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How can I derive an efficiency score from result/output when executing the DEA directional distance function (ddf)?

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Hewan Belay
Hewan Belay on 3 Jan 2020
I am new to Matlab, and using it to conduct data envelopment analysis (DEA), in particular, using the directional distance function (DDF) assuming variable returns to scale, also referred to as the directional model. For this, I am first seeking to understand the output of the DEA Matlab code that is downloadable from www.deatoolbox.com . My question pertains to how to interpret the result of a specific code that produces efficiency results based on the DEA DDF. The code in questioni is:
ddf_vrs = dea(X, Y, 'orient', 'ddf', 'rts', 'vrs', 'Gx', X, 'Gy', Y)
deadisp(ddf_vrs)
The output looks like this:
_______________________________
Data Envelopment Analysis (DEA)
DMUs: 11
Inputs: 2 Outputs: 1
Model: radial
Orientation: ddf (Directional distance function)
Returns to scale: vrs (Variable)
--------------------------------------------------------------------
DMU| X1| X2| Y| Beta| slackX1| slackX2| slackY|
--------------------------------------------------------------------
1| 5.0000| 13.0000| 12.0000| 0.0000| 0.0000| 0.0000| 0.0000|
2| 16.0000| 12.0000| 14.0000| 0.1076| 0.0000| 0.0000| 0.0000|
3| 16.0000| 26.0000| 25.0000| 0.0000| 0.0000| 0.0000| 0.0000|
4| 17.0000| 15.0000| 26.0000| 0.0000| 0.0000| 0.0000| 0.0000|
5| 18.0000| 14.0000| 8.0000| 0.2884| 0.0000| 0.0000| 0.3915|
6| 23.0000| 6.0000| 9.0000| 0.0000| 0.0000| 0.0000| 0.0000|
7| 25.0000| 10.0000| 27.0000| 0.0000| 0.0000| 0.0000| 0.0000|
8| 27.0000| 22.0000| 30.0000| 0.0000| 0.0000| 0.0000| 0.0000|
9| 37.0000| 14.0000| 31.0000| 0.0000| 0.0000| 0.0000| 0.0000|
10| 42.0000| 25.0000| 26.5000| 0.1629| 0.0000| 5.4560| 0.0000|
11| 5.0000| 17.0000| 12.0000| 0.0000| 0.0000| 4.0000| 0.0000|
--------------------------------------------------------------------
My question is: I am interested in the efficiency score for each of the units 1 through 11 based on the directional DEA model. The efficiency score should be a value between 0 (not at all efficient) to 1 (fully efficient). After getting this, I plan to discuss the differences in efficiency scores based on the input-oriented, output-oriented, and directional efficiency models. Based on my understanding reading the working paper in deatoolbox.com, the column above called "beta" is NOT such an efficiency score. Then, how can I obtain/derive the efficiency scores for the 11 DMUs? Any guidance or pointers would be extremely appreciated! I'm happy to elaborate on the question if anything is unclear

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