deaR (version 1.5.2)

model_multiplier: Multiplier DEA model

Description

Solve input-oriented and output-oriented basic DEA models (multiplicative form) under constant (CCR DEA model), variable (BCC DEA model), non-increasing, non-decreasing or generalized returns to scale. It does not take into account non-controllable, non-discretionary or undesirable inputs/outputs.

Usage

model_multiplier(datadea,
                 dmu_eval = NULL,
                 dmu_ref = NULL,
                 epsilon = 0,
                 orientation = c("io", "oo"),
                 rts = c("crs", "vrs", "nirs", "ndrs", "grs"),
                 L = 1,
                 U = 1,
                 returnlp = FALSE,
                 compute_lambda = TRUE,
                 ...)

Value

A list of class dea with the results for the evaluated DMUs (DMU component, we note that we call "targets" to the "efficient projections" in the strongly efficient frontier), 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.

epsilon

Numeric, multipliers must be >= epsilon.

orientation

A string, equal to "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).

returnlp

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

compute_lambda

Logical. If it is TRUE, it computes the dual problem and lambdas.

...

Ignored, for compatibility issues.

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

Charnes, A.; Cooper, W.W. (1962). “Programming with Linear Fractional Functionals”, Naval Research Logistics Quarterly 9, 181-185. tools:::Rd_expr_doi("10.1002/nav.3800090303")

Charnes, A.; Cooper, W.W.; Rhodes, E. (1978). “Measuring the Efficiency of Decision Making Units”, European Journal of Operational Research 2, 429–444. tools:::Rd_expr_doi("10.1016/0377-2217(78)90138-8")

Charnes, A.; Cooper, W.W.; Rhodes, E. (1979). “Short Communication: Measuring the Efficiency of Decision Making Units”, European Journal of Operational Research 3, 339. tools:::Rd_expr_doi("10.1016/0377-2217(79)90229-7")

Golany, B.; Roll, Y. (1989). "An Application Procedure for DEA", OMEGA International Journal of Management Science, 17(3), 237-250. tools:::Rd_expr_doi("10.1016/0305-0483(89)90029-7")

Seiford, L.M.; Thrall, R.M. (1990). “Recent Developments in DEA. The Mathematical Programming Approach to Frontier Analysis”, Journal of Econometrics 46, 7-38. tools:::Rd_expr_doi("10.1016/0304-4076(90)90045-U")

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_basic, cross_efficiency

Examples

# Example 1.
# Replication of results in Golany and Roll (1989).
data("Golany_Roll_1989")
data_example <- make_deadata(datadea = Golany_Roll_1989[1:10, ],
                             inputs = 2:4, 
                             outputs = 5:6) 
result <- model_multiplier(data_example, 
                           epsilon = 0, 
                           orientation = "io", 
                           rts = "crs") 
efficiencies(result)
multipliers(result)

# Example 2.
# Multiplier model with infeasible solutions (See note).
data("Fortune500")
data_Fortune <- make_deadata(datadea = Fortune500, 
                             inputs = 2:4, 
                             outputs = 5:6) 
result2 <- model_multiplier(data_Fortune, 
                           epsilon = 1e-6, 
                           orientation = "io", 
                           rts = "crs") 
# Results for General Motors and Ford Motor are not shown by deaR 
# because the solution is infeasible.
efficiencies(result2)
multipliers(result2)