MaxDEA update history
Version 
What’s
New 
7.9 Ultra 
l
Frontier type options
are available in frontier plotted through scanning. 
7.8 Ultra 
l
Undesirable Outputs
can be combined with Game Cross
Efficiency model. 
7.7 Ultra 
l
Undesirable Outputs
can be combined with Cross Efficiency
model. 
7.6 Ultra 
l
An additional option “Do Not Rescale Data” is available for
Multiplier model when the epsilon
(the minimal value of weight) is set. 
7.5 Ultra 
l
The results for
Malmquist model with RTS = “Scale Efficiency…” are improved so that it is more convenient to find the components
for different types of decomposition. 
7.4 Ultra 
l The Dynamic DEA can be
combined with the Network DEA, i.e., the
Dynamic Network DEA. 
7.3 Ultra 
l Crossefficiency and Game Crossefficiency can be combined
with Window model l Multicore CPU parallel computing is improved (faster
speed) for Window model, Cluster model, and some types of Malmquist models 
7.2 Ultra 
l The commonweights model can be applied to panel data (it can be combined with
Window model or Global Malmquist model). 
7.1 Ultra 
l The series of Weighted Additive models (simple additive,
normalized weighted additive, …, RAM, BAM, DSBM, …) can be applied to panel data, i.e., they
can be combined with Window, Malmquist (or Luenberger)
index models. 
7.0 Ultra Major
Update 
l Many new models added in MaxDEA 7
Ultra 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 Slacksbased 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 commonweight 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 Paretooptimal 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 nonconvex models Nonconvex: Free Disposal Hull (FDH). The CRS, NIRS, NDRS and GRS FDH models
are added in additional to the traditional VRS FDH model Nonconvex: Elementary Replicability Hull, ERH (AGRELL and TIND 2001) Nonconvex: Free Replicability Hull, FRH (Tulkens 1993; AGRELL and TIND
2001) Ø More secondstage methods are available for
Crossefficiency 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 crossefficiency 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 crossefficiency 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 redesigned, 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) l Interface improved: Fluent ribbon replaces traditional
menu. References AGRELL, P. J., & TIND, J.
(2001). A Dual Approach to Nonconvex Frontier Models. Journal of Productivity
Analysis, 16, 129147. Cooper, W. W., Park, K. S., &
Pastor, J. T. (1999). RAM: A range adjusted measure of inefficiency for use
with additive models, and relations to other models and measures in DEA.
Journal of Productivity Analysis, 11(1), 542. Cooper, W. W., Pastor, J. T., Borras, F., Aparicio, J., &
Pastor, D. (2011). BAM: a bounded adjusted measure of efficiency for use with
bounded additive models. Journal of Productivity Analysis, 35(2), 8594. doi: 10.1007/s1112301001902 Doyle, J. R., & Green, R. H.
(1995). Crossevaluation in DEA: Improving discrimination among DMU’s. Infor
Information Systems & Operational Research, 33(3), 205222. Entani, T., Maeda, Y., &
Tanaka, H. (2002). Dual models of interval DEA and its extension to interval
data. European Journal of Operational Research, 136(1), 3245. doi: http://dx.doi.org/10.1016/S03772217(01)000558 Färe, R., GrifellTatjé, E., Grosskopf,
S., & Knox Lovell, C. A. (1997). Biased Technical Change and the
Malmquist Productivity Index. Scandinavian Journal of Economics, 99(1),
119127. doi: 10.1111/14679442.00051 Fukuyama, H., & Weber, W. L.
(2009). A directional slacksbased measure of technical inefficiency.
SocioEconomic Planning Sciences, 43(4), 274287. doi:
10.1016/j.seps.2008.12.001 Lovell, C. A. K., & Pastor, J.
T. (1995). Units invariant and translation invariant DEA models. Operations
Research Letters, 18(3), 147151. Podinovski, V. V. (2004). On the linearisation of reference technologies for testing
returns to scale in FDH models. European Journal of Operational Research,
152(3), 800802. doi:
http://dx.doi.org/10.1016/S03772217(02)007026 Wu, J., Chu, J., Zhu, Q., Li, Y.,
& Liang, L. (2016). Determining common weights in data envelopment
analysis based on the satisfaction degree. Journal of the Operational Research
Society. doi: 10.1057/jors.2016.35 
6
Ultra/Pro 

6.19 
l Minor improvements 
6.18 
l The online registration/verification of fixed license is
faster and more stable. 
6.17 
l For Network or Dynamic model, if the “intermediate” data are
all integer values, they may be imported incorrectly. This has been fixed. l The MetaFrontier and Nonconcave Metafrontier models, and the function “Frontier Plotted
through Scanning (if RTS = 2 RTS types）” are not supported in the Access runtime environment. This
has been improved. Now all of them can run in the runtime environment. 
