DJL (version 3.9)

dm.sf: Distance measure using SF

Description

Implements Luenberger's shortage (benefit) function (radial & non-oriented measure).

Usage

dm.sf(xdata, ydata, rts="crs", g=NULL,
      wd=NULL, se=FALSE, sg="ssm", date=NULL, cv="convex", o=NULL)

Value

$eff

Efficiency score

$lambda

Intensity vector

$mu

Secondary intensity vector for weak disposability under VRS

$xslack

Input slack

$yslack

Output slack

$w

Input (dual) weight

$p

Output (dual) weight

$u

Free (dual) variable

Arguments

xdata

Input(s) vector (n by m)

ydata

Output(s) vector (n by s)

rts

Returns to scale assumption
"crs" Constant RTS (default)
"vrs" Variable RTS
"irs" Increasing RTS
"drs" Decreasing RTS

g

Directional vector indicating a measurement direction (n by (m+s))
By default (NULL), xdata & ydata will be used

wd

Weak disposability vector indicating (an) undesirable output(s) (1 by s)

se

Implements super-efficiency model alike Anderson & Peterson's model if TRUE

sg

Employs second-stage optimization
"ssm" Slack-sum maximization (default)
"max" Date-sum maximization (only if date is defined)
"min" Date-sum minimization (only if date is defined)

date

Production date (n by 1)

cv

Convexity assumption
"convex" Convexity holds (default)
"fdh" Free disposal hull (this will override rts)

o

DMU index to calc. NULL(default) will calc for all

Author

Dong-Joon Lim, PhD

References

Luenberger, David G. "Benefit functions and duality." Journal of mathematical economics 21.5 (1992): 461~481.

Chambers, Robert G., Yangho Chung, and Rolf Fare. "Profit, directional distance functions, and Nerlovian efficiency." Journal of optimization theory and applications 98.2 (1998): 351~364.

See Also

dm.ddf Distance measure using DDF
dm.dea Distance measure using DEA
dm.hdf Distance measure using HDF
dm.sbm Distance measure using SBM
dm.sf Distance measure using SF

Examples

# Additive form shortage function
  # ready
  x <- matrix(c(5, 1, 4), ncol = 1)
  y <- matrix(c(8, 3, 5, 6, 4, 1), ncol = 2)
  g <- matrix(c(1), nrow = 3, ncol = 3) 
  w <- matrix(c(1, 0), ncol = 2)
  # go
  dm.sf(x, y, "crs", g, w)

# Multiplicative form shortage function
  # ready
  g <- cbind(x, y)
  # go
  dm.sf(x, y, "crs", g, w)