Profitability Efficiency Change

Example

In this example we compute the profitability efficiency change:

using BenchmarkingEconomicEfficiency

X1 = [5 3; 2 4; 4 2; 4 8; 7 9]
Y1 = [7 4; 10 8; 8 10; 5 4; 3 6]
W1 = [2 1; 2 1; 2 1; 2 1; 2 1]
P1 = [3 2; 3 2; 3 2; 3 2; 3 2]

X2 = [14 12; 8 10; 10 8; 16 20; 14 17]
Y2 = [18 10; 36 28; 28 36; 18 14; 12 20]
W2 = [3 4; 3 4; 3 4; 3 4; 3 4]
P2 = [3 5; 3 5; 3 5; 3 5; 3 5]

X = Array{Float64,3}(undef, 5, 2, 2);
X[:, :, 1] = X1;
X[:, :, 2] = X2;

Y = Array{Float64,3}(undef, 5, 2, 2);
Y[:, :, 1] = Y1;
Y[:, :, 2] = Y2;

W = Array{Float64,3}(undef, 5, 2, 2);
W[:, :, 1] = W1;
W[:, :, 2] = W2;

P = Array{Float64,3}(undef, 5, 2, 2);
P[:, :, 1] = P1;
P[:, :, 2] = P2;

profitabilityeffch = deaprofitabilitychange(X, Y, W, P)

Profitability Change DEA Model 
DMUs = 5; Inputs = 2; Outputs = 2
alpha = 0.5; Returns to Scale = VRS
──────────────────────────────────────────────────────────────────
   Prof.Change  CRS.Change  VRS.Change  Scale.Change  Alloc.Change
──────────────────────────────────────────────────────────────────
1     0.699507    0.654762    0.702926       0.93148      1.06834
2     0.910038    1.0         1.0            1.0          0.910038
3     1.30682     1.0         1.0            1.0          1.30682
4     0.910038    1.0         1.0            1.0          0.910038
5     1.82856     1.52116     1.11794        1.36069      1.20208
──────────────────────────────────────────────────────────────────

Estimated economic, technical CRS and VRS, scale, and allocative efficiency change scores are returned with the effchange function:

effchange(profitabilityeffch, :Economic)

5-element Vector{Float64}:
 0.6995065787165716
 0.9100378939024054
 1.306818198185957
 0.9100378970578911
 1.8285648452062437

effchange(profitabilityeffch, :CRS)

5-element Vector{Float64}:
 0.6547619150417507
 1.0000000075609952
 1.000000009500969
 1.0000000262753872
 1.52116398591551

effchange(profitabilityeffch, :VRS)

5-element Vector{Float64}:
 0.7029261773466672
 1.0000000019310833
 1.0000000020495619
 1.0000000475263195
 1.1179354754110682

effchange(profitabilityeffch, :Scale)

5-element Vector{Float64}:
 0.9314803405291836
 1.0000000056299119
 1.0000000074514068
 0.9999999787490688
 1.3606903254914362

effchange(profitabilityeffch, :Allocative)

5-element Vector{Float64}:
 1.06833730344864
 0.9100378870216136
 1.3068181857699182
 0.9100378731462934
 1.2020826565294505

DEA Profitability Efficiency Change Function Documentation

BenchmarkingEconomicEfficiency.deaprofitabilitychange — Function

deaprofitabilitychange(X, Y, W, P)

Compute profitability efficiency change using data envelopment analysis for inputs X, outputs Y, price of inputs W, and price of outputs P.

Optional Arguments

alpha=0.5: alpha to use for the generalized distance function.
names: a vector of strings with the names of the decision making units.

source

BenchmarkingEconomicEfficiency.effchange — Method

effchange(model::ProfitabilityChangeDEAModel)

Return efficiency change of a profitability change DEA model.

Optional Arguments

type=Economic: type of efficiency change scores to return.

Type specification:

:Economic: returns economic efficiency change of the model.
:CRS: returns technical efficiency change under constant returns to scale.
:VRS: returns technical efficiency change under variable returns to scale.
:Scale: returns scale efficiency change.
:Allocative: returns allocative efficiency change.

source