DEA Models

Encyclopedia of DEA Models Since 1978, when DEA was originally introduced by Prof. A Charnes, Cooper and Rhodes, many different models have been developed by various researchers. Two basic models are CCR (Charnes, Cooper and Rhodes(1978)) and BCC (Banker, charnes and Cooper (1984)). However, there are numerous models and selection of an appropriate model depends on the nature of production-technology. In general these models differ in their Orientation (Input-orientation, Output-orientation, ...), Disposability (Strong, Week), Diversification and Returns to Scale (CRS, VRS, NIRS, NDRS, ...), types of measure (Radial measure, Non-radial measure, Hyperbolic measure, ...), etc. Further to these models, researcher have developed models for specific applications. The aim of this encyclopedia is to collect known DEA models. So if you deal with a model that is not listed here, or you have developed a new model please send it to me. So I can add your model to this encyclopedia. Here I assume an abbreviation name for each model, which in general shows the properties of model.

0. Basic Models

Model Code	Type of Measure	Orientation	Input Disposability	Output Disposability	Type of Model	Comment
CCR_Input	Radial	Input	X= Input Strong D	Y= Output Strong D	Primal	Known as CCR model
CCR_Output	Radial	Output	X= Input Strong D	Y= Output Strong D	Primal	Known as CCR model
BCC_Input	Radial	Input	X= Input Strong D	Y= Output Strong D	Primal	Known as BCC model
BCC_Output	Radial	Output	X= Input Strong D	Y= Output Strong D	Primal	Known as BCC model

Sorry. The mathematics of the following models have not been completed yet.

1. Radial Models

1.1. Radial Models-Input Orientation

Model Code	Type of Measure	Orientation	Input Disposability	Output Disposability	Type of Model
DEAi/p(IS-OS)	Radial	Input	X= Input Strong D	Y= Output Strong D	Primal
DEAi/p(IW-OW)	Radial	Input	X= Input Weak D	Y= Output Weak D	Primal
DEAi/p(IS-OW)	Radial	Input	X= InPut Strong D	Y= OuTput Weak D	Primal
DEAi/p(IW-OS)	Radial	Input	X= InPut Weak D	Y= OuTput Strong D	Primal
DEAi/p(ISW-OS)	Radial	Input	X= InPut Strong D , Z= Input Weak D	Y= Output Strong D	Primal
DEAi/p(ISW-OW)	Radial	Input	X= Input Strong D , Z= Input Weak D	Y= Output WeaK D	Primal
DEAi/p(IS-OSW)	Radial	Input	X= Input Strong D	Y= Output Strong D , W= Output Weak D	Primal
DEAi/p(IW-OSW)	Radial	Input	X= Input WeaK D	Y= Output Strong D , W= Output Weak D	Primal
DEAi/p(ISW-OSW)	Radial	Input	X= Input Strong D , Z= Input Weak D	Y= Output Strong D , W= Output Weak D	Primal
DEAi/d(IS-OS)	Radial	Input	X= Input Strong D	Y= Output Strong D	Dual
DEAi/d(IW-OW)	Radial	Input	X= Input WeaK D	Y= Output Weak D	Dual
DEAi/d(IS-OW)	Radial	Input	X= Input Strong D	Y= Output Weak D	Dual
DEAi/d(ISW-OS)	Radial	Input	X= Input Strong D , Z= Input Weak D	Y= Output Strong D	Dual
DEAi/d(IW-OS)	Radial	Input	X= Input Weak D	Y= Output Strong D	Dual
DEAi/d(ISW-OW)	Radial	Input	X= Input Strong D , Z= Input Weak D	Y= Output Weak D	Dual
DEAi/d(IS-OSW)	Radial	Input	X= Input Strong D	Y= Output Strong D , W= Output Weak D	Dual
DEAi/d(IW-OSW)	Radial	Input	X= Input Weak D	Y= Output Strong D , W= Output Weak D	Dual
DEAi/d(ISW-OSW)	Radial	Input	X= Input Strong D , Z= Input Weak D	Y= Output Strong D , W= Output Weak D	Dual

