DEA Models available in MaxDEA X

Model Type

1)          Envelopment Model

2)          Multiplier Model

3)          FDH Model


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 (Closest Target), with complete options: strong monotonicity algorithm; CRS, VRS, NIRS and NDRS; Non-oriented, Input-oriented and Output-oriented.

         Ref. to  (J. Aparicio et al., 2007; G. R. Jahanshahloo et al., 2012; Gholam Reza Jahanshahloo, Roshdi, & Davtalab-Olyaie, 2013; Olyaie, Roshdi, Jahanshahloo, & Asgharian, 2014; J Aparicio et al., 2017; Zhu et al., 2018; Zhu et al., 2022)

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

Direction Vector can be

a) Value of the evaluated 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)

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 Measure): (EBM, Epsilon-based Meaure,Tone and Tsutsui 2010)

8)          Cost

9)          Revenue


Orientation to measure efficiency

1)    Input-oriented

2)    Output-oriented

3)    Non-oriented


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)         Decomposition of Efficiency or TFP Index


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)

g)           Global with Sequential Malmquist

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

Three types of indices can be computed: Index(t-1, t); Index (t-n, t) n is user-defined; Index (t0, t)t0 is the initial period.


Window DEA


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


Other models

1)        Super-efficiency model

2)        Modified SBM (Sharp et al 2007)

3)        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)

Maximize/Minimize the cross-efficiency of a customized virtual DMU

g) Benevolent (customized)

h) Aggressive (customized)

4)        Game Cross Efficiency model: Nash Equilibrium model (Liang, et al 2008; Wu, et al 2009)

5)        Undesirable outputs, desirable inputs

6)        Nondiscretionary input/output model

7)        Preference (weighted) model

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


What’s more important, like MaxDEA Ultra, MaxDEA X also provides nearly all possible combinations of the above models.