| Title: | Distance Measure Based Judgment and Learning |
|---|---|
| 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. |
| Authors: | Dong-Joon Lim, Ph.D. <technometrics.org> |
| Maintainer: | Dong-Joon Lim <[email protected]> |
| License: | GPL-2 |
| Version: | 3.9 |
| Built: | 2025-03-23 06:10:38 UTC |
| Source: | https://github.com/cran/DJL |
Commercial airplanes from 1965 to 2017.
data(dataset.airplane.2017)data(dataset.airplane.2017)
[,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
Dong-Joon Lim, PhD
http://www.airbus.com/aircraftfamilies
http://www.boeing.com/commercial
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.
# Load dataset data(dataset.airplane.2017)# Load dataset data(dataset.airplane.2017)
Auto engines from MY2005 to MY2015.
data(dataset.engine.2015)data(dataset.engine.2015)
[,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
Dong-Joon Lim, PhD
http://www.fueleconomy.gov
http://www.autoevolution.com
D.-J. Lim, Internal combustion engine race: naturally aspirated vs turbo/super-charged, working paper (2015).
# Load dataset data(dataset.engine.2015)# Load dataset data(dataset.engine.2015)
Hybrid electric vehicles from MY1997 to MY2013.
data(dataset.hev.2013)data(dataset.hev.2013)
[,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
Dong-Joon Lim, PhD
http://www.fueleconomy.gov
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.
# Load dataset data(dataset.hev.2013)# Load dataset data(dataset.hev.2013)
Implements Chambers' directional distance function (non-radial & non-oriented measure).
dm.ddf(xdata, ydata, rts="crs", g=NULL, wd=NULL, se=FALSE, sg="ssm", date=NULL, cv="convex", o=NULL)dm.ddf(xdata, ydata, rts="crs", g=NULL, wd=NULL, se=FALSE, sg="ssm", date=NULL, cv="convex", o=NULL)
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. |
$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 |
Dong-Joon Lim, PhD
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.
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
# 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)# 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)
Implements Charnes & Cooper's data envelopment analysis (radial & oriented measure).
dm.dea(xdata, ydata, rts="crs", orientation, se=FALSE, sg="ssm", date=NULL, ncv=NULL, env=NULL, cv="convex", o=NULL)dm.dea(xdata, ydata, rts="crs", orientation, se=FALSE, sg="ssm", date=NULL, ncv=NULL, env=NULL, cv="convex", o=NULL)
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. |
$eff |
Efficiency score |
$lambda |
Intensity vector |
$xslack |
Input slack |
$yslack |
Output slack |
$vx |
Input (dual) weight |
$uy |
Output (dual) weight |
$w |
Free (dual) variable |
Dong-Joon Lim, PhD
Charnes, Abraham, William W. Cooper, and Edwardo Rhodes. "Measuring the efficiency of decision making units." European journal of operational research 2.6 (1978): 429~444.
Charnes, Abraham, William W. Cooper, and Edwardo Rhodes. "Evaluating program and managerial efficiency: an application of data envelopment analysis to program follow through." Management science 27.6 (1981): 668~697.
Banker, Rajiv D., and Richard C. Morey. "Efficiency analysis for exogenously fixed inputs and outputs." Operations Research 34.4 (1986): 513~521.
Ruggiero, John. "On the measurement of technical efficiency in the public sector." European Journal of Operational Research 90.3 (1996): 553~565.
Fried, Harold O., CA Knox Lovell, and Shelton S. Schmidt, eds. The measurement of productive efficiency and productivity growth. Oxford University Press, 2008.
