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R/model_fdh.R
In deaR: Conventional and Fuzzy Data Envelopment Analysis
Defines functions
model_fdh
Documented in
model_fdh
#' @title Free disposal hull (FDH) model.
#'
#' @description FDH model allows the free disposability to construct the production
#' possibility set. The central feature of the FDH model is the lack of convexity
#' for its production possibility set (Thrall, 1999).
#'
#' @usage model_fdh(datadea,
#' fdh_modelname = c("basic"),
#' ...)
#'
#' @param datadea A \code{deadata} object, including DMUs, inputs and outputs.
#' @param fdh_modelname A string containing the name of the model to apply FDH.
#' For now, only "basic" is available.
#' @param ... \code{dmu_eval}, \code{dmu_ref}, \code{orientation} and other model parameters.
#' Parameters like \code{rts}, \code{max_slack} and \code{returnlp} are ignored.
#'
#' @author
#' \strong{Vicente Coll-Serrano} (\email{vicente.coll@@uv.es}).
#' \emph{Quantitative Methods for Measuring Culture (MC2). Applied Economics.}
#'
#' \strong{Vicente Bolós} (\email{vicente.bolos@@uv.es}).
#' \emph{Department of Business Mathematics}
#'
#' \strong{Rafael Benítez} (\email{rafael.suarez@@uv.es}).
#' \emph{Department of Business Mathematics}
#'
#' University of Valencia (Spain)
#'
#' @references
#' Cherchye, L.; Kuosmanen, T.; Post, T. (2000). "What Is the Economic Meaning of
#' FDH? A Reply to Thrall". Journal of Productivity Analysis, 13(3), 263–267.
#'
#' Deprins, D.; Simar, L. and Tulkens, H. (1984). Measuring Labor-Efficiency in
#' Post Offices. In M. Marchand, P. Pestieau and H. Tulkens (eds.), The Performance
#' of Public Entreprises: Concepts and Measurement. Amsterdam: North-Holland.
#'
#' Sanei, M.; Mamizadeh Chatghayeb, S. (2013). “Free Disposal Hull Models in
#' Supply Chain Management”, International Journal of Mathematical Modelling and
#' Computations, 3(3), 125-129.
#'
#' Thrall, R. M. (1999). "What Is the Economic Meaning of FDH?", Journal of
#' Productivity Analysis, 11(3), 243–50.
#'
#' @examples
#' # Example 1. FDH input-oriented.
#' # Replication of results in Sanei and Mamizadeh Chatghayeb (2013)
#' data("Supply_Chain")
#' data_fdh1 <- make_deadata(Supply_Chain,
#' inputs = 2:4,
#' outputs = 5:6)
#' result <- model_fdh(data_fdh1) # by default orientation = "io"
#' efficiencies(result)
#'
#' # Example 2. FDH output-oriented.
#' # Replication of results in Sanei and Mamizadeh Chatghayeb (2013)
#' data("Supply_Chain")
#' data_fdh2 <- make_deadata(Supply_Chain,
#' inputs = 5:6,
#' outputs = 7:8)
#' result2 <- model_fdh(data_fdh2,
#' orientation = "oo")
#' efficiencies(result2)
#'
#' @import lpSolve
#'
#' @export
model_fdh <-
function(datadea,
fdh_modelname = c("basic"), # It can be generalized to other models in the future
...) {
# Cheking whether datadea is of class "deadata" or not...
if (!is.deadata(datadea)) {
stop("Data should be of class deadata. Run make_deadata function first!")
}
# Checking modelname
fdh_modelname <- tolower(fdh_modelname)
fdh_modelname <- match.arg(fdh_modelname)
model_modelname <- paste("model", fdh_modelname, sep = "_")
optlist <- list(...)
