model_basic: Basic (radial and directional) DEA model.

Description

It solves input and output oriented, along with directional, basic DEA models (envelopment form) under constant (CCR model), variable (BCC model), non-increasing, non-decreasing or generalized returns to scale. By default, models are solved in a two-stage process (slacks are maximized).

You can use the model_basic function to solve directional DEA models by choosing orientation = "dir".

The model_basic function allows to treat with non-discretional, non-controllable and undesirable inputs/outputs.

Usage

model_basic(datadea,
            dmu_eval = NULL,
            dmu_ref = NULL,
            orientation = c("io", "oo", "dir"),
            dir_input = NULL,
            dir_output = NULL,
            rts = c("crs", "vrs", "nirs", "ndrs", "grs"),
            L = 1,
            U = 1,
            maxslack = TRUE,
            weight_slack_i = 1,
            weight_slack_o = 1,
            vtrans_i = NULL,
            vtrans_o = NULL,
            compute_target = TRUE,
            compute_multiplier = FALSE,
            returnlp = FALSE,
            silent_ud = 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: A string, equal to "io" (input oriented), "oo" (output oriented), or "dir" (directional).
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.
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.
vtrans_i: Numeric vector of translation for undesirable inputs with non-directional orientation. If vtrans_i[i] is NA, then it applies the "max + 1" translation to the i-th undesirable input. If vtrans_i is a constant, then it applies the same translation to all undesirable inputs. If vtrans_i is NULL, then it applies the "max + 1" translation to all undesirable inputs.
vtrans_o: Numeric vector of translation for undesirable outputs with non-directional orientation, analogous to vtrans_i, but applied to outputs.
compute_target: Logical. If it is TRUE, it computes targets of the max slack solution.
compute_multiplier: Logical. If it is TRUE, it computes multipliers (dual solution) when orientation is "io" or "oo".
returnlp: Logical. If it is TRUE, it returns the linear problems (objective function and constraints) of stage 1.
silent_ud: Logical. For internal use, to avoid multiple warnings in the execution of malmquist_index function with undesirable variables.
...: 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

Charnes, A.; Cooper, W.W.; Rhodes, E. (1978). “Measuring the efficiency of decision making units”, European Journal of Operational Research 2, 429–444.

Charnes, A.; Cooper, W.W.; Rhodes, E. (1979). “Short communication: Measuring the efficiency of decision making units”, European Journal of Operational Research 3, 339.

Charnes, A.; Cooper, W.W.; Rhodes, E. (1981). "Evaluating Program and Managerial Efficiency: An Application of Data Envelopment Analysis to Program Follow Through", Management Science, 27(6), 668-697.

Banker, R.; Charnes, A.; Cooper, W.W. (1984). “Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis”, Management Science; 30; 1078-1092.

Undesirable inputs/outputs:

Pastor, J.T. (1996). "Translation Invariance in Data Envelopment Analysis: a Generalization", Annals of Operations Research, 66(2), 91-102.

Seiford, L.M.; Zhu, J. (2002). “Modeling undesirable factors in efficiency evaluation”, European Journal of Operational Research 142, 16-20.

Färe, R. ; Grosskopf, S. (2004). “Modeling undesirable factors in efficiency evaluation: Comment”, European Journal of Operational Research 157, 242-245.

Hua Z.; Bian Y. (2007). DEA with Undesirable Factors. In: Zhu J., Cook W.D. (eds) Modeling Data Irregularities and Structural Complexities in Data Envelopment Analysis. Springer, Boston, MA.

Non-discretionary/Non-controllable inputs/outputs:

Banker, R.; Morey, R. (1986). “Efficiency Analysis for Exogenously Fixed Inputs and Outputs”, Operations Research; 34; 513-521.

Ruggiero J. (2007). Non-Discretionary Inputs. In: Zhu J., Cook W.D. (eds) Modeling Data Irregularities and Structural Complexities in Data Envelopment Analysis. Springer, Boston, MA.

Directional DEA model:

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

# Example 1. Basic DEA model with desirable inputs/outputs.
# Replication of results in Charnes, Cooper and Rhodes (1981).
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_basic(PFT, 
                        orientation = "io", 
                        rts = "crs")
eff <- efficiencies(eval_pft)
s <- slacks(eval_pft) 
lamb <- lambdas(eval_pft)
tar <- targets(eval_pft)
ref <- references(eval_pft) 
returns <- rts(eval_pft)

# Example 2. Basic DEA model with undesirable outputs.
# Replication of results in Hua and Bian (2007).
data("Hua_Bian_2007")
# The third output is an undesirable output.
data_example <- make_deadata(Hua_Bian_2007, 
                             ni = 2,
                             no = 3, 
                             ud_outputs = 3) 
# Translation parameter (vtrans_o) is set to 1500                          
result <- model_basic(data_example, 
                      orientation = "oo", 
                      rts = "vrs", 
                      vtrans_o = 1500) 
eff <- efficiencies(result)
1 / eff # results M5 in Table 6-5 (p.119)

# Example 3. Basic DEA model with non-discretionary (fixed) inputs.
# Replication of results in Ruggiero (2007).
data("Ruggiero2007") 
# The second input is a non-discretionary input.
datadea <- make_deadata(Ruggiero2007, 
                        ni = 2,
                        no = 1, 
                        nd_inputs = 2) 
result <- model_basic(datadea,
                      orientation = "io", 
                      rts = "crs")
efficiencies(result)