Type: | Package |
Title: | Distance Measure Based Judgment and Learning |
Version: | 3.9 |
Date: | 2023-03-16 |
Author: | Dong-Joon Lim, Ph.D. <technometrics.org> |
Depends: | R (≥ 3.4.0), car, lpSolveAPI |
Maintainer: | Dong-Joon Lim <tgno3.com@gmail.com> |
Description: | Implements various decision support tools related to the Econometrics & Technometrics. Subroutines include correlation reliability test, Mahalanobis distance measure for outlier detection, combinatorial search (all possible subset regression), non-parametric efficiency analysis measures: DDF (directional distance function), DEA (data envelopment analysis), HDF (hyperbolic distance function), SBM (slack-based measure), and SF (shortage function), benchmarking, Malmquist productivity analysis, risk analysis, technology adoption model, new product target setting, network DEA, dynamic DEA, intertemporal budgeting, etc. |
License: | GPL-2 |
LazyData: | true |
NeedsCompilation: | no |
Packaged: | 2023-03-16 14:11:21 UTC; Technometrics |
Repository: | CRAN |
Date/Publication: | 2023-03-16 15:10:02 UTC |
Dataset of commercial airplanes from 1965 to 2017.
Description
Commercial airplanes from 1965 to 2017.
Usage
data(dataset.airplane.2017)
Columns
[,1] Name
Airplane name
[,2] EIS
Entry into service
[,3] Range
Maximum range at full payload in 1,000km
[,4] P.cap
Passenger capacity
[,5] PFE
Passenger fuel efficiency in passengers*km/L (log scale)
[,6] C.spd
Cruising speed in km/hr
[,7] M.spd
Maximum speed in km/hr
Author(s)
Dong-Joon Lim, PhD
Source
http://www.airbus.com/aircraftfamilies
http://www.boeing.com/commercial
References
Lim, Dong-Joon, and Timothy R. Anderson. Time series benchmarking analysis for new product scheduling: who are the competitors and how fast are they moving forward?. Advances in DEA Theory and Applications: with Examples in Forecasting Models. (2017): 443-458.
Examples
# Load dataset
data(dataset.airplane.2017)
Dataset of auto engines from MY2005 to MY2015.
Description
Auto engines from MY2005 to MY2015.
Usage
data(dataset.engine.2015)
Columns
[,1] Name
Vehicle name
[,2] MY
Model year
[,3] Cylinder
The number of cylinder
[,4] Displacement
Displacement in liter
[,5] CO2
CO2 emission in gram/mile
[,6] Power
Engine power in HP
[,7] Torque
Engine torque in lb.ft
[,8] Type
Engine system and fuel type
Author(s)
Dong-Joon Lim, PhD
Source
http://www.fueleconomy.gov
http://www.autoevolution.com
References
D.-J. Lim, Internal combustion engine race: naturally aspirated vs turbo/super-charged, working paper (2015).
Examples
# Load dataset
data(dataset.engine.2015)
Dataset of hybrid electric vehicles from MY1997 to MY2013.
Description
Hybrid electric vehicles from MY1997 to MY2013.
Usage
data(dataset.hev.2013)
Columns
[,1] Name
Vehicle name
[,2] MY
Model year
[,3] MSRP.2013
MSRP converted to 2013 value
[,4] Acc
Acceleration (0-100km) in km/h/s
[,5] MPG
MPG in mile/gallon
[,6] MPGe
MPG equivalence for PHEV in mile/gallon
Author(s)
Dong-Joon Lim, PhD
Source
http://www.fueleconomy.gov
References
Lim, Dong-Joon, et al. "Comparing technological advancement of hybrid electric vehicles (HEV) in different market segments." Technological Forecasting and Social Change 97 (2015): 140~153.
Examples
# Load dataset
data(dataset.hev.2013)
Distance measure using DDF
Description
Implements Chambers' directional distance function (non-radial & non-oriented measure).
Usage
dm.ddf(xdata, ydata, rts="crs", g=NULL,
wd=NULL, 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 |
g |
Directional vector indicating a measurement direction (n by (m+s)) |
wd |
Weak disposability vector indicating (an) undesirable output(s) (1 by s) |
se |
Implements super-efficiency model alike Anderson & Peterson's model if |
sg |
Employs second-stage optimization |
date |
Production date (n by 1) |
cv |
Convexity assumption |
o |
DMU index to calc. |
Value
$eff |
Efficiency score |
$lambda |
Intensity vector |
$mu |
Secondary intensity vector for weak disposability under VRS |
$beta |
Input reduction factor |
$gamma |
Output augmentation factor |
$xslack |
Input slack |
$yslack |
Output slack |
Author(s)
Dong-Joon Lim, PhD
References
Chambers, Robert G., Yangho Chung, and Rolf Fare. "Profit, directional distance functions, and Nerlovian efficiency." Journal of optimization theory and applications 98.2 (1998): 351~364.
Fare, Rolf, and Shawna Grosskopf. "Directional distance functions and slacks-based measures of efficiency." European journal of operational research 200.1 (2010): 320~322.
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
# Additive form directional distance function
# ready
x <- matrix(c(5, 1, 4), ncol = 1)
y <- matrix(c(8, 3, 5, 6, 4, 1), ncol = 2)
g <- matrix(c(1), nrow = 3, ncol = 3)
w <- matrix(c(1, 0), ncol = 2)
# go
dm.ddf(x, y, "crs", g, w)
# Multiplicative form directional distance function
# ready
g <- cbind(x, y)
# go
dm.ddf(x, y, "crs", g, w)
Distance measure using DEA
Description
Implements Charnes & Cooper's data envelopment analysis (radial & oriented measure).
