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 full features: 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)        Modified SBM (Lin et al 2019)

4)        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)

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

6)        Undesirable outputs, desirable inputs

7)        Nondiscretionary input/output model

8)        Preference (weighted) model

9)        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.