Spec target setting using DEA

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Description

Employs inverse DEA to estimate specifications(in/out-puts) to achieve a predetermined efficiency.

Usage

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target.spec.dea(xdata, ydata, date=NULL, t=NULL, dt=NULL, dmu, et="c",
                alpha=NULL, beta=NULL, wv, rts="crs", sg="ssm", ftype="d",
                ncv=NULL, env=NULL, cv="convex", bound=TRUE)

Arguments

xdata

Input(s) vector (n by m)

ydata

Output(s) vector (n by s)

date

Production date (n by 1)

t

A vantage point from which the RoC is captured

dt

Delta t i.e., specs are estimated within PPS at t+dt

dmu

DMU whose inputs(or outputs) are to be estimated

et

Efficiency target; default value ("c") retains the current efficiency

alpha

Perturbed input(s) of designated DMU (1 by m)

beta

Perturbed output(s) of designated DMU (1 by s)

wv

Weight vector for scalarization (1 by m or s)

rts

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

sg

Employs second-stage optimization
"ssm" Slack-sum maximization (default)
"max" Date-sum maximization
"min" Date-sum minimization

ftype

Frontier type
"d" Dynamic frontier (default)
"s" Static frontier

ncv

Non-controllable variable index(binary) for internal NDF (1 by (m+s))

env

Environment index for external NDF (n by 1)

cv

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

bound

Puts upper/lower bounds on alpha/beta if TRUE(default)

Value

$alpha

Estimated input(s)

$beta

Estimated output(s)

$lambda

Intensity vector

$xslack

Input slack

$yslack

Output slack

Author(s)

Dong-Joon Lim, PhD

References

Lim, Dong-Joon, "Inverse DEA with frontier changes for new product target setting." European Journal of Operational Research 254.2 (2016): 510~516.

Wei, Quanling, Jianzhong Zhang, and Xiangsun Zhang. "An inverse DEA model for inputs/outputs estimate." European Journal of Operational Research 121.1 (2000): 151~163.

See Also

dm.dea Distance measure using DEA
roc.dea RoC calculation using DEA
target.arrival.dea Arrival target setting using DEA

Examples

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# Reproduce Example 2 in Wei, Q. et al.(2000)
  # ready
  x <- matrix(c(1, 1, 1), 3)
  y <- matrix(c(4, 8, 5, 8, 4, 5), 3)
  a <- matrix(1.8, 1)
  w <- matrix(c(0.5, 0.5), 1)
  
  # go
  target.spec.dea(x, y, dmu = 3, alpha = a, wv = w, rts = "crs")$beta

# Reproduce Table 4 in Lim, D-J. (2016)
  # Load engine dataset
    df <- dataset.engine.2015
  
  # Subset for forced induction systems
    fis <- subset(df, grepl("^.C..", df[, 8]))
  
  # ready
    # Suppose one wants to estimate Porsche 911 turbo s' engine specs
    # to retain its current competitiveness with downsized 3.5 litre engine in 2018.
    # What might be the minimum specs to achieve this goal
    # considering the technological changes we've seen so far?
    # Plus, the CEO wants to put more emphasis on the torque improvement over HP.
      d <- subset(fis, select = 2)
      x <- subset(fis, select = 4)
      y <- subset(fis, select = 6 : 7)
      a <- as.matrix(3.5)
      w <- matrix(c(0.3, 0.7), 1)
    
  # go
    target.spec.dea(x, y, d, 2015, 3, 262, alpha = a, wv = w, rts = "vrs", sg = "min")$beta