BenAndMal: Benevolent and Malevolent Model

In aurokp2/MultiplierDEA: Multiplier Data Envelopment Analysis and Cross Efficiency

Benevolent and Malevolent Model

Description

Two-Phase Cross efficiency approach.

Usage

Mal_Ben(x = x, y = y, rts ="crs", orientation = "input", phase = "mal",
weightRestriction, include = TRUE)

Arguments

x	Inputs or resources used by each decision making unit.
y	Outputs or resources used by each decision making unit.
rts	Returns to scale for the application, or industry studied. Note the default rts is crs. vrs Variable returns to scale. crs Constant returns to scale. Available option: crs, vrs.
orientation	Orientation of the DEA model - primary emphasis on input-reduction input or output-augmentation output. Note that unlike the DEA functions, the default is input orientation. Available option: input, output.
weightRestriction	Weight restriction for the model. Optional parameter.
phase	Second phase of the model. Malevolent or Benevolent. Note the default is mal.Available option: mal, ben.
include	In the second phase include evaluating DMU in the calculation. Default is TRUE. Available option: TRUE, FALSE.

Value

The function returns a number of values per DMU. The standardized efficiency (all inefficiencies are between 0 and 1, for input and output orientation) Efficiency, and the lambda values, lambda, are returned.

$rts	Returns to scale of the model.
$Orientation	Orientation of the model.
$InputValues	Input Values (x) passed to the model.
$OutputValues	Output Values (y) passed to the model.
$Phase1_Efficiency	Efficiency of each DMU in the model from Phase 1.
$Phase1_Lambda	Lambdas per DMU in the model from Phase 1.
$Phase1_vx	Input weights from the model from Phase 1.
$Phase1_uy	Output weights from the model from Phase 1.
$Phase1_Free_Weights	Free weights from the model from Phase 1. Applies only to vrs returns-to-scale.
$Phase1_Model_Status	Returns the status of the phase two LP model.
$Phase2_Efficiency	Efficiency of each DMU in the model from Phase 2.
$Phase2_Lambda	Lambdas per DMU in the model from Phase 2.
$Phase2_vx	Input weights from the model from Phase 2.
$Phase2_uy	Output weights from the model from Phase 2.
$Phase2_Free_weights	Free weights from the model from Phase 2. Applies only to vrs returns-to-scale.
$Phase2_Model_Status	Returns the status of the phase two LP model.
$ceva_matrix	Returns the cross efficiency matrix. Row is the Rating DMU and Column is the Rated DMU.
$ce_ave	Returns the cross efficiency score for the DMU.
$ceva_max	Returns the maximum cross efficiency score for the DMU.
$ceva_min	Returns the minimum cross efficiency score for the DMU.

Note

ceva_matrix - cross-evaluation matrix. ceva_max - cross-evaluation maximum. ceva_min - cross-evaluation minimum. ce_ave - cross-efficiency scores.

Examples

#Example from Kenneth R. Baker: Optimization Modeling with Spreadsheets, Third Edition,p. 176,
#John Wiley and Sons, Inc.

dmu <- c("A", "B", "C", "D", "E", "F")
x <- data.frame(c(150,400,320,520,350,320),c(0.2,0.7,1.2,2.0,1.2,0.7))
rownames(x) <- dmu
colnames(x)[1] <- c("StartHours")
colnames(x)[2] <- c("Supplies")
y <- data.frame(c(14,14,42,28,19,14),c(3.5,21,10.5,42,25,15))
rownames(y) <- dmu
colnames(y)[1] <- c("Reimbursed")
colnames(y)[2] <- c("Private")

# Calculate the efficiency score
result <- Mal_Ben(x, y, rts = "crs",  orientation = "input",phase = "mal", include = TRUE)
# Examine the cross efficiency score for DMUs
print(result$ce_ave)

aurokp2/MultiplierDEA documentation built on Sept. 9, 2022, 3:35 p.m.