#' @name TPP.NW
#' @rdname TPP.NW
#' @title Transportation-Problem -- North-West-Corner-Rule
#'
#' @description Calculates the Transportationplan.
#' @param object Object of Type \code{\link{GeoSituation}}
#' @param ... \emph{Optional Parameters} See Below.
#'
#' @section Optional Parameters (\code{...}):
#' \subsection{used by \code{\link{TPP.NW}}}{
#' \describe{
#' \item{log}{\code{"logical"} Optional Parameter. Indicating, if the calculation should be logged to console. Default is \code{FALSE}.}
#' }
#' }
#' \subsection{Forwarded to the follwowing functions}{
#' You may want to check these functions for any other optional parameters.
#' \itemize{
#' \item{\code{\link{getInitialMatrix}}}
#' \item{\code{\link{TPP.Prepare}}}
#' }
#' }
#' @keywords OR Transportation-Problem TPP North-West-Corner-Rule
#' @export
#' @references Domschke
#' @seealso \code{\link{GeoSituation}}, \code{\link{Node}}, \code{\link{TPP.NW}}, \code{\link{TPP.CMM}}, \code{\link{TPP.MMM}}, \code{\link{TPP.SteppingStone}}, \code{\link{TPP.MODI}}
#' @examples
#' # demo(HNUTPP03)
#' @note
#' for citing use: Felix Lindemann (2014). HNUORTools: Operations Research Tools. R package version 1.1-0. \url{http://felixlindemann.github.io/HNUORTools/}.
#'
#' @author Dipl. Kfm. Felix Lindemann \email{felix.lindemann@@hs-neu-ulm.de}
#'
#' Wissenschaftlicher Mitarbeiter
#' Kompetenzzentrum Logistik
#' Buro ZWEI, 17
#'
#' Hochschule fur angewandte Wissenschaften
#' Fachhochschule Neu-Ulm | Neu-Ulm University
#' Wileystr. 1
#'
#' D-89231 Neu-Ulm
#'
#'
#' Phone +49(0)731-9762-1437
#' Web \url{www.hs-neu-ulm.de/felix-lindemann/}
#' \url{http://felixlindemann.blogspot.de}
setGeneric("TPP.NW", function(object,...) standardGeneric("TPP.NW") )
#' @aliases TPP.NW,GeoSituation-method
#' @rdname TPP.NW
setMethod("TPP.NW", signature(object="GeoSituation"),
function(object,...){
li<-list(...)
object <- TPP.Prepare(object, ...) # repair degenerated if needed
x <- getInitialMatrix(object, initialvalue = 0, ...) # set initial Transportation Plan
#set supply and demand
supply <- object$warehouses$supply
demand <- object$customers$demand
if(sum(supply) != sum(demand)) stop("This alg. can be used for non-degenerated solutions only: The Sums of warehouse$supply and customer$demand are not equal.")
for(i in (1:length(object$warehouses))){
for(j in (1:length(object$customers))){
x[i,j] <- min(c(supply[i],demand[j]))
supply[i] <- supply[i] - x[i,j]
demand[j] <- demand[j] - x[i,j]
}
}
object$tpp$x <- x
# check for M+N-1 variables.
TPP.CheckValidTransportationPlan(object)
return(object)
}
)
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