6.16 
l SBM Network model and SBM Dynamic model improved. Two options added under the option “Node Score Including
Intermediates”: “NonIncreasing intermediates treated
as input only” and “NonDecreasing intermediates
treated as output only”. In SBM Network model and SBM Dynamic model, when
slacks of the intermediates are included in computing node scores, these two
options can limit the node scores within 01, i.e., avoid the node scores
greater than 1 or less than 0. 
6.15 
l Problems with the EBM model are resolved. When the EBM model is combined with MetaFrontier,
the EBM parameters (epsilon and weights) are calculated separately in the MetaFrontier and GroupFrontier
models, i.e., the MetaFrontier model and the GroupFrontier model use their own parameters. The MetaFrontier scores and the GroupFrontier
scores are computed using different EBM parameters, so they are not
comparable, and the computed TGRs may be greater than 1. For the same reason, when the EBM model is used to compute
Scale Efficiency, The CRS scores and the VRS scores are computed using
different EBM parameters, so they are not comparable, and the computed scale
efficiency scores may be greater than 1. And when the EBM model is combined with Fuzzy
inputs/outputs, the upper bound score may be less than the lower bound score.
To
avoid the above problems, the user must use the “Customized” epsilon and
weights in the EBM model, i.e., the user need input the values of epsilon and
weights, so that both models use these parameters. From
MaxDEA 6.15, we resolve the above problems as
follows. 1)
when the EBM model is combined with MetaFrontier, both the MetaFrontier
model and the GroupFrontier model use the same EBM
parametersthe parameters from the MetaFrontier
model. 2)
when the EBM model is used to compute
Scale Efficiency, both the CRS model and the VRS model use the same EBM
parametersthe parameters from the CRS model. 3)
when the EBM model is combined with
Fuzzy inputs/outputs, both the lower bound model and the upper bound model
use the same EBM parametersthe parameters from the lower bound model. The
user can still use the “Customized” epsilon and weights in the EBM model to
avoid the EBM problems, and for panel data
(Malmquist or Window model), the “Customized” epsilon and weights must be
used. 
6.14 
l The algorithm for Minimum Distance to Strong Frontier model
is improved. It is much faster than before, especially for big data. 
6.13 
l Since MaxDEA version 6.9, a new
field “DMU Order in Data” is added to the results. It is the original order
of each DMU in the data. l 1) “DMU Order in Data” is optional now,
the user can choose display or not display it. l 2) For big data (such as 10000 DMUs), “DMU Order in Data”
will take much additional time at the beginning of running models, this has
been fixed. Now just a little additional time is used even for big data. 
6.12 
l Malmquist Bootstrap: In the bootstrap summary, the
GeometricMean of the bootstrapped indices can be used instead of the
ArithmeticMean, so that MI = EC * TC holds. 
6.11 
l Twostage network model (multiplier form, Kao and Hwang
2008）added The twostage network model defines a twostage
production system, in which all the outputs (intermediate) from the first
stage go into the second stage as inputs (Inputs > Intermediates >
Outputs). The twostage DEA model provides not only an overall efficiency
score for the entire system, but also yields efficiency scores for both the
individual stages. Chiang Kao and Hwang (2008) developed an approach for the
above twostage network model where the overall efficiency score of the
twostage network can be decomposed into the product of the efficiency score
of the first stage and the efficiency score the second stage. 
6.9 
l A new field “DMU Order in Data” is added to the results. It is the
original order of each DMU in the data. MaxDEA
results are sorted by DMU name, not the original order in the data. If you
want the results to keep the original order, you can sort the results using
this field, “DMU Order in Data”. 
6.8 Ultra 
V6.8 is
for MaxDEA Ultra only l Nonconcave Metafrontier can be
combined with Network DEA 
6.7 Ultra 
V6.7 is
for MaxDEA Ultra only l Nonconcave Metafrontier DEA and
Nonconcave Metafrontier Malmquist 
6.6 
l Fuzzy DEA model The
conventional DEA requires accurate input and output data. However, the
observed data in real world are sometimes imprecise. Imprecise or vague data
is often expressed with bounded intervals. In MaxDEA, the DEA model with fuzzy inputs/outputs with
bounded intervals is converted into a pair of standard DEA models, so that
the lower and upper bounds of the efficiency scores are obtained
respectively. 
6.5
Ultra 
V6.5 is
for MaxDEA Ultra only l The detailed results of bootstrap models are saved as text
files (*.csv), so after bootstrapping, MaxDEA Ultra
will not become too large, and the number of periods in Malmquist bootstrap
models are not limited any more. In MaxDEA
Pro, the detailed results of bootstrap models are saved in internal tables.
