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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/(meanof 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 optimalsatisfaction degree by Wu, Chu, Zhu, Li, and Liang 2016)
Thetraditional DEA model allows the DMUs to evaluate their maximum efficiencyscores using their most favourable weights. This kind of evaluation withtotal weight flexibility may prevent the DMUs from being fully ranked andmake the evaluation results unacceptable to the DMUs. To solve theseproblems, Wu et al (2016) introduce a common weights model with the conceptof satisfaction degree of a DMU in relation to a common set of weights. Thecommon-weight evaluation approach can generate for the DMUs a set of commonweights that maximizes the least satisfaction degrees among the DMUs, and canensure that the generated common set of weights is unique and that the finalsatisfaction degrees of the DMUs constitute a Pareto-optimal solution. All ofthese factors make the evaluation results more satisfied and acceptable byall the DMUs.
Ø Minimum Efficiency model (PessimisticDEA by Entani, Maeda, and Tanaka 2002)
Thetraditional DEA model seeks to maximize the efficiency score of the evaluatedDMU using the most favorable set of input and output weights under the constraintthat the efficiency scores of all DMUs are less than or equal to one.
Entaniet al (2002) put forth a minimum efficiency model (a pessimistic DEA model).On the contrary, the minimum efficiency model seeks to minimize theefficiency score of the evaluated DMU using the most unfavorable set of inputand output weights under the constraint that the maximum efficiency of allDMUs is equal to one.
Ø Interval DEA(Entani, Maeda, and Tanaka 2002)
Whilethe traditional DEA is the evaluation model from the optimistic viewpoint,Entani, Maeda, and Tanaka (2002) propose an evaluation model from thepessimistic viewpoint, then an interval of efficiency with the upper andlower limitscan be constructed. It is called Interval DEA. The upper limit is the efficiencyfrom the optimistic model (traditional DEA), and the lower limit is from thepessimistic 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 traditionalVRS 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 areavailable for Cross-efficiency model
1)Maximize/Minimizethe tradebalance of other DMUs as a whole (the existing method)
a) Blanket Benevolent (Type I in Doyleand Green 1995)
b) Blanket Aggressive (Type I in Doyleand Green 1995)
2)Maximize/Minimize the cross-efficiency of other DMUs as a whole (newly added)
c) Blanket Benevolent (Type II inDoyle and Green 1995)
d) Blanket Aggressive (Type II inDoyle 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 Doyleand Green 1995)
f) Targeted Aggressive (Type IV inDoyle and Green 1995)
l The results of the Malmquist modelsare re-designed,and they are easier to understand and more convenient to use. In addition, the biased technological change isadded to Malmquist results. TC=OBTC*IBTC*MATC. (Fare et al 1997)
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