# Radial Big Data Models

When the number of decision-making units is large, traditional DEA models are slow to solve. Khezrimotlagh, Zhu, Cook, and Toloo (2019), propose a framework that reduces the computational time by finding the set of best practices DMUs from a subsample and evaluating the rest of the decision-making units with respect to the best performers.

The proposed framework includes five steps:

- Select a subsample of DMU.
- Find the best practices in the subsample.
- Find the exterior DMUs with respect to the hull of the best practices.
- Identify the set of all efficient DMUs.
- Calculate performance scores as in the traditional DEA model.

This example computes the Big Data radial input-oriented DEA model under variable returns to scale, using random data drawn from a uniform distribution. 500 DMUs with six inputs and four outputs in the interval (10, 20) are generated:

```
# Generate random data
using DataEnvelopmentAnalysis
using Distributions
using Random
using StableRNGs
rng = StableRNG(1234567)
X = rand(Uniform(10, 20), 500, 6);
Y = rand(Uniform(10, 20), 500, 4);
# Calculate the Big Data DEA Model
deabig = deabigdata(X, Y)
# Get efficiency scores
efficiency(deabig)
```

```
500-element Vector{Float64}:
0.8175433842537527
0.6797433592540172
1.0000000000000002
1.0
0.9193005273802585
1.0000000000000002
0.9905911067502733
0.8611157845044615
0.8537614303167135
0.9427686204091875
⋮
0.8821018966010546
0.7943469188591539
1.0
1.0
0.7259342162524194
0.9999999999999999
1.0
0.8390397831549327
0.9145720950182838
```

### deabigdata Function Documentation

`DataEnvelopmentAnalysis.deabigdata`

— Function`deabigdata(X, Y)`

Compute the big data radial model using data envelopment analysis for inputs X and outputs Y.

**Optional Arguments**

`orient=:Input`

: chooses the radially oriented input mode. For the radially oriented output model choose`:Output`

.`rts=:CRS`

: chooses constant returns to scale. For variable returns to scale choose`:VRS`

.`atol=1e-6`

: tolerance for DMU to be considered efficient.`names`

: a vector of strings with the names of the decision making units.