dm.ddf Distance measure using DDF dm.dea Distance measure using DEA dm.hdf Distance measure using HDF dm.sbm Distance measure using SBM dm.sf Distance measure using SF
# Reproduce Table 3.9 (p.348) in Fried, H.O. et al.(2008) # ready X <- data.frame(x1 = c(8, 6, 3, 10, 6, 8, 8, 4), x2 = c(8, 4.6, 1.9, 9, 3.6, 3.6, 9, 1.9)) Y <- data.frame(y1 = c(8, 5, 2, 9, 4.5, 4.5, 7, 2)) C <- data.frame(x1 = 0, x2 = 1, y1 = 0) # go data.frame(ALL_CRS = dm.dea(X, Y, "crs", "i")$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)$eff, row.names = LETTERS[1 : 8])# Reproduce Table 3.9 (p.348) in Fried, H.O. et al.(2008) # ready X <- data.frame(x1 = c(8, 6, 3, 10, 6, 8, 8, 4), x2 = c(8, 4.6, 1.9, 9, 3.6, 3.6, 9, 1.9)) Y <- data.frame(y1 = c(8, 5, 2, 9, 4.5, 4.5, 7, 2)) C <- data.frame(x1 = 0, x2 = 1, y1 = 0) # go data.frame(ALL_CRS = dm.dea(X, Y, "crs", "i")$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])
Employs the Farrell measure on carry-over budget as well as input or output
dm.dynamic.bc(xdata, ydata, zdata, bdata, rts="crs", orientation="i", wv=NULL)dm.dynamic.bc(xdata, ydata, zdata, bdata, rts="crs", orientation="i", wv=NULL)
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) |
$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 |
Dong-Joon Lim, PhD
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).
dm.dea Distance measure using DEA
# 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)# 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)
Implements Fare's hyperbolic distance function (semi-radial & non-oriented measure).
dm.hdf(xdata, ydata, rts="crs", wd=NULL, se=FALSE, sg="ssm", date=NULL, cv="convex", o=NULL)dm.hdf(xdata, ydata, rts="crs", wd=NULL, se=FALSE, sg="ssm", date=NULL, cv="convex", o=NULL)
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. |
$eff |
Efficiency score |
$lambda |
Intensity vector |
$mu |
Secondary intensity vector for weak disposability under VRS |
$xslack |
Input slack |
$yslack |
Output slack |
$iteration |
The number of iteration to obtain the hyperbolic efficiency score |
Dong-Joon Lim, PhD
Fare, R., Shawna Grosskopf, and CA Knox Lovell. The Measurement of Efficiency of Production. Boston: Kulwer-Nijhoff (1985).
Fare, Rolf, et al. "Estimating the hyperbolic distance function: A directional distance function approach." European Journal of Operational Research 254.1 (2016): 312~319.
dm.ddf Distance measure using DDF dm.dea Distance measure using DEA dm.hdf Distance measure using HDF dm.sbm Distance measure using SBM dm.sf Distance measure using SF
# Reproduce Table 2 in Fare et al.(2016) # ready x <- data.frame(x1 = c(2, 4, 9, 6.5, 10, 6, 9)) y <- data.frame(y1 = c(3, 7, 10, 8.5, 4, 2, 8)) # go sf <- dm.sf (x, y, "vrs")$eff hdf <- dm.hdf(x, y, "vrs")$eff matrix(t(cbind(sf, hdf)), 2, 7, dimnames = list(c("SF", "HDF"), paste0("DMU_", c(letters[1:4], "o", "p", "q"))))# Reproduce Table 2 in Fare et al.(2016) # ready x <- data.frame(x1 = c(2, 4, 9, 6.5, 10, 6, 9)) y <- data.frame(y1 = c(3, 7, 10, 8.5, 4, 2, 8)) # go sf <- dm.sf (x, y, "vrs")$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"))))
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.
dm.mahalanobis(data, from="median", p=10, plot=FALSE, v.index=NULL, layout=NULL)dm.mahalanobis(data, from="median", p=10, plot=FALSE, v.index=NULL, layout=NULL)
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 |
$dist |
|
$excluded |
Excluded row(s) in row number |
$order |
Distance order (decreasing) in row number |
$suspect |
Potential outlier(s) in row number |
Dong-Joon Lim, PhD
Hair, Joseph F., et al. Multivariate data analysis. Vol. 7. Upper Saddle River, NJ: Pearson Prentice Hall, 2006.
# Generate a sample dataframe df <- data.frame(replicate(6, sample(0 : 100, 50))) # go dm.mahalanobis(df, plot = TRUE)# Generate a sample dataframe df <- data.frame(replicate(6, sample(0 : 100, 50))) # go dm.mahalanobis(df, plot = TRUE)
Implements Charnes & Cooper's data envelopment analysis (radial & oriented measure) on a two-stage network structure.
