deacost.jl
# This file contains functions for the Cost Efficiency DEA model
"""
CostDEAModel
An data structure representing a cost DEA model.
"""
struct CostDEAModel <: AbstractCostDEAModel
n::Int64
m::Int64
s::Int64
rts::Symbol
disposY::Symbol
dmunames::Union{Vector{String},Nothing}
eff::Vector
lambda::SparseMatrixCSC{Float64, Int64}
techeff::Vector
alloceff::Vector
Xtarget::Matrix
Ytarget::Matrix
end
"""
deacost(X, Y, W)
Compute cost efficiency using data envelopment analysis for
inputs `X`, outputs `Y` and price of inputs `W`.
# Optional Arguments
- `rts=:VRS`: chooses variable returns to scale. For constant returns to scale choose `:CRS`.
- `dispos=:Strong`: chooses strong disposability of outputs. For weak disposability choose `:Weak`.
- `names`: a vector of strings with the names of the decision making units.
# Examples
```jldoctest
julia> X = [5 3; 2 4; 4 2; 4 8; 7 9.0];
julia> Y = [7 4; 10 8; 8 10; 5 4; 3 6.0];
julia> W = [2 1; 2 1; 2 1; 2 1; 2 1.0];
julia> deacost(X, Y, W)
Cost DEA Model
DMUs = 5; Inputs = 2; Outputs = 2
Orientation = Input; Returns to Scale = VRS
──────────────────────────────────
Cost Technical Allocative
──────────────────────────────────
1 0.615385 0.75 0.820513
2 1.0 1.0 1.0
3 1.0 1.0 1.0
4 0.5 0.5 1.0
5 0.347826 0.375 0.927536
──────────────────────────────────
```
"""
function deacost(X::Union{Matrix,Vector}, Y::Union{Matrix,Vector},
W::Union{Matrix,Vector}; rts::Symbol = :VRS, dispos::Symbol = :Strong,
names::Union{Vector{String},Nothing} = nothing,
optimizer::Union{DEAOptimizer,Nothing} = nothing)::CostDEAModel
# Check parameters
nx, m = size(X, 1), size(X, 2)
ny, s = size(Y, 1), size(Y, 2)
nw, mw = size(W, 1), size(W, 2)
if nx != ny
throw(DimensionMismatch("number of rows in X and Y ($nx, $ny) are not equal"));
end
if nw != nx
throw(DimensionMismatch("number of rows in W and X ($nw, $nx) are not equal"));
end
if mw != m
throw(DimensionMismatch("number of columns in W and X ($mw, $m) are not equal"));
end
if dispos != :Strong && dispos != :Weak
throw(ArgumentError("`disposX` must be :Strong or :Weak"));
end
# Default optimizer
if optimizer === nothing
optimizer = DEAOptimizer(:LP)
end
# Get minimum cost targets and lambdas
n = nx
Xtarget, clambdaeff = deamincost(X, Y, W, rts = rts, dispos = dispos, optimizer = optimizer)
Ytarget = Y[:,:]
# Cost, technical and allocative efficiency
cefficiency = vec( sum(W .* Xtarget, dims = 2) ./ sum(W .* X, dims = 2) )
techefficiency = efficiency(dea(X, Y, orient = :Input, rts = rts, slack = false, disposY = dispos, optimizer = optimizer))
allocefficiency = cefficiency ./ techefficiency
return CostDEAModel(n, m, s, rts, dispos, names, cefficiency, clambdaeff, techefficiency, allocefficiency, Xtarget, Ytarget)
end
ismonetary(model::CostDEAModel)::Bool = false;
function Base.show(io::IO, x::CostDEAModel)
compact = get(io, :compact, false)
n = nobs(x)
m = ninputs(x)
s = noutputs(x)
disposY = x.disposY
dmunames = names(x)
eff = efficiency(x)
techeff = efficiency(x, :Technical)
alloceff = efficiency(x, :Allocative)
if !compact
print(io, "Cost DEA Model \n")
print(io, "DMUs = ", n)
print(io, "; Inputs = ", m)
print(io, "; Outputs = ", s)
print(io, "\n")
print(io, "Orientation = Input")
print(io, "; Returns to Scale = ", string(x.rts))
print(io, "\n")
if disposY == :Weak print(io, "Weak disposability of outputs \n") end
show(io, CoefTable(hcat(eff, techeff, alloceff), ["Cost", "Technical", "Allocative"], dmunames))
end
end