deaR (version 1.5.2)

model_sbmsupereff: Slack based measure of superefficiency model

Description

Slack based measure of superefficiency model (Tone 2002) with n DMUs, m inputs and s outputs.

Usage

model_sbmsupereff(datadea,
                  dmu_eval = NULL,
                  dmu_ref = NULL,
                  weight_input = 1,
                  weight_output = 1,
                  orientation = c("no", "io", "oo"),
                  rts = c("crs", "vrs", "nirs", "ndrs", "grs"),
                  L = 1,
                  U = 1,
                  compute_target = TRUE,
                  compute_rho = FALSE,
                  kaizen = FALSE,
                  silent = FALSE,
                  returnlp = FALSE)

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.

Arguments

datadea

A deadata object, including DMUs, inputs and 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.

weight_input

A value, vector of length m, or matrix m x ne (where ne is the length of dmu_eval) with weights to inputs corresponding to the relative importance of items.

weight_output

A value, vector of length m, or matrix m x ne (where ne is the length of dmu_eval) with weights to outputs corresponding to the relative importance of items.

orientation

A string, equal to "no" (non-oriented), "io" (input-oriented) or "oo" (output-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, superslacks (t_input and t_output) and slacks. We note that we call "targets" to the "efficient projections" in the strongly efficient frontier.

compute_rho

Logical. If it is TRUE, it computes the SBM efficiency score (applying model_sbmeff) of the DMU (project_input, project_output).

kaizen

Logical. If TRUE, the kaizen version of SBM (Tone 2010), also known as SBM-Max, is computed for the efficiency score of the DMU (project_input, project_output).

silent

Logical. If FALSE (default) it prints all the messages from function maximal_friends.

returnlp

Logical. If it is TRUE, it returns the linear problems (objective function and constraints).

Author

Vicente Coll-Serrano (). Quantitative Methods for Measuring Culture (MC2). Applied Economics.

Vicente Bolós (). Department of Business Mathematics

Rafael Benítez (). Department of Business Mathematics

University of Valencia (Spain)

References

Tone, K. (2002). "A slacks-based measure of super-efficiency in data envelopment analysis", European Journal of Operational Research, 143, 32-41. tools:::Rd_expr_doi("10.1016/S0377-2217(01)00324-1")

Tone, K. (2010). "Variations on the theme of slacks-based measure of efficiency in DEA", European Journal of Operational Research, 200, 901-907. tools:::Rd_expr_doi("10.1016/j.ejor.2009.01.027")

Cooper, W.W.; Seiford, L.M.; Tone, K. (2007). Data Envelopment Analysis. A Comprehensive Text with Models, Applications, References and DEA-Solver Software. 2nd Edition. Springer, New York. tools:::Rd_expr_doi("10.1007/978-0-387-45283-8")

See Also

model_sbmeff, model_supereff, model_addsupereff

Examples

# Replication of results in Tone(2002, p.39)
data("Power_plants")
data_example <- make_deadata(Power_plants,
                             ni = 4,
                             no = 2)
result <- model_sbmsupereff(data_example,
                            orientation = "io",
                            rts = "crs") 
efficiencies(result)
slacks(result)$slack_input
references(result)