Usage
dm.dea(xdata, ydata, rts="crs", orientation,
se=FALSE, sg="ssm", date=NULL, ncv=NULL, env=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 |
orientation |
Orientation of the measurement |
se |
Implements Andersen & Petersen's super-efficiency model if |
sg |
Employs second-stage optimization |
date |
Production date (n by 1) |
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 |
o |
DMU index to calc. |
Value
$eff |
Efficiency score |
$lambda |
Intensity vector |
$xslack |
Input slack |
$yslack |
Output slack |
$vx |
Input (dual) weight |
$uy |
Output (dual) weight |
$w |
Free (dual) variable |
Author(s)
Dong-Joon Lim, PhD
References
Charnes, Abraham, William W. Cooper, and Edwardo Rhodes. "Measuring the efficiency of decision making units." European journal of operational research 2.6 (1978): 429~444.
Charnes, Abraham, William W. Cooper, and Edwardo Rhodes. "Evaluating program and managerial efficiency: an application of data envelopment analysis to program follow through." Management science 27.6 (1981): 668~697.
Banker, Rajiv D., and Richard C. Morey. "Efficiency analysis for exogenously fixed inputs and outputs." Operations Research 34.4 (1986): 513~521.
Ruggiero, John. "On the measurement of technical efficiency in the public sector." European Journal of Operational Research 90.3 (1996): 553~565.
Fried, Harold O., CA Knox Lovell, and Shelton S. Schmidt, eds. The measurement of productive efficiency and productivity growth. Oxford University Press, 2008.
See Also
dm.ddf
Distance measure using DDF
dm.dea
Distance measure using DEA
dm.hdf
Distance measure using HDF
dm.sbm
Distance measure using SBM
dm.sf
Distance measure using SF
Examples
# Reproduce Table 3.9 (p.348) in Fried, H.O. et al.(2008)
# ready
X <- data.frame(x1 = c(8, 6, 3, 10, 6, 8, 8, 4),
x2 = c(8, 4.6, 1.9, 9, 3.6, 3.6, 9, 1.9))
Y <- data.frame(y1 = c(8, 5, 2, 9, 4.5, 4.5, 7, 2))
C <- data.frame(x1 = 0, x2 = 1, y1 = 0)
# go
data.frame(ALL_CRS = dm.dea(X, Y, "crs", "i")$eff,
ALL_VRS = dm.dea(X, Y, "vrs", "i")$eff,
NDF_CRS = dm.dea(X, Y, "crs", "i", ncv = C)$eff,
NDF_VRS = dm.dea(X, Y, "vrs", "i", ncv = C)$eff,
row.names = LETTERS[1 : 8])
Dynamic DEA in the presence of intertemporal Budget Constraints
Description
Employs the Farrell measure on carry-over budget as well as input or output
Usage
dm.dynamic.bc(xdata, ydata, zdata, bdata, rts="crs", orientation="i", wv=NULL)
Arguments
xdata |
Input array (n by m by t) |
ydata |
Output array (n by s by t) |
zdata |
Budget(spent) array (n by b by t) |
bdata |
Budget(secured) array (n by b) |
rts |
Returns to scale assumption |
orientation |
Orientation of the measurement |
wv |
Weight vector for scalarization (1 by m or s) |
Value
$eff.s |
System Efficiency |
$eff.t |
Period Efficiency |
$lambda |
Intensity vectors |
$xslack |
Input slack |
$yslack |
Output slack |
$zslack |
Budget(spent) slack |
$aslack |
Budget(available) slack |
Author(s)
Dong-Joon Lim, PhD
References
Lim, D.-J., M.-S., Kim, & K.-W., Lee. (2020). "A revised dynamic DEA model with budget constraints." International Transactions in Operational Research (In press).
See Also
dm.dea
Distance measure using DEA
Examples
# Load data
df.io <- array(c(2, 4, 8, 4, 1, 2, 2, 2, 3, 6, 12, 6,
5, 4, 3, 8, 1, 1, 1, 1, 5, 4, 3, 8),
c(4, 3, 2),
dimnames = list(LETTERS[1:4], c("X", "Y", "z"), c("t1", "t2")))
df.Z.0 <- array(c(9, 12, 18, 24), c(4, 1), dimnames = list(LETTERS[1:4], c("Z^0")))
# Run
dm.dynamic.bc(df.io[,1,], df.io[,2,], df.io[,3,], df.Z.0)
Distance measure using HDF
Description
Implements Fare's hyperbolic distance function (semi-radial & non-oriented measure).
Usage
dm.hdf(xdata, ydata, rts="crs",
wd=NULL, 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 |
wd |
Weak disposability vector indicating (an) undesirable output(s) (1 by s) |
se |
Implements super-efficiency model alike Anderson & Peterson's model if |
sg |
Employs second-stage optimization |
date |
Production date (n by 1) |
cv |
Convexity assumption |
o |
DMU index to calc. |
Value
$eff |
Efficiency score |
$lambda |
Intensity vector |
$mu |
Secondary intensity vector for weak disposability under VRS |
$xslack |
Input slack |
$yslack |
Output slack |
$iteration |
The number of iteration to obtain the hyperbolic efficiency score |
Author(s)
Dong-Joon Lim, PhD
References
Fare, R., Shawna Grosskopf, and CA Knox Lovell. The Measurement of Efficiency of Production. Boston: Kulwer-Nijhoff (1985).