if ("rts" %in% names(optlist)) {
#optlist$rts <- "vrs" # lpSolve and Rglpk do not work properly with binary variables
optlist$rts <- "crs"
}
optlist$returnlp <- TRUE
optlist$datadea <- datadea
deasol <- do.call(model_modelname,
optlist)
if (!is.null(datadea$ud_inputs) || !is.null(datadea$ud_outputs)) {
if (fdh_modelname == "basic") {
res_und <- undesirable_basic(datadea = datadea, vtrans_i = deasol$vtrans_i,
vtrans_o = deasol$vtrans_o)
datadea <- res_und$u_datadea
}
}
input <- datadea$input
output <- datadea$output
dmunames <- datadea$dmunames
inputnames <- rownames(input)
outputnames <- rownames(output)
ni <- nrow(input) # number of inputs
no <- nrow(output) # number of outputs
dmu_ref <- deasol$dmu_ref
ndr <- length(dmu_ref)
inputref <- matrix(input[, dmu_ref], nrow = ni)
outputref <- matrix(output[, dmu_ref], nrow = no)
ncd_inputs <- c(datadea$nc_inputs, datadea$nd_inputs)
ncd_outputs <- c(datadea$nc_outputs, datadea$nd_outputs)
dmu_eval <- deasol$dmu_eval
nde <- length(dmu_eval)
DMU <- vector(mode = "list", length = nde)
names(DMU) <- dmunames[dmu_eval]
binary.vec = (2 : (ndr + 1)) # lambdas. This is valid for model_basic
for (i in 1:nde) {
ii <- dmu_eval[i]
obj <- deasol$DMU[[i]]$direction
f.obj <- deasol$DMU[[i]]$objective.in
f.con <- deasol$DMU[[i]]$const.mat
f.dir <- deasol$DMU[[i]]$const.dir
f.rhs <- deasol$DMU[[i]]$const.rhs
# lpSolve and Rglpk do not work properly with binary variables
# res <- lp(obj, f.obj, f.con, f.dir, f.rhs, binary.vec = binary.vec)$solution
# kkmax <- (obj == "max")
# res <- Rglpk_solve_LP(obj = f.obj, mat = f.con, dir = f.dir, rhs = f.rhs,
# types = c("C", rep("B", ndr)), max = kkmax)$solution
### Alternative ###
scoreskk <- rep(NA, ndr)
f.objkk <- f.obj[1]
f.conkk <- matrix(f.con[, 1], ncol = 1)
for (j in 1:ndr) {
f.rhskk <- f.rhs - f.con[, j + 1]
reskk <- lp(obj, f.objkk, f.conkk, f.dir, f.rhskk)
if (reskk$status == 0) {
scoreskk[j] <- reskk$solution[1]
}
}
res <- rep(0, ndr + 1)
if (obj == "min") {
res[1] <- min(scoreskk, na.rm = TRUE)
} else {
res[1] <- max(scoreskk, na.rm = TRUE)
}
jkk <- which(scoreskk == res[1])[1]
res[jkk + 1] <- 1
### End Alternative ###
if (fdh_modelname == "basic") { # Prepared for generalization to other models
lambda <- res[binary.vec]
names(lambda) <- dmunames[dmu_ref]
target_input <- as.vector(inputref %*% lambda)
names(target_input) <- inputnames
target_output <- as.vector(outputref %*% lambda)
names(target_output) <- outputnames
if (deasol$orientation == "io") {
efficiency <- res[1]
slack_input <- efficiency * input[, ii] - target_input
slack_input[ncd_inputs] <- input[, ii] - target_input
names(slack_input) <- inputnames
slack_output <- target_output - output[, ii]
names(slack_output) <- outputnames
target_input[datadea$ud_inputs] <- deasol$vtrans_i - target_input[datadea$ud_inputs]
target_output[datadea$ud_outputs] <- deasol$vtrans_o - target_output[datadea$ud_outputs]
DMU[[i]] <- list(efficiency = efficiency,
lambda = lambda,
slack_input = slack_input, slack_output = slack_output,
target_input = target_input, target_output = target_output)
} else if (deasol$orientation == "oo") {
efficiency <- res[1]
slack_input <- input[, ii] - target_input
names(slack_input) <- inputnames
slack_output <- target_output - efficiency * output[, ii]
slack_output[ncd_outputs] <- target_output - output[, ii]
names(slack_output) <- outputnames
target_input[datadea$ud_inputs] <- deasol$vtrans_i - target_input[datadea$ud_inputs]
target_output[datadea$ud_outputs] <- deasol$vtrans_o - target_output[datadea$ud_outputs]
DMU[[i]] <- list(efficiency = efficiency,
lambda = lambda,
slack_input = slack_input, slack_output = slack_output,
target_input = target_input, target_output = target_output)
} else {
beta <- res[1]
slack_input <- input[, ii] - beta * deasol$orientation_param$dir_input[, ii] - target_input
slack_input[ncd_inputs] <- input[, ii] - target_input
names(slack_input) <- inputnames
slack_output <- target_output - output[, ii] - beta * deasol$orientation_param$dir_output[, ii]
slack_output[ncd_outputs] <- target_output - output[, ii]
names(slack_output) <- outputnames
target_input[datadea$ud_inputs] <- deasol$vtrans_i - target_input[datadea$ud_inputs]
target_output[datadea$ud_outputs] <- deasol$vtrans_o - target_output[datadea$ud_outputs]
DMU[[i]] <- list(beta = beta,
lambda = lambda,
slack_input = slack_input, slack_output = slack_output,
target_input = target_input, target_output = target_output)
}
}
}
deaOutput <- deasol
deaOutput$modelname <- paste("fdh", deasol$modelname, sep = "_")
deaOutput$DMU <- DMU
return(deaOutput)
}
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deaR documentation built on May 2, 2023, 5:13 p.m.
