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

In DJL: Distance Measure Based Judgment and Learning

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")

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)

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

Author(s)

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, ]

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