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)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)
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. |
$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 |
Dong-Joon Lim, Ph.D.
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.
dm.dea Distance measure using DEA dm.dynamic.bc Dynamic DEA for intertemporal budgeting
# 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$eff.s2)# Reproduce Table 2 in W.D. Cook et al.(2010) # ready X <- data.frame(x1 = c(1178744,1381822,1177494,601320,6699063,2627707,1942833,3789001, 1567746,1303249,1962448,2592790,2609941,1396002,2184944,1211716, 1453797,757515,159422,145442,84171,15993,54693,163297,1544215), x2 = c(673512,1352755,592790,594259,3531614,668363,1443100,1873530, 950432,1298470,672414,650952,1368802,988888,651063,415071, 1085019,547997,182338,53518,26224,10502,28408,235094,828963)) Z <- data.frame(z1 = c(7451757,10020274,4776548,3174851,37392862,9747908,10685457,17267266, 11473162,8210389,7222378,9434406,13921464,7396396,10422297,5606013, 7695461,3631484,1141950,316829,225888,52063,245910,476419,7832893), z2 = c(856735,1812894,560244,371863,1753794,952326,643412,1134600, 546337,504528,643178,1118489,811343,465509,749893,402881, 342489,995620,483291,131920,40542,14574,49864,644816,667964)) Y <- data.frame(y1 = c(984143,1228502,293613,248709,7851229,1713598,2239593,3899530, 1043778,1697941,1486014,1574191,3609236,1401200,3355197,854054, 3144484,692731,519121,355624,51950,82141,0.1,142370,1602873), y2 = c(681687,834754,658428,177331,3925272,415058,439039,622868, 264098,554806,18259,909295,223047,332283,555482,197947, 371984,163927,46857,26537,6491,4181,18980,16976,477733)) # go res.co <- dm.network.dea(xdata.s1 = X, zdata = Z, ydata.s2 = Y, type = "co") res.nc.LF <- dm.network.dea(xdata.s1 = X, zdata = Z, ydata.s2 = Y, type = "nc", leader = "1st") res.nc.FL <- dm.network.dea(xdata.s1 = X, zdata = Z, ydata.s2 = Y, type = "nc", leader = "2nd") # print data.frame(CO.s1 = res.co$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)
Implements Tone's slack-based model (non-radial & (non-)oriented measure).
dm.sbm(xdata, ydata, rts="crs", orientation="n", se=FALSE, sg="ssm", date=NULL, cv="convex", o=NULL)dm.sbm(xdata, ydata, rts="crs", orientation="n", se=FALSE, sg="ssm", date=NULL, cv="convex", o=NULL)
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. |
$eff |
Efficiency score |
$lambda |
Intensity vector |
$xslack |
Input slack |
$yslack |
Output slack |
$xtarget |
Input target |
$ytarget |
Output target |
Dong-Joon Lim, PhD
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.
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
# 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)# 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)
Implements Luenberger's shortage (benefit) function (radial & non-oriented measure).
dm.sf(xdata, ydata, rts="crs", g=NULL, wd=NULL, se=FALSE, sg="ssm", date=NULL, cv="convex", o=NULL)dm.sf(xdata, ydata, rts="crs", g=NULL, wd=NULL, se=FALSE, sg="ssm", date=NULL, cv="convex", o=NULL)
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. |
$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 |
Dong-Joon Lim, PhD
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.
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
# 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)# 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)
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.
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)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)
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 |
Dong-Joon Lim, PhD
Hair, Joseph F., et al. Multivariate data analysis. Vol. 7. Upper Saddle River, NJ: Pearson Prentice Hall, 2006.
