dm.network.dea: Distance measure using DEA on a two-stage network structure
In DJL: Distance Measure Based Judgment and Learning

dm.network.dea

R Documentation

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 `"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

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.

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)

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