Due to the limitations of Access on table columns (maximum 255) and file size
(maximum 2G), the maximum number of periods is
limited to about 50. l The P values are provided in Malmquist bootstrap models,
i.e., the probability of EC (TC or MI) equal to 1, i.e., the probability of
EC (TC or MI) not changed. 
6.4 
l MaxDEA 6.4 is more stable New data engine is used
in importing Excel data: faster and more stable. The bootstrap models use
builtin statistical functions, instead of Excel statistical functions:
bootstrapping is more stable. l Data variable name (field name) can be edited in
"Define Data". 
6.3 
l Frontier plot and frontier shift plot for panel data l MetaFrontier, including MetaFrontier DEA and MetaFrotnier Malmquist l Game Cross Efficiency model proposed by Liang L. et al
(2008) and Wu J. et al (2009) l Game Cross Efficiency can be combined with Global Malmquist
model l Global, Sequential and WindowMalmquist can be combined
with Customized Benchmarking l Window model can be combined with Cluster l Window model can be combined with Customized Benchmarking l MetaFrontier can be combined with Window model l A pivot table of efficiency scores added in the results of
Window model and Crossbenchmarking Cluster model l Newdesigned Progress Window (both 32bit and 64bit) and
“not responding” in timeconsuming models is effectively avoided l The data will be automatically rescaled, to avoid “Numeric
Failure” due to improperly scaled units l The “result decimals” in options is changed to “significant
decimals” for some result indicators to avoid being rounded to zeros l An option “Node Score Including Intermediates” is added to
SBM Network DEA and SBM Dynamic
DEA. 
6.2 
l More Combinations available New distances added in MaxDEA 6, including Minimum Distance to Weak Efficient
Frontier, Minimum Distance to Strong Efficient Frontier and EBM, now can be
combined with Malmquist, Cluster, Customized
Benchmarking. 
6.1 
l Malmquist models support unbalanced panel data In MaxDEA 6.0
or lower versions, the panel data for Malmquist models must be balanced,
i.e., there must be equal number of DMUs in each period. If the values for
some DMUs in one or more periods are missing, these DMUs must be deleted from
the dataset. However in such cases, the Malmquist indices for the periods
that have complete data should be computed, and the deleted DMUs may be used
as benchmarks for other DMUs, so exclusion of the DMUs with missing values
results in loss of information. In MaxDEA 6.1,
the panel data for Malmquist models can be unbalanced. If the values for some
DMUs in one or more periods are missing, the Malmquist indices for the
relevant periods will not be computed, but the Malmquist indices for the
periods that have complete data will be computed. In addition, the DMUs with
missing values may serve as benchmarks for other DMUs at the periods that
they have data. 
6.0 Major Update 
l Bootstrap for DEA and Malmquist models l More methods to compute
TFP change (Malmquist index) Ø Adjacent Ø Fixed Ø Global Ø SequentialMalmquist (new, Tulkens
& Vanden 1995; Shestalova
2003) Ø WindowMalmquist (new, combining Window model and
Malmquist model) l More types of distance: Ø Radial Ø Maximum distance to
frontier (SBM) Ø Hybrid Ø Minimum distance to weak
frontier (new) Ø Minimum distance to
strong frontier (new) Ø EBM Model (new, Tone
& Tsutsui, 2010) Ø Direction Vector
Scanning Model (new) Ø Range Directional Model
(new, RDM, Portelal et al 2004) Ø Modified SBM (new, Sharp
et al 2007) l More types of
intermediate in Network model Ø Free Ø Fixed Ø Nonincreasing (new) Ø Nondecreasing (new) l More types of cluster
benchmarking Ø Selfbenchmarking Ø Crossbenchmarking Ø Downwardbenchmarking Ø Upwardbenchmarking Ø Loweradjacentbenchmarking
(new) Ø Upperadjacentbenchmarking
(new) Ø Windowbenchmarking
(new) l Period weights in
Dynamic Model (Tone & Tsutsui 2010) l Parallel Network Model
(Kao 2009) l Contextdependent Model
(Seiford & Zhu, 2003) l Scale Elasticity (Degree
of Scale Economy) l Restricted Projection l GeometricMean or
ArithmeticMean added in Results of Malmquist Models l Combinations of Cluster
model (4 types) and Malmquist model (4 types) available 
5.2 
l Two methods available to
compute productivity changes in Malmquist model 1) Multiplicative method and GeometricMean; 2) Additive method and ArithmeticMean (Newly added). 