# 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)# 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)
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.
map.corr(data, from = "median", threshold = 0.3, r.name = FALSE)map.corr(data, from = "median", threshold = 0.3, r.name = FALSE)
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 |
$reliability |
Summary table |
Dong-Joon Lim, PhD
dm.mahalanobis Distance measure using Mahalanobis distance
# Generate a sample dataframe df <- data.frame(replicate(2, sample(0 : 100, 50))) # go map.corr(df)# Generate a sample dataframe df <- data.frame(replicate(2, sample(0 : 100, 50))) # go map.corr(df)
Employs dm.ddf over time to generate a state-of-the-art map.
map.soa.ddf(xdata, ydata, date, rts="crs", g=NULL, wd=NULL, sg="ssm", cv="convex", mk="dmu")map.soa.ddf(xdata, ydata, date, rts="crs", g=NULL, wd=NULL, sg="ssm", cv="convex", mk="dmu")
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 |
Dong-Joon Lim, PhD
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
# 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)# 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)
Employs dm.dea over time to generate a state-of-the-art map.
map.soa.dea(xdata, ydata, date, rts="crs", orientation, sg="ssm", ncv=NULL, env=NULL, cv="convex", mk="dmu")map.soa.dea(xdata, ydata, date, rts="crs", orientation, sg="ssm", ncv=NULL, env=NULL, cv="convex", mk="dmu")
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 |
Dong-Joon Lim, PhD
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
# 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")# 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")
Employs dm.hdf over time to generate a state-of-the-art map.
map.soa.hdf(xdata, ydata, date, rts="crs", wd=NULL, sg="ssm", cv="convex", mk="dmu")map.soa.hdf(xdata, ydata, date, rts="crs", wd=NULL, sg="ssm", cv="convex", mk="dmu")
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 |
Dong-Joon Lim, PhD
D.-J. Lim, Internal combustion engine race: naturally aspirated vs turbo/super-charged, working paper (2015).
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
# 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")# 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")
Employs dm.sbm over time to generate a state-of-the-art map.
map.soa.sbm(xdata, ydata, date, rts="crs", orientation="n", sg="ssm", cv="convex", mk="dmu")map.soa.sbm(xdata, ydata, date, rts="crs", orientation="n", sg="ssm", cv="convex", mk="dmu")
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 |
Dong-Joon Lim, PhD
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
# 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)# 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)
Employs dm.sf over time to generate a state-of-the-art map.
map.soa.sf(xdata, ydata, date, rts="crs", g=NULL, wd=NULL, sg="ssm", cv="convex", mk="dmu")map.soa.sf(xdata, ydata, date, rts="crs", g=NULL, wd=NULL, sg="ssm", cv="convex", mk="dmu")
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 |
Dong-Joon Lim, PhD
D.-J. Lim, Internal combustion engine race: naturally aspirated vs turbo/super-charged, working paper (2015).
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
# 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")# 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 an LP object line by line.
plp(x)plp(x)
x |
LP object defined by make.lp function in lpSolve library |
Dong-Joon Lim, PhD
Berkelaar, Michel, Kjell Eikland, and Peter Notebaert. "lpsolve: Open source (mixed-integer) linear programming system." Eindhoven U. of Technology 63 (2004).
# Declare an LP object lp.temp <- make.lp(0, 61) # Print the LP plp(lp.temp)# Declare an LP object lp.temp <- make.lp(0, 61) # Print the LP plp(lp.temp)
Employs dm.dea over time to calculate RoCs.
roc.dea(xdata, ydata, date, t, rts="crs", orientation, sg="ssm", ftype="d", ncv=NULL, env=NULL, cv="convex")roc.dea(xdata, ydata, date, t, rts="crs", orientation, sg="ssm", ftype="d", ncv=NULL, env=NULL, cv="convex")
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 |
$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 |
$roc_local |
Local RoC |
Dong-Joon Lim, PhD
Lim, Dong-Joon, Timothy R. Anderson, and Oliver Lane Inman. "Choosing effective dates from multiple optima in Technology Forecasting using Data Envelopment Analysis (TFDEA)." Technological Forecasting and Social Change 88 (2014): 91~97.
Lim, Dong-Joon, et al. "Comparing technological advancement of hybrid electric vehicles (HEV) in different market segments." Technological Forecasting and Social Change 97 (2015): 140~153.
