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 Cross-efficiency and Game Cross-efficiency can be combined with Window model

l Multi-core CPU parallel computing is improved (faster speed) for Window model, Cluster model, and some types of Malmquist models

7.2 Ultra

l The common-weights 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 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)

 

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, 129-147.

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), 5-42.

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), 85-94. doi: 10.1007/s11123-010-0190-2

Doyle, J. R., & Green, R. H. (1995). Cross-evaluation in DEA: Improving discrimination among DMU’s. Infor Information Systems & Operational Research, 33(3), 205-222.

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), 32-45. doi: http://dx.doi.org/10.1016/S0377-2217(01)00055-8

Färe, R., Grifell-Tatjé, E., Grosskopf, S., & Knox Lovell, C. A. (1997). Biased Technical Change and the Malmquist Productivity Index. Scandinavian Journal of Economics, 99(1), 119-127. doi: 10.1111/1467-9442.00051

Fukuyama, H., & Weber, W. L. (2009). A directional slacks-based measure of technical inefficiency. Socio-Economic Planning Sciences, 43(4), 274-287. 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), 147-151.

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), 800-802. doi: http://dx.doi.org/10.1016/S0377-2217(02)00702-6

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 Non-concave 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 0-1, 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 parameters--the 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 parameters--the 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 parameters--the 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 Geometric-Mean of the bootstrapped indices can be used instead of the Arithmetic-Mean, so that MI = EC * TC holds.

6.11

l Two-stage network model (multiplier form, Kao and Hwang 2008added

The two-stage network model defines a two-stage production system, in which all the outputs (intermediate) from the first stage go into the second stage as inputs (Inputs --> Intermediates --> Outputs). The two-stage 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 two-stage network model where the overall efficiency score of the two-stage 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 Non-concave Metafrontier can be combined with Network DEA

6.7 Ultra

V6.7 is for MaxDEA Ultra only

l Non-concave Metafrontier DEA and Non-concave 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 built-in 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 Window-Malmquist 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 Cross-benchmarking Cluster model

l New-designed Progress Window (both 32-bit and 64-bit) and “not responding” in time-consuming 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  Sequential-Malmquist (new, Tulkens & Vanden 1995; Shestalova 2003)

Ø  Window-Malmquist (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  Non-increasing (new)

Ø  Non-decreasing (new)

l More types of cluster benchmarking

Ø  Self-benchmarking

Ø  Cross-benchmarking

Ø  Downward-benchmarking

Ø  Upward-benchmarking

Ø  Lower-adjacent-benchmarking (new)

Ø  Upper-adjacent-benchmarking (new)

Ø  Window-benchmarking (new)

l Period weights in Dynamic Model (Tone & Tsutsui 2010)

l Parallel Network Model (Kao 2009)

l Context-dependent Model (Seiford & Zhu, 2003)

l Scale Elasticity (Degree of Scale Economy)

l Restricted Projection

l Geometric-Mean or Arithmetic-Mean 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 Geometric-Mean;

2) Additive method and Arithmetic-Mean (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 Non-oriented 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 Non-discretionary 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 non-discretionary and bounded inputs/outputs are optional in non-discretionary and bounded Cost/Revenue/Profit/Revenue Cost Ratio models.

l Prices of non-discretionary and bounded inputs/outputs are optional in non-discretionary 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: self-benchmarking, cross-benchmarking, downward-benchmarking and upward-benchmarking.

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: self-benchmarking, cross-benchmarking, downward-benchmarking and upward-benchmarking.

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 variable-benchmark and fixed-benchmark).

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, Non-radial (SBM) and Hybrid;

l Orientation: Input-, Output- and Non- oriented;

l RTS: CRS, VRS, NIRS, NDRS and GRS;

l FDH model;

l Super-efficiency;

l Nondiscretionary model;

l Bounded model;

l Preference (weighted) model;

l Malmquist model.