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Defines functions model_fdh
Documented in model_fdh
#' @title Free disposal hull (FDH) model.
#'
#' @description FDH model allows the free disposability to construct the production
#' possibility set. The central feature of the FDH model is the lack of convexity
#' for its production possibility set (Thrall, 1999).
#'
#' @usage model_fdh(datadea,
#' fdh_modelname = c("basic"),
#' ...)
#'
#' @param datadea A \code{deadata} object, including DMUs, inputs and outputs.
#' @param fdh_modelname A string containing the name of the model to apply FDH.
#' For now, only "basic" is available.
#' @param ... \code{dmu_eval}, \code{dmu_ref}, \code{orientation} and other model parameters.
#' Parameters like \code{rts}, \code{max_slack} and \code{returnlp} are ignored.
#'
#' @author
#' \strong{Vicente Coll-Serrano} (\email{vicente.coll@@uv.es}).
#' \emph{Quantitative Methods for Measuring Culture (MC2). Applied Economics.}
#'
#' \strong{Vicente Bolós} (\email{vicente.bolos@@uv.es}).
#' \emph{Department of Business Mathematics}
#'
#' \strong{Rafael Benítez} (\email{rafael.suarez@@uv.es}).
#' \emph{Department of Business Mathematics}
#'
#' University of Valencia (Spain)
#'
#' @references
#' Cherchye, L.; Kuosmanen, T.; Post, T. (2000). "What Is the Economic Meaning of
#' FDH? A Reply to Thrall". Journal of Productivity Analysis, 13(3), 263–267.
#'
#' Deprins, D.; Simar, L. and Tulkens, H. (1984). Measuring Labor-Efficiency in
#' Post Offices. In M. Marchand, P. Pestieau and H. Tulkens (eds.), The Performance
#' of Public Entreprises: Concepts and Measurement. Amsterdam: North-Holland.
#'
#' Sanei, M.; Mamizadeh Chatghayeb, S. (2013). “Free Disposal Hull Models in
#' Supply Chain Management”, International Journal of Mathematical Modelling and
#' Computations, 3(3), 125-129.
#'
#' Thrall, R. M. (1999). "What Is the Economic Meaning of FDH?", Journal of
#' Productivity Analysis, 11(3), 243–50.
#'
#' @examples
#' # Example 1. FDH input-oriented.
#' # Replication of results in Sanei and Mamizadeh Chatghayeb (2013)
#' data("Supply_Chain")
#' data_fdh1 <- make_deadata(Supply_Chain,
#' inputs = 2:4,
#' outputs = 5:6)
#' result <- model_fdh(data_fdh1) # by default orientation = "io"
#' efficiencies(result)
#'
#' # Example 2. FDH output-oriented.
#' # Replication of results in Sanei and Mamizadeh Chatghayeb (2013)
#' data("Supply_Chain")
#' data_fdh2 <- make_deadata(Supply_Chain,
#' inputs = 5:6,
#' outputs = 7:8)
#' result2 <- model_fdh(data_fdh2,
#' orientation = "oo")
#' efficiencies(result2)
#'
#' @import lpSolve
#'
#' @export
model_fdh <-
function(datadea,
fdh_modelname = c("basic"), # It can be generalized to other models in the future
...) {
# Cheking whether datadea is of class "deadata" or not...
if (!is.deadata(datadea)) {
stop("Data should be of class deadata. Run make_deadata function first!")
}
# Checking modelname
fdh_modelname <- tolower(fdh_modelname)
fdh_modelname <- match.arg(fdh_modelname)
model_modelname <- paste("model", fdh_modelname, sep = "_")
optlist <- list(...)