1.2. Radial Models-Output Orientation

Model Code	Type of Measure	Orientation	Input Disposability	Output Disposability	Type of Model
DEAo/p(IS-OS)	Radial	Output	X= Input Strong D	Y= Output Strong D	Primal
DEAo/p(IW-OW)	Radial	Output	X= Input Weak D	Y= Output Weak D	Primal
DEAo/p(IS-OW)	Radial	Output	X= Input Strong D	Y= Output Weak D	Primal
DEAo/p(IW-OS)	Radial	Output	X= Input Weak D	Y= Output Strong D	Primal
DEAo/p(ISW-OS)	Radial	Output	X= Input Strong D , Z= Input Weak D	Y= Output Strong D	Primal
DEAo/p(ISW-OW)	Radial	Output	X= Input Strong D , Z= Input Weak D	Y= Output Weak D	Primal
DEAo/p(IS-OSW)	Radial	Output	X= Input Strong D	Y= Output Strong D , W= Output Weak D	Primal
DEAo/p(IW-OSW)	Radial	Output	X= Input Weak D	Y= Output Strong D , W= Output Weak D	Primal
DEAo/p(ISW-OSW)	Radial	Output	X= Input Strong D , Z= Input Weak D	Y= Output Strong D , W= Output Weak D	Primal
DEAo/d(IS-OS)	Radial	Output	X= Input Strong D	Y= Output Strong D	Dual
DEAo/d(IW-OW)	Radial	Output	X= Input Weak D	Y= Output Weak D	Dual
DEAo/d(IS-OW)	Radial	Output	X= Input Strong D	Y= Output Weak D	Dual
DEAo/d(IW-OS)	Radial	Output	X= Input Weak D	Y= Output Strong D	Dual
DEAo/d(ISW-OS)	Radial	Output	X= Input Strong D , Z= Input Weak D	Y= Output Strong D	Dual
DEAo/d(ISW-OW)	Radial	Output	X= Input Strong D , Z= Input Weak D	Y= Output Weak D	Dual
DEAo/d(IS-OSW)	Radial	Output	X= Input Strong D	Y= Output Strong D , W= Output Weak D	Dual
DEAo/d(IW-OSW)	Radial	Output	X= Input Weak D	Y= Output Strong D , W= Output Weak D	Dual
DEAo/d(ISW-OSW)	Radial	Output	X= Input Strong D , Z= Input Weak D	Y= Output Strong D , W= Output Weak D	Dual

2. Ratio Models

Model Code	Type of Measure	Orientation	Input Disposability	Output Disposability	Type of Model
DEAi/r/p(IS-OS)	Ratio	Input	X= Input Strong D	Y= Output Strong D	Ratio
DEAo/r/p(IS-OS)	Ratio	Output	X= Input Strong D	Y= Output Strong D	Ratio

3. Additive Models

Model Code	Type of Measure	Orientation	Input Disposability	Output Disposability	Type of Model
DEAadd/p(IS-OS)	Radial	Additive	X= Input Strong D	Y= Output Strong D	Primal
DEAadd/d(IS-OS)	Radial	Additive	X= Input Strong D	Y= Output Strong D	Dual

4. Multiplicative Models

Model Code	Type of Measure	Orientation	Input Disposability	Output Disposability	Type of Model
DEAmult/p(IS-OS)	Radial	Multiplicative	X= Input Strong D	Y= Output Strong D	Primal
DEAmult/d(IS-OS)	Radial	Multiplicative	X= Input Strong D	Y= Output Strong D	Dual

5. Hyperbolic Models
5.1. Hyperbolic Models-Input Orientation

Model Code	Type of Measure	Orientation	Input Disposability	Output Disposability	Type of Model
DEAi/h/p (IS-OS)	Hyperbolic	Input	X= Input Strong D	Y= Output Strong D	Primal
DEAi/h/p (IW-OW)	Hyperbolic	Input	X= Input Weak D	Y= Output Weak D	Primal
DEAi/h/p (IS-OW)	Hyperbolic	Input	X= Input Strong D	Y= Output Weak D	Primal
DEAi/h/p (IW-OS)	Hyperbolic	Input	X= Input Weak D	Y= Output Strong D	Primal
DEAi/h/p (ISW-OS)	Hyperbolic	Input	X= Input Strong D , Z= Input Weak D	Y= Output Strong D	Primal
DEAi/h/p (ISW-OW)	Hyperbolic	Input	X= Input Strong D , Z= Input Weak D	Y= Output Weak D	Primal
DEAi/h/p (IS-OSW)	Hyperbolic	Input	X= Input Strong D	Y= Output Strong D	Primal
DEAi/h/p (IW-OSW)	Hyperbolic	Input	X= Input Weak D	Y= Output Strong D , W= Output Weak D	Primal
DEAi/h/p (ISW-OSW)	Hyperbolic	Input	X= Input Strong D , Z= Input Weak D	Y= Output Strong D , W= Output Weak D	Primal
DEAi/h/d (IS-OS)	Hyperbolic	Input	X= Input Strong D	Y= Output Strong D	Dual
DEAi/h/d (IW-OW)	Hyperbolic	Input	X= Input Weak D	Y= Output Weak D	Dual
DEAi/h/d (IS-OW)	Hyperbolic	Input	X= Input Strong D	Y= Output Weak D	Dual
DEAi/h/d (ISW-OS)	Hyperbolic	Input	X= Input Strong D , Z= Input Weak D	Y= Output Strong D	Dual
DEAi/h/d (ISW-OW)	Hyperbolic	Input	X= Input Strong D , Z= Input Weak D	Y= Output Weak D	Dual
DEAi/h/d (IS-OSW)	Hyperbolic	Input	X= Input Strong D	Y= Output Strong D , W= Output Weak D	Dual
DEAi/h/d (IW-OS)	Hyperbolic	Input	X= Input Weak D	Y= Output Strong D	Dual
DEAi/h/d (IW-OSW)	Hyperbolic	Input	X= Input Weak D	Y= Output Strong D , W= Output Weak D	Dual
DEAi/h/d (ISW-OSW)	Hyperbolic	Input	X= Input Strong D , Z= Input Weak D	Y= Output Strong D , W= Output Weak D	Dual

