FrontierEfficiencyAnalysis_v2.jl

Copyright © 2018 by Wen-Chih Chen. Released under the MIT License.

FrontierEfficiencyAnalysis_v2.jl is a package for Frontier Efficiency Analysis (aka Data Envelopment Analysis, DEA) computation. It is embedded in the Julia programming language, and is an extension to the JuMP modeling language. It is particularly designed to enhance large-scale DEA computation and to solve DEA problems by size-limited solvers.

Disclaimer : FrontierEfficiencyAnalysis_v2 is not developed or maintained by the JuMP developers.

Installation

In Julia, call Pkg.clone("git://github.com/wen-chih/FrontierEfficiencyAnalysis_v2.jl") to install FrontierEfficiencyAnalysis_v2.

Usage

DEA is a linear program (LP)-based method used to determine a firm’s relative efficiency. Users can use JuMP to model and solve the DEA problems (special LP problems). Rather than solve the LPs by calling JuMP.solve(), FrontierEfficiencyAnalysis_v2.jl can solve the large-scale problems more efficiently and/or by a solver with size limitation (e.g. 300 variables).

Please refer to Quick Start Guide of JuMP for modeling details. What needed is to call our FrontierEfficiencyAnalysis_v2.jl function:

solveDEA(model)

instead of calling

JuMP.solve(model)

Example

# full size example
# there are 6 cases
# please write the data output (e.g. to csv) by yourself
using JuMP
using Gurobi
using FrontierEfficiencyAnalysis_v2

include("solveDEA.jl")
include("variable.jl")

# CRS input-oriented
function case1(data)
    # make up the data set
    X = data[:,1:6] # 6
    Z = data[:,7:10] # 4
    Y = data[:,11:15] # 5
    scale = size(data)[1]
    xNo = size(X)[2]
    zNo = size(Z)[2]
    yNo = size(Y)[2]

    for k = 1:scale
        model = Model(solver = GurobiSolver(OutputFlag=0)) # Gurobi is used as the LP solver here. Users can choose their favorite solver.

        @solveDEA_varibleInit(model)
        @solveDEA_varible(model, Lambda[1:25000] >= 0, "nc") # non-critical group 1
        @solveDEA_varible(model, Gamma[1:25000] >= 0, "nc") # non-critical group 2
        @solveDEA_varible(model, middle[1:4] >= 0, "c") # critial
        @solveDEA_varible(model, Theta >= 0, "c") # critial

        @objective(model, Min, Theta)

        @constraint(model, inputConA[i=1:xNo], sum{Lambda[r]*X[r,i], r = 1:scale} <= Theta*X[k,i])
        @constraint(model, outputConA[j=1:zNo], sum{Lambda[r]*Z[r,j], r = 1:scale} >= middle[j])
        @constraint(model, inputConB[i=1:zNo], sum{Gamma[r]*Z[r,i], r = 1:scale} <= middle[i])
        @constraint(model, outputConB[j=1:yNo], sum{Gamma[r]*Y[r,j], r = 1:scale} >= Y[k,j])

        #solve(model)
        solveDEA(model)

        #println("lambdas: $(getvalue(Lambda)))")

        # retrieve results
        println("Objective value: ", getobjectivevalue(model))
    end
end


println("begins")
data = readcsv("example.csv")
case1(data)

println("done!")

Parameters

incrementSize : the incremental size to expand the sample ( default value: 100 ).

solveDEA(model, 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.

solveDEA(model, tol = 10^-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).

solveDEA(model, lpUB = 300) # set the LP size limitation to 300 variables

extremeValueSetFlag : to enable (=1) or disable (=0) performing initial sampling by selecing extreme value in each input/output dimension (default value: 0).

solveDEA(model, extremeValueSetFlag = 1) # enable

Citation

If you find FrontierEfficiencyAnalysis_v2 useful in your work, we kindly request that you cite the following papers

@article{ChenLai2017,
author = {Wen-Chih Chen and Sheng-Yung Lai},
title = {Determining radial efficiency with a large data set by solving small-size linear programs},
journal = {Annals of Operations Research},
volume = {250},
number = {1},
pages = {147-166},
year = {2017},
doi = {10.1007/s10479-015-1968-4},
}

and

@misc{chen2017b,
Author = {Wen-Chih Chen and Yueh-Shan Chung},
Title = {A generalized non-radial efficiency measure and its application in DEA computation},
Year = {2017},
Eprint = {http://dx.doi.org/10.2139/ssrn.2496847},
}

Acknowledgements

FrontierEfficiencyAnalysis_v2 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.