# DEAFrontier Models

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```					Updated January, 2011
Model Cluster

Multiplier Model
Restricted Multiplier model
Envelopment Model
Slack-based Model
Measure-specific Model
Returns to Scale Estimation
Preference Structure Model
Undesirable Measure Model
Context-dependent DEA

Variable-benchmark Model
Fixed-benchmark Model
Minimum Efficiency Model

Two-Stage Network DEA
Centralized Model
Frontier Projection
VRS Model

Congestion
Weak Disposibality
Super Efficiency
Slack-based Super Efficiency
DEA Sensitivity Analysis
FDH
Malmquist
Cost Efficiency
Revenue Efficiency
Profit Efficiency

One can use the Variable-Benchmark Model and the Envelopment Model to calculate the non-CRS Malmquist productivity inde
Suppose we have two periods A and B. We need to run four (4) DEA models to calculate the Malmquist productivity index. The

Model-1: DEA efficiency in period A

Model-2: DEA efficiency in period B

Model-3: Efficiency of period A with respect to period B; namely, period B is used as a reference set and period A is under eval

Model-4: Efficiency of period B with respect to period A; namely, period A is used as a reference set and period B is under eval

For example, if one wants to calculate VRS Malmquist productivity index. One can use the DEFrontier in the following s

Step 1: Using the VRS Envelopment Model to calculate Model-1 and Model 2;
Step 2: Using the VRS Variable-Benchmark Model to calculate Model-3 and Model-4.

To calculate Model-3, put the period B data in sheet "Benchmarks" and put the period A data in sheet "DMUs";
To calculate Model-4, put the period A data in sheet "Benchmarks" and put the period B data in sheet "DMUs".

Step 3: Once all the efficiency scores are generated, one can calculate the Malmquist productivity index. Note that you will get
Notes
References for the models
The user can specify the value of Epsilon in the model. The default Epsilon = 0)
Assurance Region Model. The user can impose ratios bounds among inputs, among outputs, and among inputs and outputs
The user can use the Multiplier Model to get the related results
Additive DEA Models where the objective function is the (weighted) sum of input/output slacks
for uncontrollable inputs/outputs. The inputs/outputs selected are the controllable ones.)
It also provides RTS Classification

Zhu, Joe, Data envelopment analysis with preference structure. Journal of Operational Research Society, Vol. 47, No.1 (1996),
Seiford, L.M. and Zhu, Joe, Modeling undesirable factors in efficiency evaluation, European Journal of Operational Research, V
Seiford, L.M. and Zhu, Joe, Context-dependent data envelopment analysis: measuring attractiveness and progress. OMEGA, V

Cook, W.D., Seiford, L.M. and Zhu, Joe, Models for performance benchmarking: Measuring the effect of e-commerce activities
Cook, W.D., Seiford, L.M. and Zhu, Joe, Models for performance benchmarking: Measuring the effect of e-commerce activities
see manual

Liang, L., Cook, W.D. and Zhu, Joe, DEA Models for two-stage processes: game approach and efficiency decomposition, Nava
Chen, Y., Cook, W.D. and Zhu, Joe, Deriving the DEA Frontier for Two-Stage Processes, European Journal of Operational Res
Liang, L., Cook, W.D. and Zhu, Joe, DEA Models for two-stage processes: game approach and efficiency decomposition, Nava
Chen, Y. and Zhu, Joe, Measuring information technology’s indirect impact on firm performance, Information Technology & Ma

Cooper, W.W., Seiford, L.M. and Zhu, Joe, A unified additive model approach for evaluating inefficiency and congestion with as

Du, J., Liang, L., and Zhu, Joe, A slacks-based measure of super-efficiency in data envelopment analysis: A Comment, Europe
Zhu, Joe, Super-efficiency and DEA sensitivity analysis. European Journal of Operational Research, Vol. 129, Issue 2 (2001), 4

See below
see manual
see Manual
see manual

e-Benchmark Model and the Envelopment Model to calculate the non-CRS Malmquist productivity index.
eriods A and B. We need to run four (4) DEA models to calculate the Malmquist productivity index. They are

riod A with respect to period B; namely, period B is used as a reference set and period A is under evaluation

riod B with respect to period A; namely, period A is used as a reference set and period B is under evaluation

ne wants to calculate VRS Malmquist productivity index. One can use the DEFrontier in the following steps:

Envelopment Model to calculate Model-1 and Model 2;
Variable-Benchmark Model to calculate Model-3 and Model-4.

el-3, put the period B data in sheet "Benchmarks" and put the period A data in sheet "DMUs";
el-4, put the period A data in sheet "Benchmarks" and put the period B data in sheet "DMUs".

ciency scores are generated, one can calculate the Malmquist productivity index. Note that you will get "infeasible" for some efficiency scores
ong inputs and outputs

ety, Vol. 47, No.1 (1996), 136-150
Operational Research, Vol. 142, Issue 1 (2002), 16-20
and progress. OMEGA, Vol. 31, Issue 5, (2003), 397-480

of e-commerce activities on banking performance, OMEGA, Vol. 32, Issue 4 (2004), 313-322
of e-commerce activities on banking performance, OMEGA, Vol. 32, Issue 4 (2004), 313-322

ency decomposition, Naval Research Logistics, Vol. 55 (2008), 643-653
ournal of Operational Research, Vol. 202 (2010), 138-142
ency decomposition, Naval Research Logistics, Vol. 55 (2008), 643-653
mation Technology & Management Journal, Vol. 5, Issue 1-2 (2004), 9-22

cy and congestion with associated measures in DEA. Socio-Economic Planning Sciences, Vol. 34, Issue 1 (2000), 1-25

ysis: A Comment, European Journal of Operational Research, Vol. 204 (2010), 694-697.
Vol. 129, Issue 2 (2001), 443-455
or some efficiency scores when Malmquist is calculated under non-CRS conditions.
e 1 (2000), 1-25

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