DEA Models available in MaxDEA Ultra


MaxDEA Ultra has the most comprehensive DEA models and nearly all their possible combinations, such as the combination of “Undesirable Outputs” and “Malmquist” (Malmquist-Luenberger Productivity Index).

Distance to measure efficiency

1)          Radial (CCR 1978; BCC 1984)

2)          Maximum Distance to Frontier (ERM, Enhanced Russel Measure, Pastor, Ruiz, and Sirvent 1999;  SBM, Slacks-based Measure, Tone 2001)

3)          Minimum Distance to Weak  Efficient Frontier (Charnes, Roussea, and Semple1996)

4)          Minimum Distance to Strong Efficient Frontier (Aparicio, Ruiz, and Sirvent 2007)

5)          Directional Distance Function (Chambers, Chung, and  Färe 1996; Chung, Färe, and Grosskopf 1997)

Direction Vector can be

a) Value of the evaluted DMU (x0, y0)

b) Mean of All DMUs

c) Vector  (1, 1,  ……, 1)

d) Range (RDM, Portela, Thanassoulis, and Simpson 2004)

e) Customized (same for all DMUs)

f) Customized (DMU specific)

g) Direction Vector Scanning

6)          A Series of Weighted Additive Models

a) Simple Additive model: Weights = (1, 1, 1, ...)

b) Normalized Weighted Additive (Lovell and Pastor 1995)

c) Weights = 1/x0, 1/y0

d) Weights = 1/(mean of x0), 1/(mean of y0)

e) Range Adjusted Measure (RAM, Cooper, Park, and Pastor 1999)

f) Bounded Adjusted Measure (BAM, Cooper, Pastor, Borras, Aparicio, and Pastor 2011)

g) Directional Slacks-based Measure (DSBM, Fukuyama and Weber 2009)

h) Customized Weights (same for all DMUs)

i) Customized Weights (DMU specific)

7)          Hybrid Distance(Radial and SBM Fields)

8)          Hybrid Distance(Radial and SBM Measure): (EBM, Epsilon-based Meaure,Tone and Tsutsui 2010)

9)          Cost /Revenue / Profit / Revenue-cost ratio


Orientation to measure efficiency

1)     Input-oriented

2)    Output-oriented

3)    Non-oriented

4)    Input-oriented (modified)

5)    Output-oriented (modified)

6)    Non-oriented (input-prioritized)

7) Non-oriented (output-prioritized)

8) Non-oriented (generalized priority)


RTS to measure efficiency

1)          Constance returns to scale (CRS)

2)          Variable returns to scale (VRS)

3)          Non-increasing returns to scale (NIRS)

4)          Non-decreasing returns to scale (NDRS)

5)          Generalized returns to scale (GRS)


Frontier type to measure efficiency

1)          Convex: Data Envelopment Analysis, DEA (RTS available: CRS, VRS, NIRS, NDRS, GRS)

2)          Non-convex: Free Disposal Hull, FDH (RTS available: CRS, VRS, NIRS, NDRS, GRS)

3)          Non-convex: Elementary Replicability Hull, ERH (Agrell and Tind 2001)

4)          Non-convex: Free Replicability Hull, FRH (Tulkens 1993; Agrell and Tind 2001)


Productivity measure (TFP Index): Malmquist Index and Hicks-Moorsteen Index (also called HMB Index)

a)           Adjacent Malmquist

b)          Fixed Malmquist

c)           Global Malmquist

d)          Sequential Malmquist

e)           Window-Malmquist (Adjacent)

f)           Window-Malmquist (Fixed)

TFP index decomposition: Efficiency Change (catch-up), Technological Change (frontier shift), Scale Efficiency Change, biased Technological Change, TC=OBTC*IBTC*MATC (Fare et al 1997)


Window model


Cluster model

a)           Self-benchmarking

b)          Cross-benchmarking

c)           Downward-benchmarking

d)          Upward-benchmarking

e)           Lower-adjacent-benchmarking

f)           Upper-adjacent-benchmarking

g)          Window-benchmarking

h)          Fixed-benchmarking


Customized reference ret model

1)          Variable-benchmark model

2)          Fixed-benchmark model


Other models

1) Super-efficiency model

2) Undesirable outputs model

3) Network model (Based on the framework by Tone, and Tsutsui 2009; Also Ref. to Tavana, Mirzagoltabar, Mirhedayatian, Saen, and Azadi 2013)

4) Two-Stage Network (Inputs --> Intermediates --> Outputs) (Kao and Hwang 2008)

5) Modified SBM (Sharp et al 2007)

6) Cross efficiency model

Second-stage methods are available:

Minimize/Maximize the trade balance of other DMUs as a whole

a) Blanket Benevolent (Type I in Doyle and Green 1995)

b) Blanket Aggressive (Type I in Doyle and Green 1995)

Maximize/Minimize the cross-efficiency of other DMUs as a whole

c) Blanket Benevolent (Type II in Doyle and Green 1995)

d) Blanket Aggressive (Type II in Doyle and Green 1995)

Maximize/Minimize the cross-efficiency of each of other DMUs one by one

e) Targeted Benevolent (Type IV in Doyle and Green 1995)

f) Targeted Aggressive (Type IV in Doyle and Green 1995)

7) Game Cross Efficiency model: Nash Equilibrium model (Liang, et al 2008; Wu, et al 2009) and Aggressive model (Liu, et al 2017)

8) Common Weights Model (Pareto optimal satisfaction degree by Wu, Chu, Zhu, Li, and Liang 2016)

9) Nondiscretionary input/output model (non-controllable model, measure specific model)

10) Bounded input/output model

11) Preference (weighted) model

12) Restricted projection model

13) Weak disposability model

14) Restricted multiplier model (assurance region model, trade-offs between inputs and outputs)

15) MetaFrontier DEA (Rao, O'Donnell, and Battese 2003)

16) Non-concave MetaFrontier DEA (Tiedemann, Francksen, and Latacz-Lohmann 2011)

17) Integer DEA: Integer-valued Inputs/Outputs (Kuosmanen and Matin 2009; Matin and Kuosmanen 2009)

18) All the above DEA models can be combined with the Malmquist model

19) Minimum Efficiency model (Pessimistic DEA) and Interval DEA (Entani, Maeda, and Tanaka 2002)

20) Parallel Network (Kao 2009)

21) Context-dependent (Seiford, and Zhu 2003)

22) Fuzzy DEA

23) Dynamic model (for panel data)

24) Bootstrap

a) Bootstrap of DEA Score

b) Bootstrap of Malmquist Index


Most important of all, MaxDEA Ultra provides nearly all the possible combinations of up-to-date DEA models. To use a combination of multiple DEA models, just choose all the relevant options.