Ø   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)

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

The  traditional DEA model allows the DMUs to evaluate their maximum efficiency  scores using their most favourable weights. This kind of evaluation with  total weight flexibility may prevent the DMUs from being fully ranked and  make the evaluation results unacceptable to the DMUs. To solve these  problems, Wu et al (2016) introduce a common weights model with the concept  of satisfaction degree of a DMU in relation to a common set of weights. The  common-weight evaluation approach can generate for the DMUs a set of common  weights that maximizes the least satisfaction degrees among the DMUs, and can  ensure that the generated common set of weights is unique and that the final  satisfaction degrees of the DMUs constitute a Pareto-optimal solution. All of  these factors make the evaluation results more satisfied and acceptable by  all the DMUs.

Ø   Minimum Efficiency model (Pessimistic  DEA by Entani, Maeda, and Tanaka 2002)

The  traditional DEA model seeks to maximize the efficiency score of the evaluated  DMU using the most favorable set of input and output weights under the constraint  that the efficiency scores of all DMUs are less than or equal to one.

Entani  et al (2002) put forth a minimum efficiency model (a pessimistic DEA model).  On the contrary, the minimum efficiency model seeks to minimize the  efficiency score of the evaluated DMU using the most unfavorable set of input  and output weights under the constraint that the maximum efficiency of all  DMUs is equal to one.

Ø   Interval DEA  (Entani, Maeda, and Tanaka 2002)

While  the traditional DEA is the evaluation model from the optimistic viewpoint,  Entani, Maeda, and Tanaka (2002) propose an evaluation model from the  pessimistic viewpoint, then an interval of efficiency with the upper and  lower limits  can be constructed. It is called Interval DEA. The upper limit is the efficiency  from the optimistic model (traditional DEA), and the lower limit is from the  pessimistic DEA (minimum efficiency model).

Ø   New types of non-convex models

Non-convex:  Free Disposal Hull (FDH). The CRS,  NIRS, NDRS and GRS FDH models are added in additional to the traditional  VRS FDH model

Non-convex:  Elementary Replicability Hull, ERH  (AGRELL and TIND 2001)

Non-convex:  Free Replicability Hull, FRH  (Tulkens 1993; AGRELL and TIND 2001)

Ø   More second-stage methods are  available for Cross-efficiency model

1)  Maximize/Minimize  the trade  balance of other DMUs as a whole (the existing method)

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

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

2)  Maximize/Minimize the cross-efficiency of other DMUs as a whole (newly added)

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

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

3)  Maximize/Minimize the cross-efficiency of each of other DMUs one by one  (newly added)

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

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

l   The results of the Malmquist models  are re-designed,  and they are easier to understand and more convenient to use. In addition, the biased technological change is  added to Malmquist results. TC=OBTC*IBTC*MATC. (Fare et al 1997)