dm.sf: Distance measure using SF

In DJL: Distance Measure Based Judgment and Learning

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)

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

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

Author(s)

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)

DJL documentation built on March 31, 2023, 9:05 p.m.