# Linear Programming for the Additive Model Solve the Additive Model under the VRS assumption ```r additive(base = NULL, frontier = NULL, noutput = 1) ``` ## 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). ## Details The additive model under the VRS assumption is as follows: character(0) character(0) character(0) character(0) c("$\n$", "$ theta^k* = max sum(s^-_m) + sum(s^+_n)\n$", "$\n$", "$ s.t. x^k_m = sum(x_m^j) l^j + s^-_m (m = 1, 2, ..., M);\n$", "$ \n$", "$ y^k_n = sum(y_n^j) l^j + s^+_n (n = 1, 2, ..., N);\n$", "$ \n$", "$ sum(l^j) = 1;\n$", "$ \n$", "$ l^j >= 0, s^-_m >= 0, s^+_n >= 0.\n$", "$ $") ## Returns A data frame with J1*(J1+M+N), which has efficiency scores, optimal weightes and optimal slacks. Take a look at the example below. ## References Cooper, W., Seiford, L. and Tone, K. (2007). **Data envelopment analysis: a comprehensive text with models, applications, references and DEA-solver software** (2nd ed.). Springer Verlag, New York. Lee, J. and Oh, D. (forthcoming). **Efficiency Analysis: Data Envelopment Analysis**. Press (in Korean). ## Author(s) Dong-hyun Oh, oh.donghyun77@gmail.com ## See Also `sbm.tone`, `sbm.vrs` ## Examples ```r ## Simple Example my.dat <- data.frame(y = c(1, 2, 4, 6, 7, 9, 9), x = c(3, 2, 6, 4, 8, 8, 10)) (re <- additive(my.dat, noutput = 1)) ## Property of the Additive Model dat1 <- data.frame(y = c(1, 1, 1, 1, 1, 1), x1 = c(2, 3, 6, 3, 6, 6), x2 = c(5, 3, 1, 8, 4, 2)) dat2 <- dat1 dat2$x1 <- dat2$x1 * 10 dat3 <- dat1 dat3$x1 <- dat3$x1 + 10 (re1 <- additive(dat1, noutput = 1)) (re2 <- additive(dat2, noutput = 1)) (re3 <- additive(dat3, noutput = 1)) ```

additive function