model_qgo: Quadratically Constrained CRS Generalized Oriented DEA model.

Description

It solves quadratically constrained CRS generalized oriented DEA models, using alabama solver. By default, models are solved in a two-stage process (slacks are maximized).

Usage

model_qgo(datadea,
            dmu_eval = NULL,
            dmu_ref = NULL,
            d_input = 1,
            d_output = 1,
            rts = c("crs", "vrs", "nirs", "ndrs", "grs"),
            L = 1,
            U = 1,
            give_X = TRUE,
            maxslack = TRUE,
            weight_slack_i = 1,
            weight_slack_o = 1,
            returnqp = 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.
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.
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.
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).
give_X: Logical. If it is TRUE, it uses an initial vector (given by the evaluated DMU) for the solver, except for "cccp". If it is FALSE, the initial vector is given internally by the solver and it is usually randomly generated.
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.
returnqp: Logical. If it is TRUE, it returns the quadratic problems (objective function and constraints) of stage 1.
...: Other parameters, like the initial vector X, to be passed to the solver.

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

"A new family of models with generalized orientation in data envelopment analysis". V. J. Bolós, R. Benítez, V. Coll-Serrano. International Transactions in Operational Research. Accepted

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_qgo(PFT, dmu_eval = 1:5)
efficiencies(eval_pft)