The author is one of the prominent researchers in the field of Data Envelopment Analysis (DEA), a powerful data analysis tool that can be used in performance evaluation and benchmarking. This book is based upon the author’s years of research and teaching experiences. It is difficult to evaluate an organization’s performance when multiple performance metrics are present. The difficulties are further enhanced when the relationships among the performance metrics are complex and involve unknown tradeoffs. This book introduces Data Envelopment Analysis (DEA) as a multiple-measure performance evaluation and benchmarking tool. The focus of performance evaluation and benchmarking is shifted from characterizing performance in terms of single measures to evaluating performance as a multidimensional systems perspective. Conventional and new DEA approaches are presented and discussed using Excel spreadsheets – one of the most effective ways to analyze and evaluate decision alternatives. The user can easily develop and customize new DEA models based upon these spreadsheets. DEA models and approaches are presented to deal with performance evaluation problems in a variety of contexts. For example, a context-dependent DEA measures the relative attractiveness of similar operations/processes/products. Sensitivity analysis techniques can be easily applied, and used to identify critical performance measures. Two-stage network efficiency models can be utilized to study performance of supply chain. DEA benchmarking models extend DEA’s ability in performance evaluation. Various cross efficiency approaches are presented to provide peer evaluation scores. This book also provides an easy-to-use DEA software – DEAFrontier. This DEAFrontier is an Add-In for Microsoft® Excel and provides a custom menu of DEA approaches. This version of DEAFrontier is for use with Excel 97-2013 under Windows and can solve up to 50 DMUs, subject to the capacity of Excel Solver. It is an extremely powerful tool that can assist decision-makers in benchmarking and analyzing complex operational performance issues in manufacturing organizations as well as evaluating processes in banking, retail, franchising, health care, public services and many other industries.