Fare, Rolf, et al. "Estimating the hyperbolic distance function: A directional distance function approach." European Journal of Operational Research 254.1 (2016): 312~319.
See Also
dm.ddf
Distance measure using DDF
dm.dea
Distance measure using DEA
dm.hdf
Distance measure using HDF
dm.sbm
Distance measure using SBM
dm.sf
Distance measure using SF
Examples
# Reproduce Table 2 in Fare et al.(2016)
# ready
x <- data.frame(x1 = c(2, 4, 9, 6.5, 10, 6, 9))
y <- data.frame(y1 = c(3, 7, 10, 8.5, 4, 2, 8))
# go
sf <- dm.sf (x, y, "vrs")$eff
hdf <- dm.hdf(x, y, "vrs")$eff
matrix(t(cbind(sf, hdf)), 2, 7,
dimnames = list(c("SF", "HDF"),
paste0("DMU_", c(letters[1:4], "o", "p", "q"))))
Distance measure using Mahalanobis distance for outlier detection
Description
Implements Mahalanobis distance measure for outlier detection. In addition to the basic distance measure, boxplots are provided with potential outlier(s) to give an insight into the early stage of data cleansing task.
Usage
dm.mahalanobis(data, from="median", p=10, plot=FALSE, v.index=NULL, layout=NULL)
Arguments
data |
Dataframe |
from |
Datum point from which the distance is measured |
p |
Percentage to which outlier point(s) is noted (default of 10) |
plot |
Switch for boxplot(s) |
v.index |
Numeric vector indicating column(s) to be printed in the boxplot.
Default value of |
layout |
Numeric vector indicating dimension of boxplots.
Default value of |
Value
$dist |
|
$excluded |
Excluded row(s) in row number |
$order |
Distance order (decreasing) in row number |
$suspect |
Potential outlier(s) in row number |
Author(s)
Dong-Joon Lim, PhD
References
Hair, Joseph F., et al. Multivariate data analysis. Vol. 7. Upper Saddle River, NJ: Pearson Prentice Hall, 2006.
Examples
# Generate a sample dataframe
df <- data.frame(replicate(6, sample(0 : 100, 50)))
# go
dm.mahalanobis(df, plot = TRUE)
Distance measure using DEA on a two-stage network structure
Description
Implements Charnes & Cooper's data envelopment analysis (radial & oriented measure) on a two-stage network structure.
Usage
dm.network.dea(xdata.s1, ydata.s1=NULL, zdata, xdata.s2=NULL, ydata.s2,
rts="crs", orientation="i", type="nc", leader="1st", ss=10^-4, o=NULL)
Arguments
xdata.s1 |
Input(s) vector in Stage 1 (n by m.s1) |
ydata.s1 |
Output(s) vector in Stage 1 (n by s.s1) |
zdata |
Intermediate product(s) vector between Stage 1 and Stage 2 (n by p) |
xdata.s2 |
Input(s) vector in Stage 2 (n by m.s2) |
ydata.s2 |
Output(s) vector in Stage 2 (n by s.s2) |
rts |
Returns to scale assumption |
orientation |
Orientation of the measurement |
type |
Solution method |
leader |
Preemptive priority for Decentralized model |
ss |
Step size for heuristic search |
o |
DMU index to operate. |
Value
$eff.s1 |
Efficiency score of Stage 1 |
$eff.s2 |
Efficiency score of Stage 2 |
$v.s1 |
Weight attached to input in Stage 1 |
$u.s1 |
Weight attached to output in Stage 1 |
$p |
Weight attached to intermediate product |
$w.s1 |
Free variable for scaling in Stage 1 |
$v.s2 |
Weight attached to input in Stage 2 |
$u.s2 |
Weight attached to output in Stage 2 |
$w.s2 |
Free variable for scaling in Stage 2 |
Author(s)
Dong-Joon Lim, Ph.D.
References
Kao, Chiang, and Shiuh-Nan Hwang. "Efficiency decomposition in two-stage data envelopment analysis: An application to non-life insurance companies in Taiwan." European journal of operational research 185.1 (2008): 418-429.
Cook, Wade D., Liang Liang, and Joe Zhu. "Measuring performance of two-stage network structures by DEA: a review and future perspective." Omega 38.6 (2010): 423-430.
Li, Yongjun, Yao Chen, Liang Liang, and Jianhui Xie. "DEA models for extended two-stage network structures." Omega 40.5 (2012): 611-618.
Lee, Hsuan-Shih. "Efficiency decomposition of the network DEA in variable returns to scale: An additive dissection in losses." Omega 100 (2021): 102212.
