dea.add {Benchmarking} | R Documentation |
Additive DEA model
Description
Calculates additive efficiency as sum of input and output slacks within different DEA models
Usage
dea.add(X, Y, RTS="vrs", XREF=NULL, YREF=NULL,
FRONT.IDX=NULL, param=NULL, TRANSPOSE=FALSE, LP=FALSE)
Arguments
X |
Inputs of firms to be evaluated, a K x m matrix
of observations of K firms with m inputs (firm x input). In case
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Y |
Outputs of firms to be evaluated, a K x n matrix
of observations of K firms with n outputs (firm x input). In case
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RTS |
Text string or a number defining the underlying DEA technology / returns to scale assumption.
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XREF |
Inputs of the firms determining the technology, defaults
to | ||||||||||||||||||
YREF |
Outputs of the firms determining the technology, defaults
to | ||||||||||||||||||
FRONT.IDX |
Index for firms determining the technology | ||||||||||||||||||
param |
Possible parameters. At the moment only used for
RTS="fdh+" to set low and high values for restrictions on lambda;
see the section details and examples for its use. Future versions
might also use | ||||||||||||||||||
TRANSPOSE |
Input and output matrices are treated as firms
times goods matrices for the default value | ||||||||||||||||||
LP |
Only for debugging. If |
Details
The sum of the slacks is maximized in a LP formulation of the DEA technology. The sum of the slacks can be seen as distance to the frontier when you only move parallel to the axes of inputs and outputs, i.e. not a usual Euclidean distance, but what is also known as an L1 norm.
Since it is the sum of slacks that is calculated, there is no exogenous ORIENTATION in the problem. Rather, there is generally both an input and an output direction in the slacks. The model considers the input excess and output shortfall simultaneously and finds a point on the frontier that is most distant to the point being evaluated.
Value
sum |
Sum of all slacks for each firm,
|
slack |
A non-NULL vector of logical variables, |
sx |
A matrix of input slacks for each firm |
sy |
A matrix of output slack for each firm |
lambda |
The lambdas, i.e. the weights of the peers for each firm |
Note
This is neither a Farrell nor a Shephard like efficiency.
The value of the slacks depends on the scaling of the different inputs and outputs. Therefore the values are not independent of how the input and output are measured.
Author(s)
Peter Bogetoft and Lars Otto larsot23@gmail.com
Source
Corresponds to Eqs. 4.34-4.38 in Cooper et al. (2007)
References
Bogetoft and Otto; Benchmarking with DEA, SFA, and R; Springer 2011
Cooper, Seiford, and Tone; Data Envelopment Analysis: A Comprehensive Text with Models, Applications, References and DEA-Solver Software; Second edition, Springer 2007
Examples
x <- matrix(c(2,3,2,4,6,5,6,8),ncol=1)
y <- matrix(c(1,3,2,3,5,2,3,5),ncol=1)
dea.plot.frontier(x,y,txt=1:dim(x)[1])
sb <- dea.add(x,y,RTS="vrs")
data.frame("sx"=sb$sx,"sy"=sb$sy,"sum"=sb$sum,"slack"=sb$slack)