dea {nonparaeff}

Linear Programming for the Data Envelopment Analysis

Description

Solve input(output)-oriented DEA under the CRS (VRS)

Usage

dea(base = NULL, frontier = NULL, noutput = 1, orientation=1, rts = 1, onlytheta = FALSE)

Arguments

base

A data set for DMUs to be evaluated. A data frame with J1*(M+N) dimention, where J1 is the number of DMUs, M for the number of inputs, and N for the number of outputs.

frontier

A data set for DMUs to be used in constructing a production possibility set (PPS). A data frame with J2*(M+N) dimention, where J2 is the number of DMUs, M for the number of inputs, and N for the number of outputs.

noutput

The number of outputs (N).

orientation

Orientation of measurement. 1 for the input-oriented measure, and 2 for the output-oriented measure.

rts

Returns to scale. 1 for the CRS assumption, and 2 for the VRS assumption.

onlytheta

Logical. If onlytheta is TRUE, then only efficiency scores are obtained. If it is FALSE, then optimal lambda's and slacks are also obtained.

Details

The input (output) -oriented DEA under the CRS (VRS) assumption are calcuated. For model specification, take a look at Cooper et al. (2007).

Value

If onlytheta is TRUE, then a (J1*1) data.frame is obtained. If onlytheta if FALSE, then a data frame with a J1*(J1+M+N) dimension is obtained, in which optimal weights, input slacks and output slacks are presented.

Author(s)

Dong-hyun Oh, [e-mail]

References

Cooper, W., Seiford, L. and Tone, K. (2007). Data envelopment analysis: a comprehensive text with models, applications, references and DEA-solver software (2nd ed.). Springer Verlag, New York.

Lee, J. and Oh, D. (forthcoming). Efficiency Analysis: Data Envelopment Analysis. Press (in Korean)

See Also

dual.dea

Examples

## input-oriented DEA under the CRS assumption (1 input and 1 output)
tab3.1.dat <- data.frame(y = c(1, 2, 4, 6, 7, 9, 9), 
                         x = c(3, 2, 6, 4, 8, 8, 10))
(re <- dea(base = tab3.1.dat, noutput = 1, orientation = 1, rts = 1,
onlytheta = FALSE))

## input-oriented DEA under the CRS assumption (2 inputs and 1 output)
tab3.3.dat <- data.frame(y = c(1, 1, 1, 1, 1, 1),
                              x1 = c(1, 3, 6, 2, 5, 9),
                              x2 = c(4, 1, 1, 8, 5, 2))
re <- dea(base=tab3.3.dat, noutput = 1, orientation = 1, rts = 1)
## finding references points
(ref <- data.frame(y = c(tab3.3.dat$y + re$slack.y1),
x1 = c(tab3.3.dat$x1 * re$eff - re$slack.x1),
x2 = c(tab3.3.dat$x2 * re$eff - re$slack.x2)))


## output-oriented DEA under the CRS assumption (1 input and 2 outputs)
tab5.1.dat <- data.frame(y1 = c(4, 8, 8, 4, 3, 1),
                         y2 = c(9, 6, 4, 3, 5, 6),
                         x = c(1, 1, 1, 1, 1, 1))
(re <- dea(tab5.1.dat, noutput = 2, orientation = 2, rts = 1))

## input-oriented DEA under the VRS assumption (1 input and 1 output)
tab6.1.dat <- data.frame(y = c(1, 2, 4, 6, 7, 9, 9),
                              x = c(3, 2, 6, 4, 8, 8, 10))
(re <- dea(tab6.1.dat, noutput = 1, orientation = 1, rts = 2))

## output-oriented DEA under the VRS assumtion (1 input and 1 output)
(re <- dea(tab6.1.dat, noutput = 1, orientation = 2, rts = 2))

## scale efficiency
re.crs <-
    dea(tab6.1.dat, noutput = 1, orientation = 1, rts = 1,onlytheta = TRUE)
re.vrs<-
    dea(tab6.1.dat, noutput = 1, orientation = 1, rts = 2,
         onlytheta = TRUE)
scale.eff <- re.crs/re.vrs

## finding DRS, IRS, CRS
dat6.1 <- data.frame(y = c(1, 2, 4, 6, 7, 9, 9),
     x = c(3, 2, 6, 4, 8, 8, 10))
re <- dea(dat6.1, noutput = 1, rts = 1)
lambdas <- re[, 2:8]
apply(lambdas, 1, sum)