See Also
dm.dea
Distance measure using DEA
dm.dynamic.bc
Dynamic DEA for intertemporal budgeting
Examples
# Reproduce Table 2 in W.D. Cook et al.(2010)
# ready
X <- data.frame(x1 = c(1178744,1381822,1177494,601320,6699063,2627707,1942833,3789001,
1567746,1303249,1962448,2592790,2609941,1396002,2184944,1211716,
1453797,757515,159422,145442,84171,15993,54693,163297,1544215),
x2 = c(673512,1352755,592790,594259,3531614,668363,1443100,1873530,
950432,1298470,672414,650952,1368802,988888,651063,415071,
1085019,547997,182338,53518,26224,10502,28408,235094,828963))
Z <- data.frame(z1 = c(7451757,10020274,4776548,3174851,37392862,9747908,10685457,17267266,
11473162,8210389,7222378,9434406,13921464,7396396,10422297,5606013,
7695461,3631484,1141950,316829,225888,52063,245910,476419,7832893),
z2 = c(856735,1812894,560244,371863,1753794,952326,643412,1134600,
546337,504528,643178,1118489,811343,465509,749893,402881,
342489,995620,483291,131920,40542,14574,49864,644816,667964))
Y <- data.frame(y1 = c(984143,1228502,293613,248709,7851229,1713598,2239593,3899530,
1043778,1697941,1486014,1574191,3609236,1401200,3355197,854054,
3144484,692731,519121,355624,51950,82141,0.1,142370,1602873),
y2 = c(681687,834754,658428,177331,3925272,415058,439039,622868,
264098,554806,18259,909295,223047,332283,555482,197947,
371984,163927,46857,26537,6491,4181,18980,16976,477733))
# go
res.co <- dm.network.dea(xdata.s1 = X, zdata = Z, ydata.s2 = Y, type = "co")
res.nc.LF <- dm.network.dea(xdata.s1 = X, zdata = Z, ydata.s2 = Y, type = "nc", leader = "1st")
res.nc.FL <- dm.network.dea(xdata.s1 = X, zdata = Z, ydata.s2 = Y, type = "nc", leader = "2nd")
# print
data.frame(CO.s1 = res.co$eff.s1,
CO.s2 = res.co$eff.s2,
NC.LF.s1 = res.nc.LF$eff.s1,
NC.LF.s2 = res.nc.LF$eff.s2,
NC.FL.s1 = res.nc.FL$eff.s1,
NC.FL.s2 = res.nc.FL$eff.s2)
Distance measure using SBM
Description
Implements Tone's slack-based model (non-radial & (non-)oriented measure).
Usage
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 |
orientation |
Orientation of the measurement |
se |
Implements super-efficiency model alike Anderson & Peterson's model if |
sg |
Employs second-stage optimization |
date |
Production date (n by 1) |
cv |
Convexity assumption |
o |
DMU index to calc. |
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
# 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)
Distance measure using SF
Description
Implements Luenberger's shortage (benefit) function (radial & non-oriented measure).
Usage
dm.sf(xdata, ydata, rts="crs", g=NULL,
wd=NULL, 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 |
g |
Directional vector indicating a measurement direction (n by (m+s)) |
wd |
Weak disposability vector indicating (an) undesirable output(s) (1 by s) |
se |
Implements super-efficiency model alike Anderson & Peterson's model if |
sg |
Employs second-stage optimization |
date |
Production date (n by 1) |
cv |
Convexity assumption |
o |
DMU index to calc. |
Value
$eff |
Efficiency score |
$lambda |
Intensity vector |
$mu |
Secondary intensity vector for weak disposability under VRS |
$xslack |
Input slack |
$yslack |
Output slack |
$w |
Input (dual) weight |
$p |
Output (dual) weight |
$u |
Free (dual) variable |
Author(s)
Dong-Joon Lim, PhD
References
Luenberger, David G. "Benefit functions and duality." Journal of mathematical economics 21.5 (1992): 461~481.
Chambers, Robert G., Yangho Chung, and Rolf Fare. "Profit, directional distance functions, and Nerlovian efficiency." Journal of optimization theory and applications 98.2 (1998): 351~364.
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
# Additive form shortage function
# ready
x <- matrix(c(5, 1, 4), ncol = 1)
y <- matrix(c(8, 3, 5, 6, 4, 1), ncol = 2)
g <- matrix(c(1), nrow = 3, ncol = 3)
w <- matrix(c(1, 0), ncol = 2)
# go
dm.sf(x, y, "crs", g, w)
# Multiplicative form shortage function
# ready
g <- cbind(x, y)
# go
dm.sf(x, y, "crs", g, w)
Combinatorial search (all possible subset) for regression analysis
Description
Implements combinatorial (exhaustive) search algorithm, aka all-possible-subsets regression. As opposed to the sequential approach (stepwise, forward addition, or backward elimination) that has a potential bias resulting from considering only one variable for selection at a time, all possible combinations of the independent variables are examined, and sets satisfying designated conditions are returned.
Usage
ma.aps.reg(dv, iv, min=1, max, mad=FALSE, aic=FALSE, bic=FALSE,
model.sig=TRUE, coeff.sig=TRUE, coeff.vif=TRUE, coeff.cor=FALSE)
Arguments
dv |
Dependent variable (r by 1) |
iv |
Independent variable(s) (r by c) |
min |
Minimum number of independent variable to explore (>=1) |
max |
Maximum number of independent variable to explore (<=r/10) |
mad |
Returns mean absolute deviation when |
aic |
Returns Akaike's information criterion when |
bic |
Returns Bayesian information criterion when |
model.sig |
Returns models statistically significant only when |
coeff.sig |
Returns models with statistically significant coefficients only when |
coeff.vif |
Returns models with allowable level of multicollinearity only when |
coeff.cor |
Returns models without suppression effects only when |
Author(s)
Dong-Joon Lim, PhD
References
Hair, Joseph F., et al. Multivariate data analysis. Vol. 7. Upper Saddle River, NJ: Pearson Prentice Hall, 2006.
Examples
# Load airplane dataset
df <- dataset.airplane.2017
# ready
dv <- subset(df, select = 2)
iv <- subset(df, select = 3 : 7)
# go
ma.aps.reg(dv, iv, 1, 3, mad = TRUE, coeff.cor = TRUE)
Correlation mapping for reliability test
Description
Implements a series of correlation analysis by dropping extreme data points one by one using Mahalanobis distance measure. Correlation reliability can be investigated with identified anchoring point(s). Correlation map as well as summary table is provided.
