model_sbmeff: Slack based measure (SBM) of efficiency model.

In deaR: Conventional and Fuzzy Data Envelopment Analysis

Slack based measure (SBM) of efficiency model.

Description

Calculate the SBM model proposed by Tone (2001).

Usage

model_sbmeff(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,
             kaizen = FALSE,
             maxfr = NULL,
             tol = 1e-6,
             silent = FALSE,
             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.
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).
kaizen	Logical. If TRUE, the kaizen version of SBM (Tone 2010), also known as SBM-Max, is computed.
maxfr	A list with the maximal friends sets, as it is returned by function maximal_friends. If NULL (default) this list is computed internally.
tol	Numeric, a tolerance margin for checking efficiency (only for the kaizen version).
silent	Logical. If FALSE (default) it prints all the messages from function maximal_friends.
compute_target	Logical. If it is TRUE, it computes targets. 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). If kaizen is TRUE it is ignored.
...	Other options (currently not implemented)

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

Tone, K. (2001). "A Slacks-Based Measure of Efficiency in Data Envelopment Analysis", European Journal of Operational Research, 130, 498-509. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/S0377-2217(99)00407-5")}

Tone, K. (2010). "Variations on the theme of slacks-based measure of efficiency in DEA", European Journal of Operational Research, 200, 901-907. \Sexpr[results=rd]{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. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/978-0-387-45283-8")}

Aparicio, J.; Ruiz, J.L.; Sirvent, I. (2007) "Closest targets and minimum distance to the Pareto-efficient frontier in DEA", Journal of Productivity Analysis, 28, 209-218. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/s11123-007-0039-5")}

See Also

model_nonradial, model_deaps, model_profit, model_sbmsupereff

Examples

# Example 1. Replication of results in Tone (2001, p.505)
data("Tone2001")
data_example <- make_deadata(Tone2001, 
                             ni = 2, 
                             no = 2)
result_SBM <- model_sbmeff(data_example, 
                           orientation = "no", 
                           rts = "crs")
result_CCR <- model_basic(data_example, 
                          orientation = "io", 
                          rts = "crs")
efficiencies(result_SBM)
efficiencies(result_CCR)
slacks(result_SBM)
slacks(result_CCR)
 
# Example 2. Replication of results in Tone (2003), pp 10-11 case 1:1.
data("Tone2003")
data_example <- make_deadata(Tone2003,
                             ni = 1,
                             no = 2,
                             ud_outputs = 2)
result <- model_sbmeff(data_example,
                       rts = "vrs")
efficiencies(result)
targets(result)

# Example 3. Replication of results in Aparicio (2007).
data("Airlines")
datadea <- make_deadata(Airlines,
                        inputs = 4:7,
                        outputs = 2:3)
result <- model_sbmeff(datadea = datadea, kaizen = TRUE)
efficiencies(result)
targets(result)  
 

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