MaxDEA update history
Version 
What’s New 
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 

6.18 
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 
V6.8
is for MaxDEA Ultra only l Nonconcave Metafrontier
can be combined with Network DEA 
6.7 
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 
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. 