Usage
map.corr(data, from = "median", threshold = 0.3, r.name = FALSE)
Arguments
data |
Dataframe |
from |
Datum point from which the distance is measured |
threshold |
Threshold of correlation change to be noted on the map |
r.name |
Dropped points are shown in row name when |
Value
$reliability |
Summary table |
Author(s)
Dong-Joon Lim, PhD
See Also
dm.mahalanobis
Distance measure using Mahalanobis distance
Examples
# Generate a sample dataframe
df <- data.frame(replicate(2, sample(0 : 100, 50)))
# go
map.corr(df)
SOA mapping using DDF
Description
Employs dm.ddf
over time to generate a state-of-the-art map.
Usage
map.soa.ddf(xdata, ydata, date,
rts="crs", g=NULL, wd=NULL, sg="ssm", cv="convex", mk="dmu")
Arguments
xdata |
Input(s) vector (n by m) |
ydata |
Output(s) vector (n by s) |
date |
Production date (n by 1) |
rts |
Returns to scale assumption |
g |
Directional vector indicating a measurement direction (n by (m+s)) |
wd |
Weak disposability vector indicating (an) undesirable output(s) (1 by s) |
sg |
Employs second-stage optimization |
cv |
Convexity assumption |
mk |
Marker on the map |
Author(s)
Dong-Joon Lim, PhD
See Also
map.soa.ddf
SOA mapping using DDF
map.soa.dea
SOA mapping using DEA
map.soa.hdf
SOA mapping using HDF
map.soa.sbm
SOA mapping using SBM
map.soa.sf
SOA mapping using SF
Examples
# Load engine dataset
df <- dataset.engine.2015
# Subset for forced induction systems
fis <- subset(df, grepl("^.C..", df[, 8]))
# Parameters
x <- subset(fis, select = 4)
y <- subset(fis, select = 6 : 7)
d <- subset(fis, select = 2)
g <- matrix(c(1), nrow = nrow(x), ncol = 3)
# Generate an SOA map
map.soa.ddf(x, y, d, "crs", g)
SOA mapping using DEA
Description
Employs dm.dea
over time to generate a state-of-the-art map.
Usage
map.soa.dea(xdata, ydata, date, rts="crs", orientation,
sg="ssm", ncv=NULL, env=NULL, cv="convex", mk="dmu")
Arguments
xdata |
Input(s) vector (n by m) |
ydata |
Output(s) vector (n by s) |
date |
Production date (n by 1) |
rts |
Returns to scale assumption |
orientation |
Orientation of the measurement |
sg |
Employs second-stage optimization |
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 |
mk |
Marker on the map |
Author(s)
Dong-Joon Lim, PhD
See Also
map.soa.ddf
SOA mapping using DDF
map.soa.dea
SOA mapping using DEA
map.soa.hdf
SOA mapping using HDF
map.soa.sbm
SOA mapping using SBM
map.soa.sf
SOA mapping using SF
Examples
# Load engine dataset
df <- dataset.engine.2015
# Subset for forced induction systems
fis <- subset(df, grepl("^.C..", df[, 8]))
# Parameters
x <- subset(fis, select = 4)
y <- subset(fis, select = 6 : 7)
d <- subset(fis, select = 2)
# Generate an SOA map
map.soa.dea(x, y, d, "crs", "o")
SOA mapping using HDF
Description
Employs dm.hdf
over time to generate a state-of-the-art map.
Usage
map.soa.hdf(xdata, ydata, date,
rts="crs", wd=NULL, sg="ssm", cv="convex", mk="dmu")
Arguments
xdata |
Input(s) vector (n by m) |
ydata |
Output(s) vector (n by s) |
date |
Production date (n by 1) |
rts |
Returns to scale assumption |
wd |
Weak disposability vector indicating (an) undesirable output(s) (1 by s) |
sg |
Employs second-stage optimization |
cv |
Convexity assumption |
mk |
Marker on the map |
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
map.soa.ddf
SOA mapping using DDF
map.soa.dea
SOA mapping using DEA
map.soa.hdf
SOA mapping using HDF
map.soa.sbm
SOA mapping using SBM
map.soa.sf
SOA mapping using SF
Examples
# Load engine dataset
df <- dataset.engine.2015
# Subset for SC/TC 8 cylinder engines
stc.8 <- subset(df, grepl("^.C..", df[, 8]) & df[, 3] == 8)
# Parameters
x <- subset(stc.8, select = 4)
y <- subset(stc.8, select = 5:7)
d <- subset(stc.8, select = 2)
# Generate an SOA map
map.soa.hdf(x, y, d, "vrs")
SOA mapping using SBM
Description
Employs dm.sbm
over time to generate a state-of-the-art map.
Usage
map.soa.sbm(xdata, ydata, date,
rts="crs", orientation="n", sg="ssm", cv="convex", mk="dmu")
Arguments
xdata |
Input(s) vector (n by m) |
ydata |
Output(s) vector (n by s) |
date |
Production date (n by 1) |
rts |
Returns to scale assumption |
orientation |
Orientation of the measurement |
sg |
Employs second-stage optimization |
cv |
Convexity assumption |
mk |
Marker on the map |
Author(s)
Dong-Joon Lim, PhD
See Also
map.soa.ddf
SOA mapping using DDF
map.soa.dea
SOA mapping using DEA
map.soa.hdf
SOA mapping using HDF
map.soa.sbm
SOA mapping using SBM
map.soa.sf
SOA mapping using SF
Examples
# Load engine dataset
df <- dataset.engine.2015
# Subset for forced induction systems
fis <- subset(df, grepl("^.C..", df[, 8]))
# Parameters
x <- subset(fis, select = 4)
y <- subset(fis, select = 6 : 7)
d <- subset(fis, select = 2)
# Generate an SOA map
map.soa.sbm(x, y, d)
SOA mapping using SF
Description
Employs dm.sf
over time to generate a state-of-the-art map.
