald Group Publishing Limited 1463-5771Likewise, 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 are18,4 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’s530 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 ROAusing DEA. The selected recent applications of DEA for benchmarking includeevaluating coffee stores ( Joo et al., 2009), third party logistics providers (Min and Joo, perspective2009), emergency medical services (Lambert et al., 2009), and telecommunicationcompanies (Kwon et al., 2008).2.2 Data envelopment analysis 531DEA 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: nXR o r¼1 ur0 yr0 Maximize E 0 ¼ nXI o ð1Þ i¼1 vi0 xi0subject to: nXR o r¼1 ur0 yrk nXI o # 1 for all k ð2Þ i¼1 vi0 xik ur0 ; vi0 $ d for all r; i; ð3Þwhere: 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
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 ROAis available in companies’ income statements. Total assets, which are entries in ﬁrms’ perspectivebalance 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. Unlike 533current 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: EAT Revenues ROA ¼ Profitability £ Speed ðor turnsÞ ¼ £ : Revenues Total assetsProﬁtability 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 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 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.
6. BIJ Revenues are generated by the various activities of ﬁrms. There are basically two types18,4 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, when534 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 ofTable I. revenues revenuesCombination 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 ROAwe are not free from all limits on the comparison of ﬁnancial data from different ﬁrms. perspective4. 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, Dollar 535General, 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 TypeAll 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 Input Other assets 26.2 16,165.0 2,664.9 4,716.5 InputCurrent 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 InputExpense 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 statisticsNote: Values in million US dollars of variables
8. BIJ DMU SBM CCR (TE) BCC (PTE) MIX SE18,4 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 80.42536 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 65.47Table III. Belk 34.63 51.86 79.31 66.78 65.39Efﬁciency scores (%) for Retail Ventures 100.00 100.00 100.00 100.00 100.00the 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 ROADMU Current assets Fixed assets Other assets perspectiveWal-Mart 0.00 0.00 0.00Target 223.12 262.56 2 67.40Sears Holdings 234.60 221.70 2 93.63Macy’s 234.94 268.29 2 98.32JC Penney 243.10 235.50 2 92.90 537Kohl’s 213.13 260.83 2 64.05Dollar General 0.00 0.00 0.00Nordstrom 240.67 234.29 2 82.35Dillard’s 227.51 266.64 2 74.36Family Dollar 0.00 0.00 0.00Saks 255.33 263.93 2 89.94Bon-Ton Stores 228.20 248.08 2 92.87Belk 241.52 261.18 2 93.40Retail Ventures 0.00 0.00 0.00 Table IV.Average 224.44 237.36 2 60.67 Potential improvement (%) of input variablesNote: Negative numbers mean reduction on input variables or resources in the SBM asset modelIn 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 externalDMU SBM CCR (TE) BCC (PTE) MIX SEWal-Mart 100.00 100.00 100.00 100.00 100.00Target 100.00 100.00 100.00 100.00 100.00Sears Holdings 39.07 51.70 53.68 75.57 96.31Macy’s 45.46 46.91 52.66 96.91 89.08JC Penney 44.51 59.06 65.13 75.36 90.68Kohl’s 100.00 100.00 100.00 100.00 100.00Dollar General 100.00 100.00 100.00 100.00 100.00Nordstrom 37.63 82.93 100.00 45.38 82.93Dillard’s 100.00 100.00 100.00 100.00 100.00Family Dollar 51.42 61.95 91.05 83.00 68.04Saks 36.88 45.07 90.77 81.83 49.65Bon-Ton Stores 100.00 100.00 100.00 100.00 100.00Belk 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 (%) forAverage 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 BCC18,4 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 more538 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 51.12 261.80Table VI. Retail Ventures 274.99 2 46.03 245.68Potential improvement Average 238.64 2 34.23 224.93(%) for the SBM currentasset model Note: Negative numbers mean reduction on input variables or resources
11. A ROADMU SBM CCR (TE) BCC (PTE) MIX SE perspectiveWal-Mart 100.00 100.00 100.00 100.00 100.00Target 93.04 96.94 100.00 95.98 96.94Sears Holdings 89.99 95.45 96.74 94.28 98.67Macy’s 100.00 100.00 100.00 100.00 100.00JC Penney 100.00 100.00 100.00 100.00 100.00 539Kohl’s 100.00 100.00 100.00 100.00 100.00Dollar General 86.40 93.66 99.38 92.25 94.24Nordstrom 100.00 100.00 100.00 100.00 100.00Dillard’s 79.81 95.33 95.82 83.72 99.49Family Dollar 92.44 95.88 100.00 96.41 95.88Saks 74.08 97.91 100.00 75.66 97.91Bon-Ton Stores 83.41 98.43 100.00 84.74 98.43Belk 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 modelDMU COGS SG&A Depreciation/amortizationWal-Mart 0.00 0.00 0.00Target 0.00 0.00 2 20.87Sears Holdings 0.00 2 8.01 2 22.03Macy’s 0.00 0.00 0.00JC Penney 0.00 0.00 0.00Kohl’s 0.00 0.00 0.00Dollar General 0.00 2 14.26 2 26.55Nordstrom 0.00 0.00 0.00Dillard’s 0.00 2 8.40 2 52.16Family Dollar 0.00 2 8.86 2 13.83Saks 0.00 2 22.06 2 55.69Bon-Ton Stores 0.00 2 10.45 2 39.33Belk 0.00 0.00 0.00Retail Ventures 0.00 0.00 0.00 Table VIII.Average 0.00 2 5.15 2 16.46 Potential improvement (%) for the SBMNote: Negative numbers mean reduction on input variables or resources expense modeldepreciation/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.
12. BIJ DMU Asset model Current asset model Expense model18,4 Wal-Mart O O O Target X O X Sears Holdings X X X Macy’s X X O540 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 XTable IX. Saks X X X100 Percent efﬁcient Bon-Ton Stores X O XDMUs in the SBM models Belk X X Owith different input Retail Ventures O X Ovariables 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,
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14. BIJ Min, H. and Joo, S. (2009), “Benchmarking third-party logistics providers using data envelopment analysis: an update”, Benchmarking: An International Journal, Vol. 16 No. 5, pp. 572-87.18,4 Nunes, B. and Bennett, D. (2010), “Green operations initiatives in the automotive industry: an environmental reports analysis and benchmarking study”, Benchmarking: An International Journal, Vol. 17 No. 3, pp. 396-420. Schneider, J.L., Wilson, A. and Rosenbeck, J.M. (2010), “Pharmaceutical companies and542 sustainability: an analysis of corporate reporting”, Benchmarking: An International Journal, Vol. 17 No. 3, pp. 421-34. Sherman, H. and Ladino, G. (1995), “Managing bank productivity using data envelopment analysis”, Interfaces, Vol. 25 No. 2, pp. 60-73. Wagner, J. and Shimshak, D. (2007), “Stepwise selection of variables in data envelopment analysis: procedures and managerial perspectives”, European Journal of Operational Research, Vol. 180 No. 1, pp. 57-67. 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: firstname.lastname@example.org 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. To purchase reprints of this article please e-mail: email@example.com Or visit our web site for further details: www.emeraldinsight.com/reprints