model_addsupereff: Additive super-efficiency DEA model.

In deaR: Conventional and Fuzzy Data Envelopment Analysis

Additive super-efficiency DEA model.

Description

Solve the additive super-efficiency model proposed by Du, Liang and Zhu (2010). It is an extension of the SBM super-efficiency to the additive DEA model.

Usage

model_addsupereff(datadea,
                  dmu_eval = NULL,
                  dmu_ref = NULL,
                  orientation = NULL,
                  weight_slack_i = NULL,
                  weight_slack_o = NULL,
                  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 super-slacks (t_input). If 0, output-oriented. If weight_slack_i is the matrix of the inverses of inputs of DMUS in dmu_eval (default), the model is unit invariant.
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 super-slacks (t_output). If 0, input-oriented. If weight_slack_o is the matrix of the inverses of outputs of DMUS in dmu_eval (default), the model is unit invariant.
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, projections and slacks. We note that we call "targets" to the "efficient projections" in the strongly efficient frontier.
returnlp	Logical. If it is TRUE, it returns the linear problems (objective function and constraints).
...	Ignored, for compatibility issues.

Value

A list of class dea with the results for the evaluated DMUs (DMU component), along with any other necessary information to replicate the results, such as the name of the model and parameters orientation, rts, dmu_eval and dmu_ref.

Author(s)

Vicente Coll-Serrano ([e-mail]). Quantitative Methods for Measuring Culture (MC2). Applied Economics.

Vicente Bolós ([e-mail]). Department of Business Mathematics

Rafael Benítez ([e-mail]). Department of Business Mathematics

University of Valencia (Spain)

References

Du, J.; Liang, L.; Zhu, J. (2010). "A Slacks-based Measure of Super-efficiency in Data Envelopment Analysis. A Comment", European Journal of Operational Research, 204, 694-697. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.ejor.2009.12.007")}

Zhu, J. (2014). Quantitative Models for Performance Evaluation and Benchmarking. Data Envelopment Analysis with Spreadsheets. 3rd Edition Springer, New York. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/978-3-319-06647-9")}

See Also

model_additive, model_supereff, model_sbmsupereff

Examples

# Replication of results in Du, Liang and Zhu (2010, Table 6, p.696)
data("Power_plants")
Power_plants <- make_deadata(Power_plants, 
                             ni = 4, 
                             no = 2)
result <- model_addsupereff(Power_plants, 
                            rts = "crs")  
efficiencies(result)

deaR documentation built on Nov. 5, 2025, 6:35 p.m.