# Additive DEA model. Solve the additive model of Charnes et. al (1985). With the current version of deaR, it is possible to solve input-oriented, output-oriented, and non-oriented additive model under constant and non-constant returns to scale. Besides, the user can set weights for the input slacks and/or output slacks. So, it is also possible to solve weighted additive models. For example: Measure of Inefficiency Proportions (MIP), Range Adjusted Measure (RAM), etc. ```r model_additive(datadea, dmu_eval = NULL, dmu_ref = NULL, orientation = NULL, weight_slack_i = 1, weight_slack_o = 1, rts = c("crs", "vrs", "nirs", "ndrs", "grs"), L = 1, U = 1, compute_target = TRUE, returnlp = FALSE, ...) ``` ## Arguments - `datadea`: A `deadata` object with `n` DMUs, `m` inputs and `s` outputs. - `dmu_eval`: A numeric vector containing which DMUs have to be evaluated. If `NULL` (default), all DMUs are considered. - `dmu_ref`: A numeric vector containing which DMUs are the evaluation reference set. If `NULL` (default), all DMUs are considered. - `orientation`: This parameter is either `NULL` (default) or a string, equal to "io" (input-oriented) or "oo" (output-oriented). It is used to modify the weight slacks. If input-oriented, `weight_slack_o` are taken 0. If output-oriented, `weight_slack_i` are taken 0. - `weight_slack_i`: A value, vector of length `m`, or matrix `m` x `ne` (where `ne` is the length of `dmu_eval`) with the weights of the input slacks. If 0, output-oriented. - `weight_slack_o`: A value, vector of length `s`, or matrix `s` x `ne` (where `ne` is the length of `dmu_eval`) with the weights of the output slacks. If 0, input-oriented. - `rts`: A string, determining the type of returns to scale, equal to "crs" (constant), "vrs" (variable), "nirs" (non-increasing), "ndrs" (non-decreasing) or "grs" (generalized). - `L`: Lower bound for the generalized returns to scale (grs). - `U`: Upper bound for the generalized returns to scale (grs). - `compute_target`: Logical. If it is `TRUE`, it computes targets. - `returnlp`: Logical. If it is `TRUE`, it returns the linear problems (objective function and constraints). - `...`: Ignored, for compatibility issues. ## Note In this model, the efficiency score is the sum of the slacks. Therefore, a DMU is efficient when the objective value (`objval`) is zero. ## Examples ```r # Example 1. # Replication of results in Charnes et. al (1994, p. 27) x <- c(2, 3, 6, 9, 5, 4, 10) y <- c(2, 5, 7, 8, 3, 1, 7) data_example <- data.frame(dmus = letters[1:7], x, y) data_example <- make_deadata(data_example, ni = 1, no = 1) result <- model_additive(data_example, rts = "vrs") efficiencies(result) slacks(result) lambdas(result) # Example 2. # Measure of Inefficiency Proportions (MIP). x <- c(2, 3, 6, 9, 5, 4, 10) y <- c(2, 5, 7, 8, 3, 1, 7) data_example <- data.frame(dmus = letters[1:7], x, y) data_example <- make_deadata(data_example, ni = 1, no = 1) result2 <- model_additive(data_example, rts = "vrs", weight_slack_i = 1 / data_example[["input"]], weight_slack_o = 1 / data_example[["output"]]) slacks(result2) # Example 3. # Range Adjusted Measure of Inefficiencies (RAM). x <- c(2, 3, 6, 9, 5, 4, 10) y <- c(2, 5, 7, 8, 3, 1, 7) data_example <- data.frame(dmus = letters[1:7], x, y) data_example <- make_deadata(data_example, ni = 1, no = 1) range_i <- apply(data_example[["input"]], 1, max) - apply(data_example[["input"]], 1, min) range_o <- apply(data_example[["output"]], 1, max) - apply(data_example[["output"]], 1, min) w_range_i <- 1 / (range_i * (dim(data_example[["input"]])[1] + dim(data_example[["output"]])[1])) w_range_o <- 1 / (range_o * (dim(data_example[["input"]])[1] + dim(data_example[["output"]])[1])) result3 <- model_additive(data_example, rts = "vrs", weight_slack_i = w_range_i, weight_slack_o = w_range_o) slacks(result3) ``` ## References Charnes, A.; Cooper, W.W.; Golany, B.; Seiford, L.; Stuz, J. (1985) "Foundations of Data Envelopment Analysis for Pareto-Koopmans Efficient Empirical Production Functions", Journal of Econometrics, 30(1-2), 91-107. tools:::Rd_expr_doi("10.1016/0304-4076(85)90133-2") Charnes, A.; Cooper, W.W.; Lewin, A.Y.; Seiford, L.M. (1994). Data Envelopment Analysis: Theory, Methology, and Application. Boston: Kluwer Academic Publishers. tools:::Rd_expr_doi("10.1007/978-94-011-0637-5") Cooper, W.W.; Park, K.S.; Pastor, J.T. (1999). "RAM: A Range Adjusted Measure of Inefficiencies for Use with Additive Models, and Relations to Other Models and Measures in DEA". Journal of Productivity Analysis, 11, p. 5-42. tools:::Rd_expr_doi("10.1023/A:1007701304281") ## See Also `model_addsupereff` ## Author(s) Vicente Coll-Serrano (vicente.coll@uv.es ). **Quantitative Methods for Measuring Culture (MC2). Applied Economics.** Vicente Bolós (vicente.bolos@uv.es ). **Department of Business Mathematics** Rafael Benítez (rafael.suarez@uv.es ). **Department of Business Mathematics** University of Valencia (Spain)

model_additive function