SDEA: Super-efficiency Data Envelopment Analysis

In TFDEA: Technology Forecasting using DEA (Data Envelopment Analysis)

Description

Calculate Data Envelopment Analysis super-efficiency

Usage

SDEA(x, y, rts="vrs", orientation="input", slack=TRUE, dual = FALSE,
  cook=FALSE,
  second="none", z=0,
  round=FALSE, debug=1)

Arguments

x	Inputs or resources used by each decision making unit
y	Outputs or products of each decision making unit
rts	Returns to scale for the application, production technology, or industry studied vrs Variable returns to scale, convexity and free disposability drs Decreasing returns to scale, convexity, down-scaling and free disposability crs Constant returns to scale, convexity and free disposability irs Increasing returns to scale, (up-scaling, but not down-scaling), convexity and free disposability
orientation	Orientation of the DEA model - primary emphasis on input-reduction input or output-augmentation output
slack	Optional: slack=TRUE indicates a secondary objective function of maximizing non-radial slacks
dual	Optional: dual=TRUE reports back the dual weights (multipliers) for the inputs and outputs
cook	Optional: cook=TRUE enables using Cook algo. to compute super efficiency of DMUs that are infeasible under the standard model.
round	Optional: round=TRUE rounds efficiency values to 0 and 1 if close.
second	Optional: Enables an alternate secondary objective function based on lambda and the z matrix. The default is second=none. Other options include min or max which will then minimize or maximize z*lambda while holding efficiency constant for each decision making unit. Note that this precludes slack maximization in the current implementation
z	Optional: a matrix with one column and the same number of rows (decision making units) as x and y, it is required when second=min or max
debug	Optional: Only for debugging. If debug is a integer greater then zero debug information is output.

Details

This function implements either the standard super-efficiency model or the Cook's extended model whereby each decision making unit is compared to all other decision making units but not itself. This allows for efficiency scores that are "better" than 1 for most efficient Decision Making Units. Note that the standard super-efficiency model can cause infeasibilities especially when the Varialbe Returns to Scale is assumed. (Ex. rts=vrs)

Value

$status	If the solver returned a non-zero status for each decision making unit
$eff	Efficiency score for each decision making unit
$lambda	Lambda values for each decision making unit
$se.eff	Tau(Gamma) in input(output)-orientated model, only returned when cook=TRUE
$se.excess	Beta(Delta) in input(output)-oriented model, only returned when cook=TRUE
$vx	Input weights used by each decision making unit, only returned when dual=TRUE
$uy	Output weights used by each decision making unit, only returned when dual=TRUE
$w	W value for each decision making unit, only returned when dual=TRUE
$sx	Radial input slacks, only returned when slack=TRUE
$sy	Radial output slacks, only returned when slack=TRUE

References

P. Andersen, N.C. Petersen, A Procedure for Ranking Efficient Units in Data Envelopment Analysis, Manage. Sci. 39 (1993) 1261~1264.

W.D. Cook, L. Liang, Y. Zha, J. Zhu, A modified super-efficiency DEA model for infeasibility, J. Oper. Res. Soc. 60 (2009) 276~281.

See Also

DEA Data Envelopment Analysis - provides a variety of standard DEA models for examining the efficiency of different decision making units.

TFDEA Technology Forecasting Using Data Envelopment Analysis - a method of technology forecasting using past data to predict future capabilities

Examples

x <- matrix(c(1,2,3,4),ncol=1,dimnames=list(LETTERS[1:4],"X"))
y <- matrix(c(1,3,4,3),ncol=1,dimnames=list(LETTERS[1:4],"Y"))

# Simple radial DEA super-efficiency
SDEA(x, y, rts="vrs", orientation="input")

# Simple radial DEA super-efficiency with slack maximization
SDEA(x, y, rts="vrs", orientation="input", slack=TRUE)

# Cook's super-efficiency with slack maximization
SDEA(x, y, rts="vrs", orientation="input", slack=TRUE, cook=TRUE)

# Example of secondary objective function
x <- matrix(c(8,2,4,7,10,12,2,8,4,3,2,2),ncol=2,dimnames=list(LETTERS[1:6]))
colnames(x) = c("X1", "X2")
y <- matrix(c(1,1,1,1,1,1),ncol=1,dimnames=list(LETTERS[1:6],"Y"))
z <- matrix(c(1:6),ncol=1,dimnames=list(LETTERS[1:6],"Z"))

SDEA (x, y, rts="crs", orientation="input", slack=FALSE, second="min", z=z)

TFDEA documentation built on May 29, 2017, 11:55 a.m.