Usage
map.soa.sf(xdata, ydata, date,
rts="crs", g=NULL, wd=NULL, sg="ssm", cv="convex", mk="dmu")
Arguments
xdata |
Input(s) vector (n by m) |
ydata |
Output(s) vector (n by s) |
date |
Production date (n by 1) |
rts |
Returns to scale assumption |
g |
Directional vector indicating a measurement direction (n by (m+s)) |
wd |
Weak disposability vector indicating (an) undesirable output(s) (1 by s) |
sg |
Employs second-stage optimization |
cv |
Convexity assumption |
mk |
Marker on the map |
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
map.soa.ddf
SOA mapping using DDF
map.soa.dea
SOA mapping using DEA
map.soa.hdf
SOA mapping using HDF
map.soa.sbm
SOA mapping using SBM
map.soa.sf
SOA mapping using SF
Examples
# Reproduce Table 2 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 <- data.frame(0, y)
w <- matrix(c(1, 0, 0), ncol = 3)
# Generate an SOA map
map.soa.sf(x, y, d, "crs", g, w, mk = "eff")
Print LP object
Description
Print an LP object line by line.
Usage
plp(x)
Arguments
x |
LP object defined by make.lp function in lpSolve library |
Author(s)
Dong-Joon Lim, PhD
References
Berkelaar, Michel, Kjell Eikland, and Peter Notebaert. "lpsolve: Open source (mixed-integer) linear programming system." Eindhoven U. of Technology 63 (2004).
Examples
# Declare an LP object
lp.temp <- make.lp(0, 61)
# Print the LP
plp(lp.temp)
Rate of change (RoC) calculation using DEA
Description
Employs dm.dea
over time to calculate RoCs.
Usage
roc.dea(xdata, ydata, date, t, rts="crs", orientation,
sg="ssm", ftype="d", ncv=NULL, env=NULL, 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 |
orientation |
Orientation of the measurement |
sg |
Employs second-stage optimization |
ftype |
Frontier type |
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 |
Value
$eff_r |
Efficiency at release (i.e., at each production date) |
$eff_t |
Efficiency at |
$lambda_t |
Intensity vector at |
$eft_date |
Effective date |
$roc_past |
RoC observed from the obsolete DMUs in the past |
$roc_avg |
Average RoC |
$roc_local |
Local RoC |
Author(s)
Dong-Joon Lim, PhD
References
Lim, Dong-Joon, Timothy R. Anderson, and Oliver Lane Inman. "Choosing effective dates from multiple optima in Technology Forecasting using Data Envelopment Analysis (TFDEA)." Technological Forecasting and Social Change 88 (2014): 91~97.
Lim, Dong-Joon, et al. "Comparing technological advancement of hybrid electric vehicles (HEV) in different market segments." Technological Forecasting and Social Change 97 (2015): 140~153.
Lim, Dong-Joon, and Dong-Hyuk Yang. "Assessment of Regulatory Requirements on Technological Changes: The Increasing Dominance of Downsized Turbo/Super-Charged Engines Over Naturally Aspirated Engines." IEEE Access 7 (2019): 84839-84848.
See Also
dm.dea
Distance measure using DEA
roc.dea
RoC calculation using DEA
map.soa.dea
SOA mapping using DEA
target.arrival.dea
Arrival target setting using DEA
target.spec.dea
Spec target setting using DEA
Examples
# Reproduce Table 3 in Lim, D-J. et al.(2014)
# Load airplane dataset
df <- dataset.airplane.2017
# ready
x <- data.frame(Flew = rep(1, 28))
y <- subset(df, select = 3 : 7)
d <- subset(df, select = 2)
# go
roc.dea(x, y, d, 2007, "vrs", "o", "min", "d")$roc_past
# Reproduce Table 3 in Lim, D-J. et al.(2015)
# Load hev dataset
df <- dataset.hev.2013
# ready
x <- subset(df, select = 3)
y <- subset(df, select = 4 : 6)
d <- subset(df, select = 2)
c <- subset(df, select = 7)
# go
results <- roc.dea(x, y, d, 2013, "vrs", "o", "min", "d", env = c)
hev <- which(results$roc_local > 0)
data.frame(Class = c[hev, ],
SOA = hev,
LocalRoC = results$roc_local[hev, ])[order(c[hev, ]), ]
# NOTE: the published results include a typo on roc_local[82,]
# this has been corrected in Lim, D-J. et al. (2016).
Rate of change (RoC) calculation using HDF
Description
Employs dm.hdf
over time to calculate RoCs.
