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,
                 ...)

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 (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)

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")

Examples

Run this code

# 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)