数据包络分析工具箱 EDA 算法分析
数据包络分析工具箱是MATLAB的新包，包括计算效率和生产率测量的功能。该软件包涵盖了径向，定向，添加，分配，Malmquist和Malmquist-Luenberger配方。
dea
function [ out ] = dea( X, Y, varargin)
%DEA Data envelopment analysis radial and directional model
% Computes data envelopment analysis radial and directional model
%
% out = DEA(X, Y, Name, Value) computes data envelopment analysis model
% with inputs X and outputs Y. Model properties are specified using
% one or more Name ,Value pair arguments.
%
% Additional properties:
% - 'orient': orientation. Input oriented 'io', output oriented 'oo',
% directional distane function 'ddf'.
% - 'rts': returns to scale. Constant returns to scale 'crs', variable
% returns to scale 'vrs'.
% - 'Gx': input directions for 'ddf' orientation. Default is Xeval.
% - 'Gy': output directions for 'ddf' orientation. Default is Yeval.
% - 'names': DMU names.
% - 'secondstep': 1 to compute input and output slacks. Default is 1.
%
% Advanced parameters:
% - 'Xeval: inputs to evaluate if different from X.
% - 'Yeval': outputs to evaluate if different from Y.
%
% Example
%
% io = dea(X, Y, 'orient', 'io');
% oo_vrs = dea(X, Y, 'orient', 'oo', 'rts', 'vrs');
% ddf = dea(X, Y, 'ddf', 'Gx', X, 'Gy', Y);
%
% See also DEAOUT, DEASCALE, DEAMALM, DEAADDIT, DEASUPER
%
% Copyright 2016 Inmaculada C. 脕lvarez, Javier Barbero, Jos茅 L. Zof铆o
% http://www.deatoolbox.com
%
% Version: 1.0
% LAST UPDATE: 1, August, 2017
%
% Check size
if size(X,1) ~= size(Y,1)
error('Number of rows in X must be equal to number of rows in Y')
end
% Get number of DMUs (n), inputs (m) and outputs (s)
[n, m] = size(X);
s = size(Y,2);
% Get DEA options
options = getDEAoptions(n, varargin{:});
% Orientation
switch(options.orient)
case {'io','input'}
orient = 'io';
case {'oo','output'}
orient = 'oo';
case {'ddf'}
orient = 'ddf';
case {'none'}
error('Radial Model is Oriented');
end
% RETURNS TO SCALE
rts = options.rts;
switch(rts)
case 'crs'
AeqRTS1 = [];
beqRTS1 = [];
AeqRTS2 = [];
beqRTS2 = [];
case 'vrs'
AeqRTS1 = [ones(1,n), 0];
beqRTS1 = 1;
AeqRTS2 = [ones(1,n), zeros(1,m), zeros(1,s)];
beqRTS2 = 1;
end
% If evaluate DMU at different X or Y
if ~isempty(options.Xeval)
Xeval = options.Xeval;
else
Xeval = X;
end
if ~isempty(options.Yeval)
Yeval = options.Yeval;
else
Yeval = Y;
end
if size(Xeval,1) ~= size(Yeval,1)
% Check size: rows
error('Number of rows in Xeval and Yeval must be equal')
end
if size(Xeval,2) ~= size(X,2)
% Check columns Xref
error('Number of columns in Xeval and X must be equal')
end
if size(Yeval,2) ~= size(Y,2)
% Check columns Yref
error('Number of columns in Yeval and Y must be equal')
end
neval = size(Xeval,1);
% OPTIMIZATION OPTIONS:
optimopts = options.optimopts;
% Create variables to store results
lambda = nan(neval, n);
slackX = nan(neval, m);