if ("rts" %in% names(optlist)) {
#optlist$rts <- "vrs" # lpSolve and Rglpk do not work properly with binary variables
optlist$rts <- "crs"
}
optlist$returnlp <- TRUE
optlist$datadea <- datadea
deasol <- do.call(model_modelname,
optlist)
if (!is.null(datadea$ud_inputs) || !is.null(datadea$ud_outputs)) {
if (fdh_modelname == "basic") {
res_und <- undesirable_basic(datadea = datadea, vtrans_i = deasol$vtrans_i,
vtrans_o = deasol$vtrans_o)
datadea <- res_und$u_datadea
}
}
input <- datadea$input
output <- datadea$output
dmunames <- datadea$dmunames
inputnames <- rownames(input)
outputnames <- rownames(output)
ni <- nrow(input) # number of inputs
no <- nrow(output) # number of outputs
dmu_ref <- deasol$dmu_ref
ndr <- length(dmu_ref)
inputref <- matrix(input[, dmu_ref], nrow = ni)
outputref <- matrix(output[, dmu_ref], nrow = no)
ncd_inputs <- c(datadea$nc_inputs, datadea$nd_inputs)
ncd_outputs <- c(datadea$nc_outputs, datadea$nd_outputs)
dmu_eval <- deasol$dmu_eval
nde <- length(dmu_eval)
DMU <- vector(mode = "list", length = nde)
names(DMU) <- dmunames[dmu_eval]
binary.vec = (2 : (ndr + 1)) # lambdas. This is valid for model_basic
for (i in 1:nde) {
ii <- dmu_eval[i]
obj <- deasol$DMU[[i]]$direction
f.obj <- deasol$DMU[[i]]$objective.in
f.con <- deasol$DMU[[i]]$const.mat
f.dir <- deasol$DMU[[i]]$const.dir
f.rhs <- deasol$DMU[[i]]$const.rhs
# lpSolve and Rglpk do not work properly with binary variables
# res <- lp(obj, f.obj, f.con, f.dir, f.rhs, binary.vec = binary.vec)$solution
# kkmax <- (obj == "max")
# res <- Rglpk_solve_LP(obj = f.obj, mat = f.con, dir = f.dir, rhs = f.rhs,
# types = c("C", rep("B", ndr)), max = kkmax)$solution
### Alternative ###
scoreskk <- rep(NA, ndr)
f.objkk <- f.obj[1]
f.conkk <- matrix(f.con[, 1], ncol = 1)
for (j in 1:ndr) {
f.rhskk <- f.rhs - f.con[, j + 1]
reskk <- lp(obj, f.objkk, f.conkk, f.dir, f.rhskk)
if (reskk$status == 0) {
scoreskk[j] <- reskk$solution[1]
}
}
res <- rep(0, ndr + 1)
if (obj == "min") {
res[1] <- min(scoreskk, na.rm = TRUE)
} else {
res[1] <- max(scoreskk, na.rm = TRUE)
}
jkk <- which(scoreskk == res[1])[1]
res[jkk + 1] <- 1
### End Alternative ###
if (fdh_modelname == "basic") { # Prepared for generalization to other models
lambda <- res[binary.vec]
names(lambda) <- dmunames[dmu_ref]
target_input <- as.vector(inputref %*% lambda)
names(target_input) <- inputnames
target_output <- as.vector(outputref %*% lambda)
names(target_output) <- outputnames
if (deasol$orientation == "io") {
efficiency <- res[1]
slack_input <- efficiency * input[, ii] - target_input
slack_input[ncd_inputs] <- input[, ii] - target_input
names(slack_input) <- inputnames
slack_output <- target_output - output[, ii]
names(slack_output) <- outputnames
target_input[datadea$ud_inputs] <- deasol$vtrans_i - target_input[datadea$ud_inputs]
target_output[datadea$ud_outputs] <- deasol$vtrans_o - target_output[datadea$ud_outputs]
DMU[[i]] <- list(efficiency = efficiency,
lambda = lambda,
slack_input = slack_input, slack_output = slack_output,
target_input = target_input, target_output = target_output)
} else if (deasol$orientation == "oo") {
efficiency <- res[1]
slack_input <- input[, ii] - target_input
names(slack_input) <- inputnames
slack_output <- target_output - efficiency * output[, ii]
slack_output[ncd_outputs] <- target_output - output[, ii]
names(slack_output) <- outputnames
target_input[datadea$ud_inputs] <- deasol$vtrans_i - target_input[datadea$ud_inputs]
target_output[datadea$ud_outputs] <- deasol$vtrans_o - target_output[datadea$ud_outputs]
DMU[[i]] <- list(efficiency = efficiency,
lambda = lambda,
slack_input = slack_input, slack_output = slack_output,
target_input = target_input, target_output = target_output)
} else {
beta <- res[1]
slack_input <- input[, ii] - beta * deasol$orientation_param$dir_input[, ii] - target_input
slack_input[ncd_inputs] <- input[, ii] - target_input
names(slack_input) <- inputnames
slack_output <- target_output - output[, ii] - beta * deasol$orientation_param$dir_output[, ii]
slack_output[ncd_outputs] <- target_output - output[, ii]
names(slack_output) <- outputnames
target_input[datadea$ud_inputs] <- deasol$vtrans_i - target_input[datadea$ud_inputs]
target_output[datadea$ud_outputs] <- deasol$vtrans_o - target_output[datadea$ud_outputs]
DMU[[i]] <- list(beta = beta,
lambda = lambda,
slack_input = slack_input, slack_output = slack_output,
target_input = target_input, target_output = target_output)
}
}
}
deaOutput <- deasol
deaOutput$modelname <- paste("fdh", deasol$modelname, sep = "_")
deaOutput$DMU <- DMU
return(deaOutput)
}
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