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}:
0.9443166747955681
0.9543433550948335
0.9759522991840279
0.9790697646919239
0.9492405455403267
0.8434690825376188
0.9038735725245473
0.7464778255026098
0.8246436759251636
0.7863832229341852
⋮
0.9018335373646374
0.9425238373580438
1.0
0.937474824652036
0.5369262942592442
0.9599514759375228
1.0
0.694898164000674
0.920645990787349
deabigdata Function Documentation
DataEnvelopmentAnalysis.deabigdata
— Functiondeabigdata(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.