SearchRef.jl is a high-performance Julia package for Frontier Efficiency Analysis (aka Data Envelopment Analysis, DEA) computation. In particular, it determines a firm’s relative efficiency. SearchRef.jl is desiged to enhance the large-scale DEA computation. The theoretical foundation can be found in the paper: A reference-searching–based algorithm for large-scale data envelopment analysis computation. Currently, it solves the input-oriented VRS model.
SearchRef.jl requires Gurobi solver.
# The example determines the efficiencies for all DMUs based on the VRS input-oriented model (VRS model)
using Gurobi
include("SearchRef.jl")
dataMatrix = readcsv("data.csv") # reed input-ouput data
numInput = 2 # the first two columns are inputs and the others are outputs
scale, dimension = size(dataMatrix)
GurobiTol = 10.0^-6
efficiency = 0.0
env = Gurobi.Env()
setparams!(env; OutputFlag=0, OptimalityTol=GurobiTol)
for k = 1:scale
efficiency, extremeValueSet = SearchRef(k, dataMatrix, numInput, env)
# k: DMU (row) k of the dataMatrix
end
# The following can give better performance.
# eSet = Array{Int64}(0)
# for k = 1:scale
# efficiency, eSet = SearchRef(k, dataMatrix, numInput, env, extremeValueSet=eSet, initialSampling = "extreme value")
# # k: DMU (row) k of the dataMatrix
# endincrementSize : the incremental size to expand the sample (default value: 150).
SearchRef(k, dataMatrix, numInput, env, incrementSize = 200) # set the incremental size to 200
tol : the solution tolerance for solving DEA problem (default value: 1e-6). It also resets the dual feasibility tolerance in the solver to the given value.
SearchRef(k, dataMatrix, numInput, env, tol = 10.0^-4) # set the solution tolerance to 1e-4
lpUB : the size limit of the LP, i.e. the limitation of number of variables in the LP (default value: Inf).
SearchRef(k, dataMatrix, numInput, env, lpUB = 300) # set the LP size limitation to 300 variables
initialSize : to size of the initial sample (default value: dimension+1).
SearchRef(k, dataMatrix, numInput, env, initialSize = 300) # set the size of the initial sample to be 300
M : a posive-value parameter to avoid the degenercy (default value: 10). Note that M>1 yields loss in numerical accuracy of the efficiency determination. For example, M=10 and tol=10^-6 give accuracy of 10^-5.
SearchRef(k, dataMatrix, numInput, env, M = 5) # set M = 5
maxIteration : the maximum number of iteration of the computation (default value: 300).
SearchRef(k, dataMatrix, numInput, env, maxIteration = 100) # set maxIteration = 100
initialSampling : the initial sampling policy: can be "random" or "extreme value"), which will select DMUs with extreme values on each dimension (default value: "random").
SearchRef(k, dataMatrix, numInput, env, initialSampling = "extreme value")
extremeValueSet : the index set of DMUs with extreme vale for each dimension (default is empty).
SearchRef(k, dataMatrix, numInput, env, extremeValueSet = aSet)
# aSet is Vector{Int} containing indices of DMUs with extreme values
If you find FrontierEfficiencyAnalysis useful in your work, we kindly request that you cite the following papers
@misc{chen2017,
Author = {Wen-Chih Chen},
Title = {A reference-searching–based algorithm for large-scale data envelopment analysis computation},
Year = {2017},
Eprint = {https://arxiv.org/abs/1710.10482},
}
SearchRef.jl has been developed under the financial support of the Ministry of Science and Technology, Taiwan (Grant No. 104-2410-H-009-026-MY2). The contributors include Yueh-Shan Chung and Hao-Yun Chen.