mea {Benchmarking} | R Documentation |
MEA multi-directional efficiency analysis
Description
Potential improvements PI or multi-directional efficiency analysis. The result is an excess value measures by the direction.
The direction is determined by the direction corresponding to the minimum input/maximum direction each good can be changed when they are changed one at a time.
Usage
mea(X, Y, RTS = "vrs", ORIENTATION = "in", XREF = NULL, YREF = NULL,
FRONT.IDX = NULL, param=NULL, TRANSPOSE = FALSE,
LP = FALSE, CONTROL = NULL, LPK = NULL)
mea.lines(N, X, Y, ORIENTATION="in")
Arguments
X |
K times m matrix with K firms and m inputs as in | |||||||||||||||||||||
Y |
K times n matrix with K firms and n outputs as in | |||||||||||||||||||||
RTS |
Text string or a number defining the underlying DEA technology / returns to scale assumption.
| |||||||||||||||||||||
ORIENTATION |
Input efficiency "in" (1) or output efficiency "out" (2), and also the additional option "in-out" (0) for both input and output direction. | |||||||||||||||||||||
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 in | |||||||||||||||||||||
TRANSPOSE |
as in | |||||||||||||||||||||
LP |
as in | |||||||||||||||||||||
CONTROL |
as in | |||||||||||||||||||||
LPK |
as in | |||||||||||||||||||||
N |
Number of firms where directional lines are to be drawn on an already existing frontier plot (dea.plot.frontier) |
Details
Details can be found in Bogetoft and Otto (2011, 121–124).
This method is for input directional efficiency only interesting when there are 2 or more inputs, and for output only when there are 2 or more outputs.
Value
The results are returned in a Farrell object with the following components.
eff |
Excess value in DIRECT units of measurement, this is not Farrell efficiency |
lambda |
The lambdas, i.e. the weight of the peers, for each firm |
objval |
The objective value as returned from the LP program, normally the same as eff |
RTS |
The return to scale assumption as in the option |
ORIENTATION |
The efficiency orientation as in the call |
direct |
A K times m|n|m+n matrix with directions for each firm: the number of columns depends on whether it is input, output or in-out orientated. |
TRANSPOSE |
As in the call |
Note
The calculation is done in dea
after a
calculation of the direction that then is used in the argument
DIRECT
. The calculation of the direction is done in a series
LP programs, one for each good in the direction.
Author(s)
Peter Bogetoft and Lars Otto larsot23@gmail.com
References
Peter Bogetoft and Lars Otto; Benchmarking with DEA, SFA, and R; Springer 2011
See Also
dea
and the argument DIRECT
.
Examples
X <- matrix(c(2, 2, 5, 10, 10, 3, 12, 8, 5, 4, 6,12), ncol=2)
Y <- matrix(rep(1,dim(X)[1]), ncol=1)
dea.plot.isoquant(X[,1], X[,2],txt=1:dim(X)[1])
mea.lines(c(5,6),X,Y)
me <- mea(X,Y)
me
peers(me)
# MEA potential saving in inputs, exces inputs
eff(me) * me$direct
me$eff * me$direct
# Compare to traditionally Farrell efficiency
e <- dea(X,Y)
e
peers(e)
# Farrell potential saving in inputs, excess inputs
(1-eff(e)) * X