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#' @title Safety stock over lead-time
#'
#' @description
#' \code{SSL} computes the safety stock level over lead-time for three forecasting
#' methods: Minimum Mean Square Error (MMSE), Simple Moving Average (SMA) and
#' Exponential Smoothing (ES) when the demand follows a stationary AR(1) stochastic process.
#'
#' @param method Character string specifing which method to use
#' @param phi A vector of autoregressive parameters
#' @param L A positive lead-time
#' @param p Order to be used in the SMA method
#' @param alpha Smoothing factor to be used in the ES method (0 < alpha < 1)
#' @param SL Service level
#'
#' @return Safety stock level over lead-time
#'
#' @details
#' The \code{SSL} function has been deprecated and will be made defunct; use
#' the bullwhipgame package.
#'
#' @examples
#'
#' \dontrun{
#'
#' SSL("MMSE",0.15,2,4,0.7,0.95)
#'
#' SSL("SMA",0.15,2,4,0.7,0.95)
#'
#' SSL("ES",0.15,2,4,0.7,0.95)
#' }
#'
#' @name SSL-deprecated
#' @usage SSL(method, phi, L, p, alpha, SL)
#' @seealso \code{\link{pkgSCperf-deprecated}}
#' @keywords internal
NULL
#' @rdname pkgSCperf-deprecated
#' @details
#' The \code{SSL} function has been deprecated and will be made defunct; use
#' the bullwhipgame package.
#'
#' @export
#'
SSL=function(method=c("MMSE","SMA","ES"),phi,L,p,alpha,SL)
{ .Deprecated("bullwhipgame", package = "pkgSCperf")
z<- qnorm(SL, mean = 0, sd = 1)
if (method=="MMSE"){ #Calculating the variance during the LT
arma1<-ARMAtoMA(ar=phi, ma=0,L);
arma2<-c(1,arma1);
totalLT <- 0
for (i in 1:L)
{ valsumLT<- (sum(arma2[1:i]))^2;
totalLT<- totalLT + valsumLT;
}
VarLT<-totalLT;
return(z*(VarLT^0.5))
}
else{ if (method=="SMA"){var_SMA<-(1/(1-phi^2))*(L*(1+phi)/(1-phi)-2*phi*(1-phi^L)/(1-phi)^2+((L/p)^2)*(p*(1+phi)/(1-phi)-2*phi*(1-phi^p)/(1-phi)^2)-2*(L/p)*(phi*(1-phi^L)*(1-phi^p)/(1-phi)^2))
return(z*(var_SMA^0.5))
}
else{ if (method=="ES"){var_ES<-(1/(1-phi^2))*(L*(1+phi)/(1-phi)-2*phi*(1-phi^L)/(1-phi)^2+((alpha*L)^2)*(1+(1-alpha)*phi)/(alpha*(2-alpha)*(1-(1-alpha)*phi))-2*alpha*L*(phi-phi^(L+1))/((1-phi)*(1-(1-alpha)*phi)))
return(z*(var_ES^0.5))
}
else {return("error")
}
}
}
}
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