Lim, Dong-Joon, and Dong-Hyuk Yang. "Assessment of Regulatory Requirements on Technological Changes: The Increasing Dominance of Downsized Turbo/Super-Charged Engines Over Naturally Aspirated Engines." IEEE Access 7 (2019): 84839-84848.
dm.dea Distance measure using DEA roc.dea RoC calculation using DEA map.soa.dea SOA mapping using DEA target.arrival.dea Arrival target setting using DEA target.spec.dea Spec target setting using DEA
# Reproduce Table 3 in Lim, D-J. et al.(2014) # Load airplane dataset df <- dataset.airplane.2017 # ready x <- data.frame(Flew = rep(1, 28)) y <- subset(df, select = 3 : 7) d <- subset(df, select = 2) # go roc.dea(x, y, d, 2007, "vrs", "o", "min", "d")$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).# 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).
Employs dm.hdf over time to calculate RoCs.
roc.hdf(xdata, ydata, date, t, rts="crs", wd=NULL, sg="ssm", ftype="d", cv="convex")roc.hdf(xdata, ydata, date, t, rts="crs", wd=NULL, sg="ssm", ftype="d", cv="convex")
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 |
$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 |
Dong-Joon Lim, PhD
D.-J. Lim, Internal combustion engine race: naturally aspirated vs turbo/super-charged, working paper (2015).
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
# 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")# 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")
Employs distance measure over time to calculate the productivity changes.
roc.malmquist(xdata, ydata, tm=NULL, dm="dea", rts="crs", orientation, g=NULL, wd=NULL, ncv=NULL, env=NULL, cv="convex")roc.malmquist(xdata, ydata, tm=NULL, dm="dea", rts="crs", orientation, g=NULL, wd=NULL, ncv=NULL, env=NULL, cv="convex")
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 |
$cu |
Catching Up (aka technical efficiency change: TEC) index |
$fs |
Frontier Shift (FS) Index |
$mi |
Malmquist Index |
Dong-Joon Lim, PhD
R. Fare, S. Grosskopf, and C. A. K. Lovell, Production Frontiers. Cambridge University Press, 1994.
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
# 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")# 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")
Employs dm.sf over time to calculate RoCs. This function is valid only when multiplicative form of directional vector is used.
roc.sf(xdata, ydata, date, t, rts="crs", g=NULL, wd=NULL, sg="ssm", ftype="d", cv="convex")roc.sf(xdata, ydata, date, t, rts="crs", g=NULL, wd=NULL, sg="ssm", ftype="d", cv="convex")
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 |
$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 |
$roc_local |
Local RoC |
Dong-Joon Lim, PhD
D.-J. Lim, Internal combustion engine race: naturally aspirated vs turbo/super-charged, working paper (2015).
dm.sf Distance measure using SF roc.sf RoC calculation using SF map.soa.sf SOA mapping using SF target.arrival.sf Arrival target setting using SF
# Reproduce Mercedes-Benz CLA45 AMG's local RoC in Table 5 in Lim, D-J. (2015) # Load engine dataset df <- dataset.engine.2015 # Subset for 4 cylinder engines fce <- subset(df, df[, 3] == 4) # Parameters x <- subset(fce, select = 4) y <- subset(fce, select = 5 : 7) d <- subset(fce, select = 2) g <- as.matrix(data.frame(0, y)) w <- matrix(c(1, 0, 0), ncol = 3) # Calc local Roc roc.sf(x, y, d, 2014, "crs", g, w, "min")$roc_local[348, ]# 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, ]
Employs dm.dea over time to estimate the arrival of known specifications.
target.arrival.dea(xdata, ydata, date, t, rts="crs", orientation, sg="ssm", ftype="d", ncv=NULL, env=NULL, cv="convex", anc=FALSE)target.arrival.dea(xdata, ydata, date, t, rts="crs", orientation, sg="ssm", ftype="d", ncv=NULL, env=NULL, cv="convex", anc=FALSE)
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 |
$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 |
$arrival_seg |
Estimated arrival using |
Dong-Joon Lim, PhD
Lim, Dong-Joon, Timothy R. Anderson, and Oliver Lane Inman. "Choosing effective dates from multiple optima in Technology Forecasting using Data Envelopment Analysis (TFDEA)." Technological Forecasting and Social Change 88 (2014): 91~97.
