model_sbmsupereff function

Slack based measure of superefficiency model

Slack based measure of superefficiency model (Tone 2002) with n

DMUs, m inputs and s outputs.

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)

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.
• 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).

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)

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

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)