1 Data Envelopment Analysis 1

1.1 Performance Evaluation and Tradeoffs 1

1.2 Data Envelopment Analysis 3

1.3 Performance Metrics Classified as Inputs and Outputs 5

1.4 Number of DMUs vs Number of Inputs and Outputs 7

1.5 Measuring and Managing Performance 8

References 9

2 Envelopment DEA Models 11

2.1 Introduction 11

2.2 Variable Returns-to-Scale (VRS) Model 12

2.3 DEA Slacks 17

2.4 Other Envelopment Models 19

2.5 Envelopment Models in Spreadsheets 21

      2.5.1 Input-Oriented VRS Envelopment Spreadsheet Model 22

      2.5.2 Using Solver 23

      2.5.3 Setting the Objective Cell and Changing Variable Cells 24

      2.5.4 Adding Constraints and Selecting Solving Method 24

      2.5.5 Solving the Model 26

      2.5.6 Automating the DEA Calculation 27

      2.5.7 Second-Stage Slack Calculation 32

      2.5.8 Other Input-Oriented Envelopment Spreadsheet Models 34

2.6 Output-Oriented Envelopment Spreadsheet Models 34

2.7 Using OpenSolver 39

2.8 Solving DEA Using DEAFrontier Software 42

      2.8.1 Data Sheet Format 44

      2.8.2 Envelopment Models 45

      References 48

3 Multiplier DEA Model 49

3.1 Multiplier Models in Spreadsheets 49

3.2 Weight Restrictions in Multiplier Models 54

3.3 Solving Multiplier Models Using DEAFrontier 58

References 60

4 DEA Cross Efficiency 61

4.1 Introduction 61

4.2 Cross Efficiency 62

4.3 Cross Efficiency in Spreadsheets 65

4.4 Game Cross Efficiency 66

      4.4.1 Input-oriented Game Cross Efficiency 67

      4.4.2 Output-oriented Game Cross Efficiency 73

      4.4.3 Output-oriented VRS Game Cross Efficiency 77

4.5 Maximum Log Cross Efficiency 81

      4.5.1 Multiplicative DEA Model 81

      4.5.2 Maximum Log Cross Efficiency 86

      References 92

5 Slack-Based DEA Models 93

5.1 Slack-Based Models 93

5.2 Slack-Based Models in Spreadsheets 95

5.3 Solving Slack-Based DEA Model Using DEAFrontier Software 100

References 101

6 Measure-Specific DEA Models 103

6.1 Measure-Specific Models 103

6.2 Measure-Specific Models in Spreadsheets 105

6.3 Performance Evaluation of Fortune 500 Companies 106

      6.3.1 Identification of Best Practice Frontier 107

      6.3.2 Measure-Specific Performance 108

      6.3.3 Benchmark Share 112

6.4 Solving Measure-Specific Models Using DEAFrontier Software 119 References 119

7 Non-radial DEA Models and DEA with Preference 121

7.1 Non-radial DEA Models 121

7.2 DEA with Preference Structure and Cost/Revenue Efficiency 123

7.3 DEA/Preference Structure Models in Spreadsheets 127

7.4 DEA and Multiple Objective Linear Programming 128

      7.4.1 Output-oriented DEA 129

      7.4.2 Input-oriented DEA 133

      7.4.3 Non-Orientation DEA 134

7.5 Using DEAFrontier Software 135

      7.5.1 Non-radial Models 135

      7.5.2 Preference-Structure Models 135

      7.5.3 Cost Efficiency, Revenue Efficiency and Profit Efficiency 137 References 140

8 Modeling Undesirable Measures 141

8.1 Introduction 141

8.2 Efficiency Invariance 141

8.3 Undesirable Outputs 143

8.4 Undesirable Inputs 145

8.5 Solving DEA Using DEAFrontier Software 148

8.6 Negative Data 148

References 151

9 Context-dependent Data Envelopment Ana lysis 153

9.1 Introduction. 153

9.2 Stratification DEA Method 154

9.3 Input-oriented Context-dependent DEA 158

      9.3.1 Attractiveness 158

      9.3.2 Progress 164

9.4 Output-oriented Context-dependent DEA 166

9.5 Solving DEA Using DEAFrontier Software 171

References 174

10 Super Efficiency 175

10.1 Super-Efficiency DEAModels 175

10.2 Infeasibility of Super-efficiency DEA Models 177

      10.2.1 Output-Oriented VRS Super-Efficiency Model 183

      10.2.2 Other Output-oriented Super-efficiency Models 188

      10.2.3 Input-Oriented VRS Super-Efficiency Model 188

      10.2.4 Other Input-oriented Super-efficiency Models 192

10.3 Models for Dealing with Infeasibility 193

10.4 Zero Data and Infeasibility 197

10.5 Slack-Based Super Efficiency 201

10.6 Solving Super-Efficiency Using DEA Frontier 203

References 205

11 Sensitivity Analysis 207

11.1 DEA Sensitivity Analysis 207

11.2 Stability Region 209

      11.2.1 Input Stability Region 209

      11.2.2 Output Stability Region 213

      11.2.3 Geometrical Presentation of Input Stability Region 215

11.3 Infeasibility and Stability 222

11.4 Simultaneous Data Change 226

      11.4.1 Sensitivity Analysis Under CRS 228

      11.4.2 Sensitivity Analysis Under VRS 237

      11.4.3 Spreadsheet Models for Sensitivity Analysis 239

11.5 Sensitivity Analysis Using DEAFrontier 243

References 244

12 Benchmarking Models 245

12.1 Introduction 245

12.2 Variable-benchmark Model 245

12.3 Fixed-benchmark Model 255

12.4 Fixed-benchmark Model and Efficiency Ratio 259

12.5 Minimum Efficiency Model 263

12.6 Buyer-seller Efficiency Model 267

12.7 Acceptance System Decision 270

12.8 Solving Benchmarking Models Using DEAFrontier 274

      12.8.1 Variable-Benchmark Models 274

      12.8.2 Fixed-Benchmark Models 275

      12.8.3 Minimum Efficiency Models 275

      References 276

13 Returns-to-Scale 277

13.1 Introduction 277

13.2 RTS Regions 277

13.3 RTS Estimation 278

      13.3.1 VRS and CRS RTS Methods 278

      13.3.2 Improved RTS Method 280

      13.3.3 Spreadsheets for RTS Estimation 282

13.4 Scale Efficient Targets 286

13.5 Solving DEA Using DEAFrontier Software 288

References 289

14 DEA Models for Two-Stage Network Processes 291

14.1 Introduction 291

14.2 VRS Two-Stage Model 292

14.3 CRS Two-Stage Model: Centralized Model 298

14.4 CRS Two-Stage Model: Equivalence 301

14.5 Frontier Projection 304

14.6 CRS Two-Stage Model: Leader-Follower Model 305

14.7 Solving Two-Stage Network Process Using DEAFrontier 307

References 309

15 Models for Evaluating Supply Chains and Network Structures 311

15.1 Supply Chain Efficiency 311

15.2 Supply Chain Efficiency 312

      15.2.1 Supply Chain as an Input-Output System 313

      15.2.2 Supply Chain Efficiency Model 316

      15.2.3 An example 319

15.3 Cooperative and Non-Cooperative Approaches 324

      15.3.1 The Non-Cooperative Model 325

      15.3.2 The Cooperative Model 331

15.4 Additive Efficiency Decomposition to Network Structures 334

      15.4.1 DEA Model for General Multi-Stage Serial Processes 335

      15.4.2 General Multistage Processes 338

      15.4.3 An Illustrative Application 340

      References 344

16 Congestion 345

16.1 Congestion Measure 345

16.2 Congestion and Slacks 350

16.3 Slack-Based Congestion Measure 353

16.4 Solving Congestion Using DEAFrontier 359

References 360

17 Identifying Critical Measures in DEA 363

17.1 Introduction 363

17.2 Performance Evaluation and DEA 363

17.3 Identifying Critical Output Measures 368

17.4 Identifying Critical Input Measures 369

17.5 Numerical Example and Extension 370

17.6 Application to Fortune E-Companies 372

References 381

18 Interval and Ordinal Data in DEA 383

18.1 Introduction 383

18.2 Imprecise Data 384

18.3 Multiplier IDEA (M1DEA): Standard DEA Model Approach 387

      18.3.1 Converting the Bounded Data into a Set of Exact Data 387

      18.3.2 Converting the Weak Ordinal Data into a Set of Exact Data 388

      18.3.3 Numerical Illustration 389

      18.3.4 Converting the Strong Ordinal Data and Ratio Bounded Data into a Set of Exact Data 392

18.4 Treatment of Weight Restrictions 393

18.5 Envelopment IDEA (EIDEA) 395

18.6 Conclusions 397

References 398

19 DEAFrontier Software 399

19.1 Introduction 399

19.2 DEA Bootstrapping 399

19.3 Free Disposal Hull (FDH) 400

19.4 Mamquist Approach 402

19.5 DEAFrontier Models 404

References 407

Licensing and Warranty Agreement 409

Index 411

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