Distance measure using SBM

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Description

Implements Tone's slack-based model (non-radial & (non-)oriented measure).

Usage

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dm.sbm(xdata, ydata, rts="crs", 
       orientation="n", 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

orientation

Orientation of the measurement
"n" Non-orientation (default)
"i" Input-orientation
"o" Output-orientation

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

$xslack

Input slack

$yslack

Output slack

$xtarget

Input target

$ytarget

Output target

Author(s)

Dong-Joon Lim, PhD

References

Tone, Kaoru. "A slacks-based measure of efficiency in data envelopment analysis." European journal of operational research 130.3 (2001): 498~509.

Tone, Kaoru. "A slacks-based measure of super-efficiency in data envelopment analysis." European journal of operational research 143 (2002): 32~41.

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

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# Reproduce Table 2 in Tone.(2001)
  # ready
  X <- data.frame(x1 = c(4, 6, 8, 8, 2),
                  x2 = c(3, 3, 1, 1, 4))
  Y <- data.frame(y1 = c(2, 2, 6, 6, 1),
                  y2 = c(3, 3, 2, 1, 4))
  # go
  dm.sbm(X, Y)

# Reproduce Table 1 in Tone.(2002)
  # Published input slacks are alternate optima (confirmed by Tone)
  # ready
  X <- data.frame(x1 = c(4, 7, 8, 4, 2, 10, 12),
                  x2 = c(3, 3, 1, 2, 4, 1,  1))
  Y <- data.frame(y1 = c(1, 1, 1, 1, 1, 1,  1))
  # go
  dm.sbm(X, Y, se = TRUE)

# Reproduce Table 4 in Tone.(2002)
  # ready
  X <- data.frame(x1 = c(80,  65,  83,  40,   52,  94),
                  x2 = c(600, 200, 400, 1000, 600, 700),
                  x3 = c(54,  97,  72,  75,   20,  36),
                  x4 = c(8,   1,   4,   7,    3,   5))
  Y <- data.frame(y1 = c(90,  58,  60,  80,   72,  96),
                  y2 = c(5,   1,   7,   10,   8,   6))
  # go
  dm.sbm(X, Y, "crs", "i", se = TRUE)