Rate of change (RoC) calculation using SF

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Description

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

Usage

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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

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# 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, ]