deaR (version 1.5.2)

model_qgo: Quadratically Constrained CRS Generalized Oriented DEA model.

Description

It solves quadratically constrained CRS generalized oriented DEA models (see Bolós et al. 2026), 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,
            force_quad = FALSE,
            maxslack = TRUE,
            weight_slack_i = 1,
            weight_slack_o = 1,
            returnqp = FALSE,
            ...)

Value

A list of class dea with the results for the evaluated DMUs (DMU component, we note that we call "targets" to the "efficient projections" in the strongly efficient frontier), along with any other necessary information to replicate the results, such as the name of the model and parameters d_input, d_output, rts,

dmu_eval and dmu_ref.

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 (default), it uses an initial vector (given by the evaluated DMU) for the solver. If it is FALSE, the initial vector is given internally by the solver and it is usually randomly generated.

force_quad

Logical. If it is FALSE (default) it uses the linear model model_lgo to get the results, in some particular cases in which the results of model_qgo can be deduced from the results of model_lgo, see V. J. Bolós et al. (2026).

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 to be passed to the solver solvecop from package optiSolve.

Author

Vicente Coll-Serrano (). Quantitative Methods for Measuring Culture (MC2). Applied Economics.

Vicente Bolós (). Department of Business Mathematics

Rafael Benítez (). Department of Business Mathematics

University of Valencia (Spain)

References

Bolós, V.J.; Benítez, R.; Coll-Serrano, V (2026). "A new family of models with generalized orientation in data envelopment analysis". International Transactions in Operational Research. tools:::Rd_expr_doi("10.1111/itor.70063")

See Also

model_basic, model_dir, model_lgo

Examples

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)