5.2. Hyperbolic Models-Output Orientation

Model Code	Type of Measure	Orientation	Input Disposability	Output Disposability	Type of Model
DEAo/h/p (IS-OS)	Hyperbolic	Output	X= Input Strong D	Y= Output Strong D	Primal
DEAo/h/p (IW-OW)	Hyperbolic	Output	X= Input Weak D	Y= Output Weak D	Primal
DEAo/h/p (IS-OW)	Hyperbolic	Output	X= Input Strong D	Y= Output Weak D	Primal
DEAo/h/p (ISW-OS)	Hyperbolic	Output	X= Input Strong D , Z= Input Weak D	Y= Output Strong D	Primal
DEAo/h/p (ISW-OW)	Hyperbolic	Output	X= Input Strong D , Z= Input Weak D	Y= Output Weak D	Primal
DEAo/h/p (IS-OSW)	Hyperbolic	Output	X= Input Strong D	Y= Output Strong D , W= Output Weak D	Primal
DEAo/h/p (IW-OS)	Hyperbolic	Output	X= Input Weak D	Y= Output Strong D	Primal
DEAo/h/p (IW-OSW)	Hyperbolic	Output	X= Input Weak D	Y= Output Strong D , W= Output Weak D	Primal
DEAo/h/p (ISW-OSW)	Hyperbolic	Output	X= Input Strong D , Z= Input Weak D	Y= Output Strong D , W= Output Weak D	Primal
DEAo/h/d (IS-OS)	Hyperbolic	Output	X= Input Strong D	Y= Output Strong D	Dual
DEAo/h/d (IW-OW)	Hyperbolic	Output	X= Input Weak D	Y= Output Weak D	Dual
DEAo/h/d (IS-OW)	Hyperbolic	Output	X= Input Strong D	Y= Output Weak D	Dual
DEAo/h/d (ISW-OS)	Hyperbolic	Output	X= Input Strong D , Z= Input Weak D	Y= Output Strong D	Dual
DEAo/h/d (ISW-OW)	Hyperbolic	Output	X= Input Strong D , Z= Input Weak D	Y= Output Weak D	Dual
DEAo/h/d (IS-OSW)	Hyperbolic	Output	X= Input Strong D	Y= Output Strong D , W= Output Weak D	Dual
DEAo/h/d (IW-OSW)	Hyperbolic	Output	X= Input Weak D	Y= Output Strong D , W= Output Weak D	Dual
DEAo/h/d (IW-OS)	Hyperbolic	Output	X= Input Weak D	Y= Output Strong D	Dual
DEAo/h/d (ISW-OSW)	Hyperbolic	Output	X= Input Strong D , Z= Input Weak D	Y= Output Strong D , W= Output Weak D	Dual

