The method sdea calculates super-efficiency and
returns the same class of object as dea.
sdea(X, Y, RTS = "vrs", ORIENTATION = "in", DIRECT = NULL, param = NULL,
TRANSPOSE = FALSE, LP = FALSE, CONTROL = NULL)The object returned is a Farrell object with the component
described in dea. The relevant components are
The efficiencies. Note when DIRECT is used then the efficencies are not Farrell efficiencies but rather excess values in DIRECT units of measurement.
The lambdas, i.e. the weight of the peers, for each Firm.
The objective value as returned from the LP program; normally the same as eff.
The return to scale assumption as in the option
RTS in the call.
The efficiency orientation as in the call.
Inputs of firms to be evaluated, a K x m matrix
of observations of K firms with m inputs (firm x input). In case
TRANSPOSE=TRUE the input matrix is transposed to input x
firm.
Outputs of firms to be evaluated, a K x n matrix
of observations of K firms with n outputs (firm x input). In case
TRANSPOSE=TRUE the output matrix is transposed to output x
firm.
Text string or a number defining the underlying DEA
technology / returns to scale assumption, the same values as for
dea.
| 0 | fdh | Free disposability hull, no convexity assumption |
| 1 | vrs | Variable returns to scale, convexity and free disposability |
| 2 | drs | Decreasing returns to scale, convexity, down-scaling and free disposability |
| 3 | crs | Constant returns to scale, convexity and free disposability |
| 4 | irs | Increasing returns to scale, (up-scaling, but not down-scaling), convexity and free disposability |
| 5 | irs2 | Increasing returns to scale (up-scaling, but not down-scaling), additivity, and free disposability |
| 6 | add | Additivity (scaling up and down, but only with integers), and free disposability |
| 7 | fdh+ | A combination of free disposability and restricted or local constant return to scale |
Input efficiency "in" (1), output efficiency
"out" (2), and graph efficiency "graph" (3). For use with
DIRECT, an additional option is "in-out" (0).
Directional efficiency, DIRECT is either a
scalar, an array, or a matrix with non-negative elements.
If the argument is a scalar, the direction is (1,1,...,1) times the scalar; the value of the efficiency depends on the scalar as well as on the unit of measurements.
If the argument an array, this is used for the direction for
every firm; the length of the array must correspond to the
number of inputs and/or outputs depending on the
ORIENTATION.
If the argument is a matrix then different directions are used
for each firm. The dimensions depends on the ORIENTATION,
the number of firms must correspond to the number of firms in
X and Y.
DIRECT must not be used in connection with
DIRECTION="graph".
Argument is at present only used when
RTS="fdh+", see dea for a description.
See the description in dea.
Only for debugging, see the description in
dea.
Possible controls to lpSolveAPI, see the
documentation for that package. For examples of use see the
function dea.
Peter Bogetoft and Lars Otto larsot23@gmail.com
Super-efficiency measures are constructed by avoiding that the evaluated firm can help span the technology, i.e. if the firm in qestuen is a firm on the frontier in a normal dea approach then this firm in super efficiency might be outside the technology set.
Peter Bogetoft and Lars Otto; Benchmarking with DEA, SFA, and R; Springer 2011. Sect. 5.2 page 115
P Andersen and NC Petersen; “A procedure for ranking efficient units in data envelopment analysis”; Management Science 1993 39(10):1261--1264
dea
x <- matrix(c(100,200,300,500,100,200,600),ncol=1)
y <- matrix(c(75,100,300,400,25,50,400),ncol=1)
se <- sdea(x,y)
se
# Leave out firm 3 as a determining firm of the technology set
n <- 3
dea.plot.frontier(x[-n], y[-n], txt=(1:dim(x)[1])[-n])
# Plot and label firm 3
points(x[n],y[n],cex=1.25,pch=16)
text(x[n],y[n],n,adj=c(-.75,.75))
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