DJL (version 3.9)

roc.sf: Rate of change (RoC) calculation using SF

Description

Employs dm.sf over time to calculate RoCs. This function is valid only when multiplicative form of directional vector is used.

Usage

roc.sf(xdata, ydata, date, t, 
       rts="crs", g=NULL, wd=NULL, sg="ssm", ftype="d", cv="convex")

Value

$eff_r

Efficiency at release (i.e., at each production date)

$eff_t

Efficiency at t

$lambda_t

Intensity vector at t

$eft_date

Effective date

$roc_past

RoC observed from the obsolete DMUs in the past

$roc_avg

Average RoC

$roc_local

Local RoC

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

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)

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

cv

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

Author

Dong-Joon Lim, PhD

References

D.-J. Lim, Internal combustion engine race: naturally aspirated vs turbo/super-charged, working paper (2015).

See Also

dm.sf Distance measure using SF
roc.sf RoC calculation using SF
map.soa.sf SOA mapping using SF
target.arrival.sf Arrival target setting using SF

Examples

# Reproduce Mercedes-Benz CLA45 AMG's local RoC in Table 5 in Lim, D-J. (2015)
  # Load engine dataset
    df <- dataset.engine.2015
  
  # Subset for 4 cylinder engines
    fce <- subset(df, df[, 3] == 4)
    
  # Parameters
    x <- subset(fce, select = 4)
    y <- subset(fce, select = 5 : 7)
    d <- subset(fce, select = 2)
    g <- as.matrix(data.frame(0, y))
    w <- matrix(c(1, 0, 0), ncol = 3)

  # Calc local Roc
    roc.sf(x, y, d, 2014, "crs", g, w, "min")$roc_local[348, ]