model_dir: Directional DEA model.

Description

It solves directional, basic DEA models under constant, variable, non-increasing, non-decreasing or generalized returns to scale. By default, models are solved in a two-stage process (slacks are maximized).

Usage

model_dir(datadea,
            dmu_eval = NULL,
            dmu_ref = NULL,
            dir_input = NULL,
            dir_output = NULL,
            d_input = 1,
            d_output = 1,
            rts = c("crs", "vrs", "nirs", "ndrs", "grs"),
            L = 1,
            U = 1,
            maxslack = TRUE,
            weight_slack_i = 1,
            weight_slack_o = 1,
            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.
dir_input: A value, vector of length m, or matrix m x ne (where ne is the length of dmu_eval) with the input directions. If dir_input == input matrix (of DMUS in dmu_eval) and dir_output == 0, it is equivalent to input oriented (beta = 1 - efficiency). If dir_input is omitted, input matrix (of DMUS in dmu_eval) is assigned.
dir_output: A value, vector of length s, or matrix s x ne (where ne is the length of dmu_eval) with the output directions. If dir_input == 0 and dir_output == output matrix (of DMUS in dmu_eval), it is equivalent to output oriented (beta = efficiency - 1). If dir_output is omitted, output matrix (of DMUS in dmu_eval) is assigned.
d_input: A value, vector of length m, or matrix m x ne (where ne is the length of dmu_eval) with the input orientation parameters. If d_input == 1 (default) and d_output == 0, it is equivalent to input oriented. It is an alternative for dir_input.
d_output: A value, vector of length s, or matrix s x ne (where ne is the length of dmu_eval) with the output orientation parameters. If d_input == 0 and d_output == 1 (default), it is equivalent to output oriented. It is an alternative to dir_output.
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).
maxslack: Logical. If it is TRUE, it computes the max slack solution.
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 for the max slack solution.
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 for the max slack solution.
returnlp: Logical. If it is TRUE, it returns the linear problems (objective function and constraints) of stage 1.
...: 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

Chambers, R.G.; Chung, Y.; Färe, R. (1996). "Benefit and Distance Functions", Journal of Economic Theory, 70(2), 407-419.

Chambers, R.G.; Chung, Y.; Färe, R. (1998). "Profit Directional Distance Functions and Nerlovian Efficiency", Journal of Optimization Theory and Applications, 95, 351-354.

Examples

Run this code


data("PFT1981") 
# Selecting DMUs in Program Follow Through (PFT)
PFT <- PFT1981[1:49, ] 
PFT <- make_deadata(PFT, 
                    inputs = 2:6, 
                    outputs = 7:9 )
eval_pft <- model_dir(PFT)
efficiencies(eval_pft)