5.1 
l Support indicators
(inputs and outputs) with negative values 
5.0 Major Update 
l Completely support for
Directional Distance Function Model. MaxDEA 5.0
provides a unified method to compute the efficiency score for directional
distance function Model. Directional distance function model is a generalized
form of radial model. l Three types of reference
for Malmquist Model: Adjacent, Fixed and Global. Both the new types (Fixed
and Global) of Malmquist indices are circular. And the Global Malmquist model
doesn’t suffer from the infeasibility problem. l Dual Solution and
Sensitivity Analysis, including Dual prices and their Sensitivity Analysis
for envelopment models, benchmarks with values of lambda and projections for
multiplier models, and Sensitivity Analysis of Objective function. l Interface improved.
Cost/Revenue/Profit and FDH models are moved from advanced models to basic
models. The number of the combinations of basic models is over 200. 
4.4 
l MaxDEA uses the method
developed by Maniadakis and Thanassoulis
to compute Cost Malmquist Model, and uses similar methods to compute Revenue,
Profit, and Revenue Cost Ratio Malmquist Index l The option “α = β” is
added to Radial Nonoriented models. 
4.3 
l The results of Scale
Efficiency are separated from other results. To avoid misunderstanding of the
scale efficiency and the scale effect in Malmquist models, the results of
scale efficiency are provided separately. The option is moved from the tab of
“Results” to “RTS” in the tab of “Basic Models”. l The scale effect in
Malmquist model is decomposed into two parts: one is scale effect on
efficiency change and the other is scale effect on technological change. 
4.2 
l Inseparable good and bad
outputs model is added. l Undesirable model can be
combined with weak disposability model. l Nondiscretionary and
bounded models can be combined with weak disposability model. 
4.1 
l Portable licence is available. This licence
type uses a flash disk as the USB key. The license holder may work with MaxDEA on any computer the USB key is plugged into. This licence allows for extreme flexibility. l Two additional LP
formats are available: one is mps format, which is
supported by most solvers; and the other is lp format, which is similar to the mathematical
formulation. l Variables (columns) and
constraints (rows) are named according to their meanings in the exported LPs. l When the number of the
columns of the results is over 255, which MS Access does not support, the
results will be exported to a comma delimited text file (*.csv), which can be
opened by text editor, statistic software, or Excel 2007. l Bugs fixed or improvements
made for: 1) Super Revenue/Profit/Revenue Cost Ratio Models; 2)
Cost/Revenue/Profit/RevenueCost Ratio Network
Models with Nondiscretionary or Bounded inputs/outputs/intermediates; and 3)
Super Network model with VRS. 
4.0 Major Update 
l Model Orientation is
extended from 3 types to 8 types. l Linear programming
equations of DEA models can be exported to text files. (details in MaxDEA Linear Programming Manual) l Dynamic model is added. l User interface is
improved. 
3.2 
l Nondiscretionary and
bounded options can be applied to indirect inputs/outputs (intermediate) in
Network DEA models. l Prices of
nondiscretionary and bounded inputs/outputs are optional in
nondiscretionary and bounded Cost/Revenue/Profit/Revenue Cost Ratio models. l Prices of nondiscretionary
and bounded inputs/outputs are optional in nondiscretionary and bounded
Cost/Revenue/Profit/Revenue Cost Ratio models. l “Profit Ratio” model was
renamed as “Revenue/Cost Ratio” model. 
3.1 
l Cluster model was
redesigned. There are four types of cluster models: selfbenchmarking,
crossbenchmarking, downwardbenchmarking and upwardbenchmarking. l A bug fixed for Radial
and Hybrid Network DEA models. 
3.0 Major Update 
l The only file needed for
running the program is MaxDEA.mdb, which is further convenient to run and
backup your DEA models. l User interface is
improved. l Cluster model is added.
Cluster model deals with the situation that the DMUs are categorized
according to their characteristics. There are four types of cluster models:
selfbenchmarking, crossbenchmarking, downwardbenchmarking and
upwardbenchmarking. l Window model is added.
Both balanced and unbalance panel data can be analyzed. 
Earlier 
l MaxDEA 2.7 added cross
efficiency models. l MaxDEA 2.6 added the "two
stage" method for computing input/output weights in multiplier models. l MaxDEA 2.5 added Network DEA. l MaxDEA 2.4 added the
customized benchmarking model (including variablebenchmark and
fixedbenchmark). l MaxDEA 2.3 added directional
distance function model for undesirable outputs. l MaxDEA 2.2 added Malmquist for
multiplier models. l MaxDEA 2.0 （Major Update） added Cost, Revenue, Profit and Revenue/Cost Ratio models,
and undesirable output model. l MyDEA 1.0 ( renamed as MaxDEA from 2.0) l Distance: Radial,
Nonradial (SBM) and Hybrid; l Orientation: Input,
Output and Non oriented; l RTS: CRS, VRS, NIRS,
NDRS and GRS; l FDH model; l Superefficiency; l Nondiscretionary model; l Bounded model; l Preference (weighted)
model; l Malmquist model. 