Usage
roc.hdf(xdata, ydata, date, t,
rts="crs", 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 |
wd |
Weak disposability vector indicating (an) undesirable output(s) (1 by s) |
sg |
Employs second-stage optimization |
ftype |
Frontier type |
cv |
Convexity assumption |
Value
$eff_r |
Efficiency at release (i.e., at each production date) |
$eff_t |
Efficiency at |
$lambda_t |
Intensity vector at |
$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.hdf
Distance measure using HDF
roc.hdf
RoC calculation using HDF
map.soa.hdf
SOA mapping using HDF
target.arrival.hdf
Arrival target setting using HDF
Examples
# Load engine dataset
df <- dataset.engine.2015
# Subset for 8 cylinder TC-P engines
et <- subset(df, df[, 3] == 8 & df[, 8] == "TC-P")
# Parameters
x <- subset(et, select = 4)
y <- subset(et, select = 5 : 7)
d <- subset(et, select = 2)
w <- matrix(c(1, 0, 0), ncol = 3)
# Calc local Roc
roc.hdf(x, y, d, 2015, "vrs", w, "min")
Malmquist Index: time-series productivity analysis
Description
Employs distance measure over time to calculate the productivity changes.
Usage
roc.malmquist(xdata, ydata, tm=NULL, dm="dea", rts="crs", orientation,
g=NULL, wd=NULL, ncv=NULL, env=NULL, cv="convex")
Arguments
xdata |
Input(s) array (n by m by t) |
ydata |
Output(s) array (n by s by t) |
tm |
Tick mark of production dates (a vector length of t) |
dm |
Distance measure to calculate the productivity |
rts |
Returns to scale assumption |
orientation |
Orientation of the measurement |
g |
Directional vector indicating a measurement direction (n by (m+s)) |
wd |
Weak disposability vector indicating (an) undesirable output(s) (1 by s) |
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 |
Value
$cu |
Catching Up (aka technical efficiency change: TEC) index |
$fs |
Frontier Shift (FS) Index |
$mi |
Malmquist Index |
Author(s)
Dong-Joon Lim, PhD
References
R. Fare, S. Grosskopf, and C. A. K. Lovell, Production Frontiers. Cambridge University Press, 1994.
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
# Load data
df <- array(c(4, 3, 9, 10, 7, 4, 3, 5,
5, 12, 3, 8, 1, 4, 14, 3,
1, 1, 1, 1, 1, 1, 1, 1,
3.4, 2, 10, 8, 10, 4, 1, 5,
6, 10, 3.5, 7, 2, 4, 12, 3,
1, 1, 1, 1, 1, 1, 1, 1,
2.8, 1.8, 8, 7, 10, 3, 1, 5,
5.7, 8.8, 2.8, 5, 2, 5, 9, 3,
1, 1, 1, 1, 1, 1, 1, 1,
2.2, 1.5, 8, 5, 8, 3, 1, 5,
6, 8, 2.3, 3.5, 2, 5, 7, 3,
1, 1, 1, 1, 1, 1, 1, 1),
c(8, 3, 4))
# Run
roc.malmquist(df[,1:2,], df[,3,], dm = "sbm", orientation = "n")
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 |
g |
Directional vector indicating a measurement direction (n by (m+s)) |
wd |
Weak disposability vector indicating (an) undesirable output(s) (1 by s) |
sg |
Employs second-stage optimization |
ftype |
Frontier type |
cv |
Convexity assumption |
Value
$eff_r |
Efficiency at release (i.e., at each production date) |
$eff_t |
Efficiency at |
$lambda_t |
Intensity vector at |
$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, ]
Arrival target setting using DEA
Description
Employs dm.dea
over time to estimate the arrival of known specifications.
Usage
target.arrival.dea(xdata, ydata, date, t, rts="crs", orientation,
sg="ssm", ftype="d", ncv=NULL, env=NULL, cv="convex", anc=FALSE)
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 |
orientation |
Orientation of the measurement |
sg |
Employs second-stage optimization |
ftype |
Frontier type |
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 |
anc |
Implements a stepwise RoC computation if |
Value
$eff_t |
Efficiency at |
$lambda_t |
Intensity vector at |
$eft_date |
Effective date |
$roc_avg |
Average RoC |
$roc_anc |
Local RoCs across the periods |
$roc_local |
Local RoC |
$roc_ind |
Individualized RoC |
$arrival_avg |
Estimated arrival using |
$arrival_seg |
Estimated arrival using |
Author(s)
Dong-Joon Lim, PhD
References
Lim, Dong-Joon, Timothy R. Anderson, and Oliver Lane Inman. "Choosing effective dates from multiple optima in Technology Forecasting using Data Envelopment Analysis (TFDEA)." Technological Forecasting and Social Change 88 (2014): 91~97.
Lim, Dong-Joon, and Timothy R. Anderson. Time series benchmarking analysis for new product scheduling: who are the competitors and how fast are they moving forward?. Advances in DEA Theory and Applications: with Examples in Forecasting Models. (2017): 443-458.
See Also
dm.dea
Distance measure using DEA
roc.dea
RoC calculation using DEA
map.soa.dea
SOA mapping using DEA
target.arrival.dea
Arrival target setting using DEA
target.spec.dea
Spec target setting using DEA
Examples
# Reproduce Table 4 in Lim, D-J., and Timothy R. Anderson.(2016)
# Load airplane dataset
df <- dataset.airplane.2017
# ready
x <- data.frame(Flew = rep(1, 28))
y <- subset(df, select = 3 : 7)
d <- subset(df, select = 2)
# go
target.arrival.dea(x, y, d, 2007, "vrs", "o", "min", "d")$arrival_seg
Arrival target setting using HDF
Description
Employs dm.hdf
over time to estimate the arrival of known specifications.
