model_additive {deaR}

Additive DEA model.

Description

Solve the additive model of Charnes et. al (1985). With the current version of deaR, it is possible to solve input-oriented, output-oriented, and non-oriented additive model under constant and non-constant returns to scale.

Besides, the user can set weights for the input slacks and/or output slacks. So, it is also possible to solve weighted additive models. For example: Measure of Inefficiency Proportions (MIP), Range Adjusted Measure (RAM), etc.

Usage

model_additive(datadea,
               dmu_eval = NULL,
               dmu_ref = NULL,
               orientation = NULL,
               weight_slack_i = 1,
               weight_slack_o = 1,
               rts = c("crs", "vrs", "nirs", "ndrs", "grs"),
               L = 1,
               U = 1,
               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.

orientation

This parameter is either NULL (default) or a string, equal to "io" (input-oriented) or "oo" (output-oriented). It is used to modify the weight slacks. If input-oriented, weight_slack_o are taken 0. If output-oriented, weight_slack_i are taken 0.

weight_slack_i

A value, vector of length m, or matrix m x ne (where ne is the length of dmu_eval) with the weights of the input slacks. If 0, output-oriented.

weight_slack_o

A value, vector of length s, or matrix s x ne (where ne is the length of dmu_eval) with the weights of the output slacks. If 0, input-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.

returnlp

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

...

Ignored, for compatibility issues.

Note

In this model, the efficiency score is the sum of the slacks. Therefore, a DMU is efficient when the objective value (objval) is zero.

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.; Golany, B.; Seiford, L.; Stuz, J. (1985) "Foundations of Data Envelopment Analysis for Pareto-Koopmans Efficient Empirical Production Functions", Journal of Econometrics, 30(1-2), 91-107. doi:10.1016/0304-4076(85)90133-2

Charnes, A.; Cooper, W.W.; Lewin, A.Y.; Seiford, L.M. (1994). Data Envelopment Analysis: Theory, Methology, and Application. Boston: Kluwer Academic Publishers. doi:10.1007/978-94-011-0637-5

Cooper, W.W.; Park, K.S.; Pastor, J.T. (1999). "RAM: A Range Adjusted Measure of Inefficiencies for Use with Additive Models, and Relations to Other Models and Measures in DEA". Journal of Productivity Analysis, 11, p. 5-42. doi:10.1023/A:1007701304281

See Also

model_addsupereff

Examples

# Example 1. 
# Replication of results in Charnes et. al (1994, p. 27)
x <- c(2, 3, 6, 9, 5, 4, 10) 
y <- c(2, 5, 7, 8, 3, 1, 7)
data_example <- data.frame(dmus = letters[1:7], x, y)
data_example <- make_deadata(data_example, 
                             ni = 1, 
                             no = 1)
result <- model_additive(data_example, 
                         rts = "vrs")
efficiencies(result)
slacks(result)
lambdas(result)

# Example 2.
# Measure of Inefficiency Proportions (MIP).
x <- c(2, 3, 6, 9, 5, 4, 10) 
y <- c(2, 5, 7, 8, 3, 1, 7)
data_example <- data.frame(dmus = letters[1:7], x, y)
data_example <- make_deadata(data_example,
                             ni = 1,
                             no = 1)
result2 <- model_additive(data_example,
                          rts = "vrs",
                          weight_slack_i = 1 / data_example[["input"]],
                          weight_slack_o = 1 / data_example[["output"]])
slacks(result2)

# Example 3.
# Range Adjusted Measure of Inefficiencies (RAM).
x <- c(2, 3, 6, 9, 5, 4, 10) 
y <- c(2, 5, 7, 8, 3, 1, 7)
data_example <- data.frame(dmus = letters[1:7], x, y)
data_example <- make_deadata(data_example,
                             ni = 1,
                             no = 1)
range_i <- apply(data_example[["input"]], 1, max) -
           apply(data_example[["input"]], 1, min)
range_o <- apply(data_example[["output"]], 1, max) -
           apply(data_example[["output"]], 1, min)
w_range_i <- 1 / (range_i * (dim(data_example[["input"]])[1] +
                             dim(data_example[["output"]])[1]))
w_range_o <- 1 / (range_o * (dim(data_example[["input"]])[1] +
                             dim(data_example[["output"]])[1]))
result3 <- model_additive(data_example,
                          rts = "vrs",
                          weight_slack_i = w_range_i,
                          weight_slack_o = w_range_o)
slacks(result3)