model_addsupereff function

Additive super-efficiency DEA model.

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.

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.
• returnlp: Logical. If it is TRUE, it returns the linear problems (objective function and constraints).
• ...: Ignored, for compatibility issues.

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)

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. 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. tools:::Rd_expr_doi("10.1007/978-3-319-06647-9")

See Also

model_additive, model_supereff, model_sbmsupereff

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)