model_sbmeff function

Slack based measure (SBM) of efficiency model.

Calculate the SBM model proposed by Tone (2001).

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.
• 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)

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)

References

Tone, K. (2001). "A Slacks-Based Measure of Efficiency in Data Envelopment Analysis", European Journal of Operational Research, 130, 498-509. 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. 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")

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. tools:::Rd_expr_doi("10.1007/s11123-007-0039-5")

See Also

model_nonradial, model_deaps, model_profit, 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)