R/Sim_min_q_normal.R

In inventorize: Inventory Analytics, Pricing and Markdowns

#' sim_min_Q_normal
#'
#' Simulating a Min,Q policy or also calleD S,Q policy,  .
#'
#' The Function takes a demand vector, mean of demand ,sd,lead time and requested service level to simulate and inventory system, 
#' orders are lost if inventory level is less than requested demand, also ordering is made at
#'  day t+1, metrics like item fill rate and cycle service level are calculated. the min is calculated based on a normal distribution.
#' @param  demand  A vector of demand in N time periods.
#' @param  mean  average demand in N time periods.
#' @param sd  standard deviation in N time periods.
#' @param service_level  cycle service level requested
#' @param leadtime  lead time from order to arrival
#' @param shortage_cost  shortage cost per unit of sales lost
#' @param Quantity  Fixed order quantity to be ordered at min
#' @param inventory_cost  inventory cost per unit.
#' @param ordering_cost  ordering cost for every time an order is made.
#' @return a list of two date frames, the simulation and the metrics.
#' @importFrom stats dnorm
#' @importFrom stats lm
#' @importFrom stats median
#' @importFrom stats optim
#' @importFrom stats optimize
#' @importFrom stats pnorm
#' @importFrom stats ppois
#' @importFrom stats predict
#' @importFrom stats qnorm
#' @author "haytham omar  email: <haytham@rescaleanalytics.com>"
#' @export
#' @examples
#' sim_min_Q_normal(demand = rpois(50,8),mean = 5,sd=1,
#' service_level = 0.9,leadtime = 4,
#' shortage_cost = 5, Quantity = 12,inventory_cost = 1,ordering_cost = 50)







sim_min_Q_normal<- function(demand,mean,sd,leadtime,service_level,Quantity,
                        shortage_cost= FALSE,inventory_cost=FALSE,
                        ordering_cost=FALSE){

mu = mean
L = leadtime
Q =Quantity
min= round((mean *leadtime)+ ((sd*sqrt(leadtime))* qnorm(service_level)),digits = 0)
saftey_stock= ((sd*sqrt(leadtime))* qnorm(service_level))                        

  
  
N = length(demand) 

order = rep(NA,N+1) 
I = rep(NA,N+1)
IP = rep(NA,N+1)
sales = rep(NA,N+1)
recieved = rep(NA,N+1)
demand<- c(0,demand)
IP[1] = I[1] = min+Q
order[1]=0
sales[1]<-0
for(t in 2: (L)){
  sales[t] <- min(demand[t], I[t-1])
  I[t] <- I[t-1] - sales[t]
  order[t] <- Q * (IP[t-1] <= min)
  IP[t] <-  IP[t-1] + order[t] - sales[t]

}

for (t in seq((L+1),(N))){
  sales[t] = min(demand[t], I[t-1] + order[t-L])
  I[t] = I[t-1] + order[t-L] - sales[t]
  order[t] = Q * (IP[t-1] <= min)
  IP[t] = IP[t-1] + order[t] - sales[t]
  recieved[t]<- order[t-L]
}

data<-data.frame(period= seq(1:(N+1)),demand=demand,sales=sales,inventory_level=I,
                 inventory_position=IP,s= rep(min,N+1),order= order,
                 recieved=recieved)

data$lost_order<- data$demand -data$sales
message('this function is deprecated, kindly use sim_min_Q() instead')

metrics<- data.frame(shortage_cost= sum(data$lost_order,na.rm = TRUE)*shortage_cost,
                     inventory_cost= sum(data$inventory_level,na.rm = TRUE)*inventory_cost,
                     ordering_cost=length(which(data$order >0))*ordering_cost,
                     average_inventory_level= mean(data$inventory_level,na.rm = TRUE),
                     total_lost_sales= sum(data$lost_order,na.rm = TRUE),
                     Item_fill_rate= 1-(sum(data$lost_order,na.rm = TRUE)/sum(demand[1:(length(demand)-1)])),
                     cycle_service_level= 1-(length(which(data$lost_order >0))/(length(demand)-1))
                     ,saftey_stock=saftey_stock)
     return(list(simu_data=data,metrics=metrics))                

}