adea (version 1.5.1)

cadea: Make a constrained ADEA analysis

Description

This function calculates an efficiency score for each DMU and computes a load for each variable within the current model. However, it's essential to note that the loads or contributions of input or output variables are subject to constraints within specified values. As a result, the efficiencies of DMUs may deviate from those obtained in regular DEA or ADEA models.

Usage

cadea(
  input,
  output,
  orientation = c("input", "output"),
  load.orientation = c("inoutput", "input", "output"),
  name = "",
  load.min,
  load.max,
  solver = "lpsolve"
)

Value

The function returns a cadea object with the follosing named members:

• name: A label of the model

• orientation: DEA model orientation 'input' or 'output'

• load.orientation: load DEA model orientation 'input', 'output', or 'inoutput'

• inputnames: Variable input names

• outputnames: Variable output names

• eff: is a vector with DMU's scores

• loads: A list with all information about loads:

  • load: The lowest load, which is the load of the ADEA model

  • input: A vector with loads of input variables

  • iinput: Index of input variable that reach the load of the model

  • output: A vector with loads of output variables

  • ioutput: Index of output variable that reach the load of the model

  • load.min: Miniminum allowed value for variable loads when load.orientation is ioutput, for input variable loads when load.orientation is input, and for output variable loads when load.orientation is output.

  • load.max: Mamixum allowed value for all, input or output variable loads as for load.min.

• ux: A set of weights for inputs

• vy: A set of weights for output

• iterations: Number of iterations to reach the stop rule

• vinput: Standardized virtual input dividing by the sum of the weights, see [Costa2006] in adea-package.

• voutput: Standardized virtual output dividing by the sum of the weights, see [Costa2006] in adea-package efficiency scores, one set of weights for inputs and other for outputs, number of efficient units, variable loads and model load.

• solver: The solver used for the resolution of the optimization problem

Arguments

input

A matrix or a data frame containing the inputs of the units to be evaluated, with one row for each DMU and one column for each input.

output

A matrix or a data frame containing the outputs of the units to be evaluated, with one row for each DMU and one column for each output.

orientation

Use "input" for input orientation or "output" for output orientation in DEA model. The default is "input".

load.orientation

This parameter allows the selection of variables to be included in load analysis. The default is "inoutput" which means that all input and output variables will be included. Use "input" or "output" to include only input or output variables in load analysis.

name

An optional descriptive name for the model. The default is an empty string. This name will be displayed in printed and summarized results.

load.min

A numeric value or vector giving minimum values for loads. Values for load.min must belongs to [0, 1).

load.max

A numeric value or vector giving maximum values for loads. Values for load.max must be greater than 1. If load.min or load.max are vectors then its length must be the same as the number of loads to compute. This means, number of inputs when load.orientation is input, number of outputs when load.orientation is output, and the sum of both when load.orientation is inoutput.

solver

The solver used by ROI to solve the DEA optimization problem. The default is "auto." The solver must be installed and capable of solving linear programming problems. Use ROI_installed_solvers() to list them.

Details

A variable load is a numerical value between 0 and 1, with 0 signifying that the variable's contribution to the efficiency calculations is negligible. In an ideal scenario, each input or output variable would have a load of 1. This model enforces input and output weights in a manner that ensures the final variable loads fall within specified values.

In a raw variable selection procedure, it's possible to inadvertently remove a variable from a DEA model, leading to a non-natural model. In other cases, there may be political or tactical reasons for certain variables to be considered. In a standard DEA model, the weights associated with these variables might be reduced to very small values, effectively rendering their contributions nearly negligible.

The constraints for variable loads in these models prevent such scenarios by ensuring that the contributions of variables reach the desired levels. This maintains the integrity and significance of variables in the DEA model.

For more information about loads or ADEA model see adea

See Also

adea-package.

Examples

data('cardealers4')
input <- cardealers4[, c('Employees', 'Depreciation')]
output <- cardealers4[, c('CarsSold', 'WorkOrders')]

# Compute adea model
model <- adea(input, output)
model
# Dealer A  Dealer B  Dealer C  Dealer D  Dealer E  Dealer F
# 0.9915929 1.0000000 0.8928571 0.8653846 1.0000000 0.6515044

# Get input variable loads
model$loads$input
# Employees Depreciation
# 0.6666667    1.3333333
# Get output variable loads
model$loads$output
#  CarsSold WorkOrders
# 1.2663476  0.7336524 

# Compute a constrained adea model to force load between .8 and 1.5
cmodel <- cadea(input, output, load.min = .8, load.max = 1.5)
cmodel
#  Dealer A  Dealer B  Dealer C  Dealer D  Dealer E  Dealer F 
# 0.9915929 1.0000000 0.8928571 0.8653846 1.0000000 0.5920826 

# Get loads
cmodel$loads
# $load
# [1] 0.8
# $input
# Employees Depreciation
#       0.8          1.2
# $iinput
# Employees
# 1 
# $output
# CarsSold WorkOrders
#      1.2        0.8
# $ioutput
# WorkOrders
# 2
# $load.min
# [1] 0.8 0.8 0.8 0.8
# $load.max
# [1] 1.5 1.5 1.5 1.5
# See differences of efficiencies in both models
model$eff - cmodel$eff
#      Dealer A      Dealer B      Dealer C      Dealer D      Dealer E      Dealer F
# -2.220446e-16 -1.332268e-15 -1.110223e-16  2.220446e-16 -1.110223e-16  5.942183e-02