DJL (version 3.9)

dm.network.dea: 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)

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

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
"crs" Constant RTS (default)
"vrs" Variable RTS
"irs" Increasing RTS
"drs" Decreasing RTS

orientation

Orientation of the measurement
"i" Input-orientation (default)
"o" Output-orientation

type

Solution method
"nc" Decentralized model (Stackelberg game approach) (default)
"co" Centralized model (cooperative game approach)

leader

Preemptive priority for Decentralized model
"1st" 1st stage as the leader (default)
"2nd" 2nd stage as the leader

ss

Step size for heuristic search 10^-4 (default)

o

DMU index to operate. NULL (default) will operate for all

Author

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)