Lim, Dong-Joon, and Timothy R. Anderson. Time series benchmarking analysis for new product scheduling: who are the competitors and how fast are they moving forward?. Advances in DEA Theory and Applications: with Examples in Forecasting Models. (2017): 443-458.
dm.dea Distance measure using DEA roc.dea RoC calculation using DEA map.soa.dea SOA mapping using DEA target.arrival.dea Arrival target setting using DEA target.spec.dea Spec target setting using DEA
# Reproduce Table 4 in Lim, D-J., and Timothy R. Anderson.(2016) # Load airplane dataset df <- dataset.airplane.2017 # ready x <- data.frame(Flew = rep(1, 28)) y <- subset(df, select = 3 : 7) d <- subset(df, select = 2) # go target.arrival.dea(x, y, d, 2007, "vrs", "o", "min", "d")$arrival_seg# 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
Employs dm.hdf over time to estimate the arrival of known specifications.
target.arrival.hdf(xdata, ydata, date, t, rts="crs", wd=NULL, sg="ssm", ftype="d", cv="convex", anc=FALSE)target.arrival.hdf(xdata, ydata, date, t, rts="crs", wd=NULL, sg="ssm", ftype="d", cv="convex", anc=FALSE)
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 |
$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 |
Dong-Joon Lim, PhD
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.
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
# 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")# 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")
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.
target.arrival.sf(xdata, ydata, date, t, rts="crs", g=NULL, wd=NULL, sg="ssm", ftype="d", cv="convex", anc=FALSE)target.arrival.sf(xdata, ydata, date, t, rts="crs", g=NULL, wd=NULL, sg="ssm", ftype="d", cv="convex", anc=FALSE)
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 |
$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 |
$arrival_seg |
Estimated arrival using |
Dong-Joon Lim, PhD
Lim, Dong-Joon, et al. "Comparing technological advancement of hybrid electric vehicles (HEV) in different market segments." Technological Forecasting and Social Change 97 (2015): 140~153.
Lim, Dong-Joon, and Timothy R. Anderson. Time series benchmarking analysis for new product scheduling: who are the competitors and how fast are they moving forward?. Advances in DEA Theory and Applications: with Examples in Forecasting Models. (2017): 443-458.
dm.sf Distance measure using SF roc.sf RoC calculation using SF map.soa.sf SOA mapping using SF target.arrival.sf Arrival target setting using SF
# Estimate arrivals of MY2013 hev models # Load hev dataset df <- dataset.hev.2013 # ready x <- subset(df, select = 3) y <- subset(df, select = 4 : 6) d <- subset(df, select = 2) g <- data.frame(x, y) # go target.arrival.sf(x, y, d, 2012, "vrs", g)$arrival_seg# 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
Employs inverse DEA to estimate specifications(in/out-puts) to achieve a predetermined efficiency.
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)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)
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 |
$alpha |
Estimated input(s) |
$beta |
Estimated output(s) |
$lambda |
Intensity vector |
$xslack |
Input slack |
$yslack |
Output slack |
Dong-Joon Lim, PhD
Lim, Dong-Joon, "Inverse DEA with frontier changes for new product target setting." European Journal of Operational Research 254.2 (2016): 510~516.
Wei, Quanling, Jianzhong Zhang, and Xiangsun Zhang. "An inverse DEA model for inputs/outputs estimate." European Journal of Operational Research 121.1 (2000): 151~163.
dm.dea Distance measure using DEA roc.dea RoC calculation using DEA target.arrival.dea Arrival target setting using DEA
# Reproduce Example 2 in Wei, Q. et al.(2000) # ready x <- matrix(c(1, 1, 1), 3) y <- matrix(c(4, 8, 5, 8, 4, 5), 3) a <- matrix(1.8, 1) w <- matrix(c(0.5, 0.5), 1) # go target.spec.dea(x, y, dmu = 3, alpha = a, wv = w, rts = "crs")$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")$beta# Reproduce Example 2 in Wei, Q. et al.(2000) # ready x <- matrix(c(1, 1, 1), 3) y <- matrix(c(4, 8, 5, 8, 4, 5), 3) a <- matrix(1.8, 1) w <- matrix(c(0.5, 0.5), 1) # go target.spec.dea(x, y, dmu = 3, alpha = a, wv = w, rts = "crs")$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