Usage
target.arrival.hdf(xdata, ydata, date, t, rts="crs",
wd=NULL, sg="ssm", ftype="d", cv="convex", anc=FALSE)
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 |
wd |
Weak disposability vector indicating (an) undesirable output(s) (1 by s) |
sg |
Employs second-stage optimization |
ftype |
Frontier type |
cv |
Convexity assumption |
anc |
Implements a stepwise RoC computation if |
Value
$eff_t |
Efficiency at |
$lambda_t |
Intensity vector at |
$eft_date |
Effective date |
$roc_avg |
Average RoC |
$roc_anc |
Local RoCs across the periods |
$roc_local |
Local RoC |
$roc_ind |
Individualized RoC |
$arrival_avg |
Estimated arrival using |
$arrival_seg |
Estimated arrival using |
Author(s)
Dong-Joon Lim, PhD
References
Lim, Dong-Joon, et al. "Comparing technological advancement of hybrid electric vehicles (HEV) in different market segments." Technological Forecasting and Social Change 97 (2015): 140~153.
Lim, Dong-Joon, and Timothy R. Anderson. Time series benchmarking analysis for new product scheduling: who are the competitors and how fast are they moving forward?. Advances in DEA Theory and Applications: with Examples in Forecasting Models. (2017): 443-458.
See Also
dm.hdf
Distance measure using HDF
roc.hdf
RoC calculation using HDF
map.soa.hdf
SOA mapping using HDF
target.arrival.hdf
Arrival target setting using HDF
Examples
# Estimate arrivals of MY2015 SC/TC 8 cylinder engines
# Load engine dataset
df <- dataset.engine.2015
# Subset for SC/TC 8 cylinder engines
stc.8 <- subset(df, grepl("^.C..", df[, 8]) & df[, 3] == 8)
# Parameters
x <- subset(stc.8, select = 4)
y <- subset(stc.8, select = 5:7)
d <- subset(stc.8, select = 2)
# Generate an SOA map
target.arrival.hdf(x, y, d, 2014, "vrs")
Arrival target setting using SF
Description
Employs dm.sf
over time to estimate the arrival of known specifications. This function is valid only when multiplicative form of directional vector is used.
Usage
target.arrival.sf(xdata, ydata, date, t, rts="crs", g=NULL,
wd=NULL, sg="ssm", ftype="d", cv="convex", anc=FALSE)
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 |
g |
Directional vector indicating a measurement direction (n by (m+s)) |
wd |
Weak disposability vector indicating (an) undesirable output(s) (1 by s) |
sg |
Employs second-stage optimization |
ftype |
Frontier type |
cv |
Convexity assumption |
anc |
Implements a stepwise RoC computation if |
Value
$eff_t |
Efficiency at |
$lambda_t |
Intensity vector at |
$eft_date |
Effective date |
$roc_avg |
Average RoC |
$roc_anc |
Local RoCs across the periods |
$roc_local |
Local RoC |
$roc_ind |
Individualized RoC |
$arrival_avg |
Estimated arrival using |
$arrival_seg |
Estimated arrival using |
Author(s)
Dong-Joon Lim, PhD
References
Lim, Dong-Joon, et al. "Comparing technological advancement of hybrid electric vehicles (HEV) in different market segments." Technological Forecasting and Social Change 97 (2015): 140~153.
Lim, Dong-Joon, and Timothy R. Anderson. Time series benchmarking analysis for new product scheduling: who are the competitors and how fast are they moving forward?. Advances in DEA Theory and Applications: with Examples in Forecasting Models. (2017): 443-458.
See Also
dm.sf
Distance measure using SF
roc.sf
RoC calculation using SF
map.soa.sf
SOA mapping using SF
target.arrival.sf
Arrival target setting using SF
Examples
# Estimate arrivals of MY2013 hev models
# Load hev dataset
df <- dataset.hev.2013
# ready
x <- subset(df, select = 3)
y <- subset(df, select = 4 : 6)
d <- subset(df, select = 2)
g <- data.frame(x, y)
# go
target.arrival.sf(x, y, d, 2012, "vrs", g)$arrival_seg
Spec target setting using DEA
Description
Employs inverse DEA
to estimate specifications(in/out-puts) to achieve a predetermined efficiency.
Usage
target.spec.dea(xdata, ydata, date=NULL, t=NULL, dt=NULL, dmu, et="c",
alpha=NULL, beta=NULL, wv=NULL, rts="crs", sg="ssm", ftype="d",
ncv=NULL, env=NULL, cv="convex", bound=TRUE, pin=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 |
sg |
Employs second-stage optimization |
ftype |
Frontier type |
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 |
bound |
Puts upper/lower bounds on alpha/beta if |
pin |
Includes the perturbed DMU in the PPS if |
Value
$alpha |
Estimated input(s) |
$beta |
Estimated output(s) |
$lambda |
Intensity vector |
$xslack |
Input slack |
$yslack |
Output slack |
Author(s)
Dong-Joon Lim, PhD
References
Lim, Dong-Joon, "Inverse DEA with frontier changes for new product target setting." European Journal of Operational Research 254.2 (2016): 510~516.
Wei, Quanling, Jianzhong Zhang, and Xiangsun Zhang. "An inverse DEA model for inputs/outputs estimate." European Journal of Operational Research 121.1 (2000): 151~163.
See Also
dm.dea
Distance measure using DEA
roc.dea
RoC calculation using DEA
target.arrival.dea
Arrival target setting using DEA
Examples
# Reproduce Example 2 in Wei, Q. et al.(2000)
# ready
x <- matrix(c(1, 1, 1), 3)
y <- matrix(c(4, 8, 5, 8, 4, 5), 3)
a <- matrix(1.8, 1)
w <- matrix(c(0.5, 0.5), 1)
# go
target.spec.dea(x, y, dmu = 3, alpha = a, wv = w, rts = "crs")$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