# Basic (radial and directional) DEA model. 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. ```r 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. ## Examples ```r # 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) ``` ## 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` ## Author(s) 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)