model_basic {deaR}

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.

Note

(1) Model proposed by Seiford and Zhu (2002) is applied for undesirable inputs/outputs and non-directional orientation (i.e., input or output oriented). You should select "vrs" returns to scale (BCC model) in order to maintain translation invariance. If deaR detects that you are not specifying rts = "vrs", it makes the change to "vrs" automatically.

(2) With undesirable inputs and non-directional orientation use input-oriented BCC model, and with undesirable outputs and non-directional orientation use output-oriented BCC model. Alternatively, you can also treat the undesirable outputs as inputs and then apply the input-oriented BCC model (similarly with undesirable inputs).

(3) Model proposed by Fare and Grosskopf (2004) is applied for undesirable inputs/outputs and directional orientation.

(4) With orientation = "dir" (directional distance function model), efficient DMUs are those for which beta = 0.

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.; 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.

See Also

model_multiplier, model_supereff

Examples

# 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)