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): ( -|x0|, |y0|, -|b0| )'
b): ( -|x̅|, |y̅|, -|b̅| )'
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/|x̅|, 1/|y̅|
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) Constant 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
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)
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 other DMUs as a whole
e) Blanket Benevolent (Ruiz (2013))
f) Blanket Aggressive (Ruiz (2013))
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 (Set Input/output Weights)
9) Restricted multiplier model (assurance region model, trade-offs between inputs and outputs)
What's more important, MaxDEA X provides nearly all possible combinations of the above models.