slackY = nan(neval, s);
eff = nan(neval, 1);
Eflag = nan(neval, 2);
Xeff = nan(neval, m);
Yeff = nan(neval, s);
dualineqlin = nan(neval, m + s);
dualeqlin = nan(neval, 1);
% OPTIMIZE: SOLVE LINEAR PROGRAMMING MODEL
switch(orient)
case 'io'
% For each DMU
for j=1:neval
% FIRST STEP:
% Objective function
f = [zeros(1,n), 1];
% Constraints
A = [ X', -Xeval(j,:)';
-Y', zeros(s,1)];
b = [zeros(m,1);
-Yeval(j,:)'];
Aeq = AeqRTS1;
beq = beqRTS1;
lb = zeros(1, n + 1);
% Optimize
[z, ~, exitflag, ~, dual] = linprog(f, A, b, Aeq, beq, lb, [], [], optimopts);
if exitflag ~= 1
if options.warning
warning('DMU %i. First Step. Optimization exit flag: %i', j, exitflag)
end
end
if isempty(z)
if options.warning
warning('DMU %i. First Step. Optimization doesn''t return a result. Efficiency set to NaN.', j)
end
z = nan(n + 1, 1);
dual.ineqlin = nan(1, m + s);
dual.eqlin = nan(1, 1);
end
% Get efficiency
theta = z(end);
Eflag(j, 1) = exitflag;
eff(j) = theta;
% Get dual results
dualineqlin(j, :) = dual.ineqlin;
if ~isempty(beqRTS1)
dualeqlin(j, 1) = dual.eqlin;
else
dualeqlin(j, 1) = NaN;
end
% SECOND STEP
if(options.secondstep) && ~isnan(theta)
% Objective function
f = [zeros(1, n), -ones(1, m + s)];
% Constraints
Aeq = [ X', eye(m,m) , zeros(m,s);
Y', zeros(s,m), -eye(s,s);
AeqRTS2];
beq = [theta .* Xeval(j,:)';
Yeval(j,:)';
beqRTS2];
lb = zeros(n + s + m, 1);
% Optimize
[z, ~, exitflag] = linprog(f, [], [], Aeq, beq, lb, [], [], optimopts);
if exitflag ~= 1
if options.warning
warning('DMU %i. Second Step. Optimization exit flag: %i', j, exitflag)
end
end
if isempty(z)
if options.warning
warning('DMU %i. Second Step. Optimization doesn''t return a result. Results set to NaN.', j)
end
z = nan(n + m + s, 1);
end
% Get results
lambda(j,:) = z(1:n);
slackX(j,:) = z(n + 1 : n + m);
slackY(j,:) = z(n + m + 1 : n + m + s);
Eflag(j, 2) = exitflag;
% Compute efficient inputs and outputs
Xeff(j,:) = repmat(eff(j), 1, m) .* Xeval(j,:) - slackX(j,:);
Yeff(j,:) = Yeval(j,:) + slackY(j,:);
end
end
% Compute efficient inputs and outputs
% Xeff = repmat(eff, 1, m) .* Xeval - slackX;
% Yeff = Yeval + slackY;
case 'oo'
% For each DMU
for j=1:neval
% FIRST STEP:
% Objective function (maximize)
f = -[zeros(1,n), 1];
% Constraints
A = [ X', zeros(m,1);
-Y', Yeval(j,:)'];
b = [Xeval(j,:)';
zeros(s,1)];
Aeq = AeqRTS1;
beq = beqRTS1;
lb = zeros(1, n + 1);
% Optimize
[z, ~, exitflag, ~, dual] = linprog(f, A, b, Aeq, beq, lb, [], [], optimopts);
if exitflag ~= 1
if options.warning
warning('DMU %i. First Step. Optimization exit flag: %i', j, exitflag)
end
end
if isempty(z)
if options.warning
warning('DMU %i. First Step. Optimization doesn''t return a result. Efficiency set to NaN.', j)
end
z = nan(n + 1, 1);
dual.ineqlin = nan(1, m + s);
dual.eqlin = nan(1, 1);
end
