Distance measure using HDF

Description

Implements Fare's hyperbolic distance function (semi-radial & non-oriented measure).

Usage

1
2
dm.hdf(xdata, ydata, rts="crs", 
       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

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

$iteration

The number of iteration to obtain the hyperbolic efficiency score

Author(s)

Dong-Joon Lim, PhD

References

Fare, R., Shawna Grosskopf, and CA Knox Lovell. The Measurement of Efficiency of Production. Boston: Kulwer-Nijhoff (1985).

Fare, Rolf, et al. "Estimating the hyperbolic distance function: A directional distance function approach." European Journal of Operational Research 254.1 (2016): 312~319.

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

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
# Reproduce Table 2 in Fare et al.(2016)
  # ready
  x <- data.frame(x1 = c(2, 4, 9, 6.5, 10, 6, 9))
  y <- data.frame(y1 = c(3, 7, 10, 8.5, 4, 2, 8))

  # go
  sf  <- dm.sf (x, y, "vrs")$eff
  hdf <- dm.hdf(x, y, "vrs")$eff
  matrix(t(cbind(sf, hdf)), 2, 7, 
         dimnames = list(c("SF", "HDF"), 
                         paste0("DMU_", c(letters[1:4], "o", "p", "q"))))