sdea {Benchmarking}

Super efficiency

Description

The method sdea calculates super-efficiency and returns the same class of object as dea.

Usage

sdea(X, Y, RTS = "vrs", ORIENTATION = "in", DIRECT = NULL, param = NULL,
     TRANSPOSE = FALSE, LP = FALSE, CONTROL = NULL)

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 TRANSPOSE=TRUE the input matrix is transposed to input x firm.

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 TRANSPOSE=TRUE the output matrix is transposed to output x firm.

RTS

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

ORIENTATION

Input efficiency "in" (1), output efficiency "out" (2), and graph efficiency "graph" (3). For use with DIRECT, an additional option is "in-out" (0).

DIRECT

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".

param

Argument is at present only used when RTS="fdh+", see dea for a description.

TRANSPOSE

See the description in dea.

LP

Only for debugging, see the description in dea.

CONTROL

Possible controls to lpSolveAPI, see the documentation for that package. For examples of use see the function dea.

Details

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.

Value

The object returned is a Farrell object with the component described in dea. The relevant components are

eff

The efficiencies. Note when DIRECT is used then the efficencies are not Farrell efficiencies but rather excess values in DIRECT units of measurement.

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 RTS in the call.

ORIENTATION

The efficiency orientation as in the call.

Note

Calculation of slacks for super efficiency should be done by using the option SLACK=TRUE in the call of the method sdea. If the two phases are done in two steps as first a call to sdea and then a call to slacks the user must make sure to set the reference technology to the one corresponding to super-efficiency in the call to slack and this requires a loop with calls to slack.

Author(s)

Peter Bogetoft and Lars Otto [e-mail]

References

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

See Also

dea

Examples

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))