6. Non-Radial Models

6.1. Non-Radial Models-Input Orientation

Model Code	Type of Measure	Orientation	Input Disposability	Output Disposability	Type of Model
DEAi/n/p(IS-OS)	Non-Radial	Input	X= Input Strong D	Y= Output Strong D	Primal
DEAi/n/p(IW-OW)	Non-Radial	Input	X= Input Weak D	Y= Output Weak D	Primal
DEAi/n/p(IS-OW)	Non-Radial	Input	X= Input Strong D	Y= Output Weak D	Primal
DEAi/n/p(IW-OS)	Non-Radial	Input	X= Input Weak D	Y= Output Strong D	Primal
DEAi/n/p(ISW-OS)	Non-Radial	Input	X= Input Strong D , Z= Input Weak D	Y= Output Strong D	Primal
DEAi/n/p(ISW-OW)	Non-Radial	Input	X= Input Strong D , Z= Input Weak D	Y= Output Weak D	Primal
DEAi/n/p(IS-OSW)	Non-Radial	Input	X= Input Strong D	Y= Output Strong D , W= Output Weak D	Primal
DEAi/n/p(IW-OSW)	Non-Radial	Input	X= Input Weak D	Y= Output Strong D , W= Output Weak D	Primal
DEAi/n/p(ISW-OSW)	Non-Radial	Input	X= Input Strong D , Z= Input Weak D	Y= Output Strong D , W= Output Weak D	Primal
DEAi/n/d(IS-OS)	Non-Radial	Input	X= Input Strong D	Y= Output Strong D	Dual
DEAi/n/d(IW-OW)	Non-Radial	Input	X= Input Weak D	Y= Output Weak D	Dual
DEAi/n/d(IS-OW)	Non-Radial	Input	X= Input Strong D	Y= Output Weak D	Dual
DEAi/n/d(IW-OS)	Non-Radial	Input	X= Input Weak D	Y= Output Strong D	Dual
DEAi/n/d(ISW-OS)	Non-Radial	Input	X= Input Strong D , Z= Input Weak D	Y= Output Strong D	Dual
DEAi/n/d(ISW-OW)	Non-Radial	Input	X= Input Strong D , Z= Input Weak D	Y= Output Weak D	Dual
DEAi/n/d(IS-OSW)	Non-Radial	Input	X= Input Strong D	Y= Output Strong D , W= Output Weak D	Dual
DEAi/n/d(IW-OSW)	Non-Radial	Input	X= Input Weak D	Y= Output Strong D , W= Output Weak D	Dual
DEAi/n/d(ISW-OSW)	Non-Radial	Input	X= Input Strong D , Z= Input Weak D	Y= Output Strong D , W= Output Weak D	Dual

6.2. Non-Radial Models-Output Orientation

Model Code	Type of Measure	Orientation	Input Disposability	Output Disposability	Type of Model
DEAo/n/p(IS-OS)	Non-Radial	Output	X= Input Strong D	Y= Output Strong D	Primal
DEAo/n/p(IW-OW)	Non-Radial	Output	X= Input Weak D	Y= Output Weak D	Primal
DEAo/n/p(IS-OW)	Non-Radial	Output	X= Input Strong D	Y= Output Strong D	Primal
DEAo/n/p(IW-OS)	Non-Radial	Output	X= Input Weak D	Y= Output Strong D	Primal
DEAo/n/p(ISW-OS)	Non-Radial	Output	X= Input Strong D , Z= Input Weak D	Y= Output Strong D	Primal
DEAo/n/p(ISW-OW)	Non-Radial	Output	X= Input Strong D , Z= Input Weak D	Y= Output Weak D	Primal
DEAo/n/p(IS-OSW)	Non-Radial	Output	X= Input Strong D	Y= Output Strong D , W= Output Weak D	Primal
DEAo/n/p(IW-OSW)	Non-Radial	Output	X= Input Weak D	Y= Output Strong D , W= Output Weak D	Primal
DEAo/n/p(ISW-OSW)	Non-Radial	Output	X= Input Strong D , Z= Input Weak D	Y= Output Strong D , W= Output Weak D	Primal
DEAo/n/d(IS-OS)	Non-Radial	Output	X= Input Strong D	Y= Output Strong D	Dual
DEAo/n/d(IW-OW)	Non-Radial	Output	X= Input Weak D	Y= Output Weak D	Dual
DEAo/n/d(IS-OW)	Non-Radial	Output	X= Input Strong D	Y= Output Weak D	Dual
DEAo/n/d(IW-OS)	Non-Radial	Output	X= Input Weak D	Y= Output Strong D	Dual
DEAo/n/d(ISW-OS)	Non-Radial	Output	X= Input Strong D , Z= Input Weak D	Y= Output Strong D	Dual
DEAo/n/d(ISW-OW)	Non-Radial	Output	X= Input Strong D , Z= Input Weak D	Y= Output Weak D	Dual
DEAo/n/d(IS-OSW)	Non-Radial	Output	X= Input Strong D	Y= Output Strong D , W= Output Weak D	Dual
DEAo/n/d(IW-OSW)	Non-Radial	Output	X= Input Weak D	Y= Output Strong D , W= Output Weak D	Dual
DEAo/n/d(ISW-OSW)	Non-Radial	Output	X= Input Strong D , Z= Input Weak D	Y= Output Strong D , W= Output Weak D	Dual

7. Miscellaneous Models

Model Code	Type of Measure	Orientation	Input Disposability	Output Disposability	Type of Model	Comment
Your Model here	....	......	......	......	......	.....
Your Model here	....	......	......	......	......	.....