% Get efficiency
phi = z(end);
eff(j) = phi;
Eflag(j, 1) = exitflag;
% Get dual results
dualineqlin(j, :) = dual.ineqlin;
if ~isempty(beqRTS1)
dualeqlin(j, 1) = dual.eqlin;
else
dualeqlin(j, 1) = NaN;
end
% SECOND STEP
if(options.secondstep) && ~isnan(phi)
% Objective function
f = -[zeros(1, n), ones(1, m + s)];
% Constraints
Aeq = [ X', eye(m,m) , zeros(m,s), ;
Y', zeros(s,m), -eye(s,s) ;
AeqRTS2];
beq = [Xeval(j,:)'
phi .* Yeval(j,:)';
beqRTS2];
lb = zeros(n + s + m, 1);
% Optimize
[z, ~, exitflag] = linprog(f, [], [], Aeq, beq, lb, [], [], optimopts);
if exitflag ~= 1
if options.warning
warning('DMU %i. Second Step. Optimization exit flag: %i', j, exitflag)
end
end
if isempty(z)
if options.warning
warning('DMU %i. Second Step. Optimization doesn''t return a result. Results set to NaN.', j)
end
z = nan(n + m + s, 1);
end
% Get results
lambda(j,:) = z(1:n);
slackX(j,:) = z(n + 1 : n + m);
slackY(j,:) = z(n + m + 1 : n + m + s);
Eflag(j, 2) = exitflag;
% Compute efficient inputs and outputs
Xeff(j,:) = Xeval(j,:) - slackX(j,:);
Yeff(j,:) = repmat(eff(j), 1, s) .* Yeval(j,:) + slackY(j,:);
end
end
% Compute efficient inputs and outputs
% Xeff = Xeval - slackX;
% Yeff = repmat(eff, 1, s) .* Yeval + slackY;
case 'ddf'
% Get directions
Gx = options.Gx;
Gy = options.Gy;
if length(Gx) == 1
Gx = repmat(Gx, size(X,1), size(X,2));
elseif size(Gx, 1) == 1
Gx = repmat(Gx, size(X,1), 1);
end
if length(Gy) == 1
Gy = repmat(Gy, size(Y,1), size(Y,2));
elseif size(Gy, 1) == 1
Gy = repmat(Gy, size(Y,1), 1);
end
if isempty(Gx)
Gx = Xeval;
end
if isempty(Gy)
Gy = Yeval;
end
% For each DMU
for j=1:neval
% FIRST STEP:
% Objective function (maximize)
f = -[zeros(1,n), 1];
% Constraints
A = [ X', Gx(j,:)';
-Y', Gy(j,:)'];
b = [ Xeval(j,:)';
-Yeval(j,:)'];
Aeq = AeqRTS1;
beq = beqRTS1;
%lb = zeros(1, n + 1);
lb = [zeros(1, n), -inf];
% Optimize
[z, ~, exitflag, ~, dual] = linprog(f, A, b, Aeq, beq, lb, [], [], optimopts);
if exitflag ~= 1
if options.warning
warning('DMU %i. First Step. Optimization exit flag: %i', j, exitflag)
end
end
if isempty(z)
if options.warning
warning('DMU %i. First Step. Optimization doesn''t return a result. Efficiency set to NaN.', j)
end
z = nan(n + 1, 1);
dual.ineqlin = nan(1, m + s);
dual.eqlin = nan(1, 1);
end
% Get efficiency
beta = z(end);
eff(j) = beta;
Eflag(j, 1) = exitflag;
% Get dual results
dualineqlin(j, :) = dual.ineqlin;
if ~isempty(beqRTS1)
dualeqlin(j, 1) = dual.eqlin;
else
dualeqlin(j, 1) = NaN;
end
% SECOND STEP
if(options.secondstep) && ~isnan(beta)
% Objective function
f = -[zeros(1, n), ones(1, m + s)];
% Constraints
Aeq = [ X', eye(m,m) , zeros(m,s), ;
Y', zeros(s,m), -eye(s,s) ;
AeqRTS2];
beq = [-beta .* Gx(j,:)' + Xeval(j,:)'
beta .* Gy(j,:)' + Yeval(j,:)';
beqRTS2];
lb = zeros(n + s + m, 1);
