model_multiplier {deaR}

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.

Note

(1) Very important with the multiplier model: "The optimal weights for an efficient DMU need not be unique" (Cooper, Seiford and Tone, 2007:31). "Usually, the optimal weights for inefficient DMUs are unique, the exception being when the line of the DMU is parallel to one of the boundaries of the feasible region" (Cooper, Seiford and Tone, 2007:32).

(2) The measure of technical input (or output) efficiency obtained by using multiplier DEA models is better the smaller the value of epsilon.

(3) Epsilon is usually set equal to 10^-6. However, if epsilon is not set correctly, the multiplier model can be infeasible (Zhu,2014:49).

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

Charnes, A.; Cooper, W.W. (1962). “Programming with Linear Fractional Functionals”, Naval Research Logistics Quarterly 9, 181-185. 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. 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. 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. 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. 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. 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)