# Linear Programming for the Data Envelopment Analysis Solve input(output)-oriented DEA under the CRS (VRS) ```r 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). ## Returns 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. ## 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) ## Author(s) Dong-hyun Oh, oh.donghyun77@gmail.com ## See Also `dual.dea` ## Examples ```r ## 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) ```

dea function