% Optimize
[z, ~, exitflag] = linprog(f, [], [], Aeq, beq, lb, [], [], optimopts);
if exitflag ~= 1
if options.warning
warning('DMU %i. Second Step. Optimization exit flag: %i', j, exitflag)
end
end
if isempty(z)
if options.warning
warning('DMU %i. Second Step. Optimization doesn''t return a result. Results set to NaN.', j)
end
z = nan(n + m + s, 1);
end
% Get results
lambda(j,:) = z(1:n);
slackX(j,:) = z(n + 1 : n + m);
slackY(j,:) = z(n + m + 1 : n + m + s);
Eflag(j, 2) = exitflag;
% Compute efficient inputs and outputs
Xeff(j,:) = Xeval(j,:) - repmat(eff(j), 1, m) .* Gx(j,:) - slackX(j,:);
Yeff(j,:) = Yeval(j,:) + repmat(eff(j), 1, s) .* Gy(j,:) + slackY(j,:);
end
end
end
% Slacks structure
slack.X = slackX;
slack.Y = slackY;
% Dual structure
dual.X = dualineqlin(:, 1:m);
dual.Y = dualineqlin(:, m+1: m+s);
if ~isempty(beqRTS2)
dual.rts = dualeqlin(:);
else
dual.rts = nan(neval,1);
end
% SAVE results and input data
out = deaout('n', n, 'neval', neval', 's', s, 'm', m,...
'X', X, 'Y', Y, 'names', options.names,...
'model', 'radial', 'orient', orient, 'rts', rts,...
'lambda', lambda, 'slack', slack,...
'eff', eff, 'Xeff', Xeff, 'Yeff', Yeff,...
'dual', dual,...
'exitflag', Eflag,...
'dispstr', 'names/X/Y/eff/slack.X/slack.Y');
end
dea2table
function [ T ] = ( out, dispstr )
%DEA2TABLE Convert 'deaodea2tableut' results into a table object
% Convert data envelopment analysis results in a 'deaout' structure into
% a MATLAB table object.
%
% T = DEA2TABLE( out ) Converts 'deaout' structure into a MATLAB table
% object.
% T = DEA2TABLE( out, dispstr ) Converts 'deaout' structure into a MATLAB
% table object using the specified 'dispstr' structure.
%
% Example
%
% io = dea(X, Y, 'orient', 'io');
% T = dea2table(io);
%
% T2 = dea2table(io, 'names/lambda/eff');
%
% See also DEAOUT, DEADISP
%
% Copyright 2016 Inmaculada C. 羖varez, Javier Barbero, Jos� L. Zof韔
% http://www.deatoolbox.com
%
% Version: 1.0
% LAST UPDATE: 9, May, 2017
%
if nargin < 2
dispstr = out.dispstr;
end
% Convert to table
dispstr = strsplit(dispstr, '/');
% Create empty table
T = table();
% Build Header and Body
for i=1:length(dispstr)
% Get param name
paramstr = char(dispstr(i));
% Get data
dat = eval(sprintf('out.%s', paramstr));
% Append to Table
T = [T table(dat)];
% Get variable name
[name, ~] = getDEAformat(paramstr, out.orient);
% If no name in output structure
if isempty(name)
disptext_field = sprintf('disptext_%s', strrep(paramstr,'.','_'));
if isfield(out, disptext_field)
% If custom name exists in the output structure use it
name = eval(sprintf('out.%s',disptext_field));
else
% If not, display paramstr name without eff.
name = strrep(paramstr, 'eff.', '');
end
end
% Store variable name
T.Properties.VariableNames(size(T,2)) = cellstr(name);
end
end