Nothing
R/sim_min_q.R
In inventorize: Inventory Analytics, Pricing and Markdowns
#' sim_min_Q
#'
#' 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 an 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 or a poisson distribution, also min can be set manually.
#' Q (fixed quantity) is ordered whenever inventory position reaches min
#' @param demand A vector of demand in N time periods.
#' @param mean average demand in N time periods.default is FALSE and is automatically calculated. otherwise set manually.
#' @param sd standard deviation in N time periods.default is FALSE and is automatically calculated. otherwise set manually.
#' @param leadtime lead time from order to arrival
#' @param service_level cycle service level requested
#' @param initial_inventory_level integer,Default is False and simulation starts with min as inventory level
#' @param min integer,Default is False and min is calculated based on mean,demand and leadtime unless set manually
#' @param Quantity Fixed order quantity to be ordered at min
#' @param shortage_cost numeric,Default is FALSE shortage cost per unit of sales lost
#' @param inventory_cost numeric,Default is FALSE inventory cost per unit.
#' @param ordering_cost numeric,Default is FALSE ordering cost for every time an order is made.
#' @param distribution distribution to calculate safety stock based on demand distribution, current choices are 'normal'
#' 'poisson','gamma' and negative binomial 'nbinom'
#' @param recalculate Logical, if true the mean and sd is recalculated every period from first period to t,default is FALSE .
#' @param recalculate_windows integer, the min mean and sd windows to recalculate , for example if it is set to 4 mean and sd
#' is calculated from t to t-4,,default is FALSE, if TRUE, recalculate has to be TRUE Also.
#' @param plot Logical, Default is False, if true a plot is generated
#' @param Backlogs Logical, Default is False, if true inventory level accounts for previous lost orders
#' is calculated from t to t-4,,default is FALSE .
#' @importFrom plotly ggplotly
#' @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
#' @importFrom stats qgamma
#' @return a list of two date frames, the simulation and the metrics.
#' @author "haytham omar email: <haytham@rescaleanalytics.com>"
#' @export
#' @examples
#'sim_min_Q(demand = rpois(90,7),leadtime = 5,service_level = 0.95,Quantity = 80,
#'recalculate = TRUE,distribution = 'normal',recalculate_windows = 5,Backlogs=FALSE)
sim_min_Q<- function (demand, mean=FALSE, sd=FALSE, leadtime, service_level, initial_inventory_level = FALSE, min= FALSE,
Quantity, shortage_cost = FALSE, inventory_cost = FALSE,
ordering_cost = FALSE,distribution= 'normal',recalculate=FALSE,recalculate_windows=FALSE,plot=FALSE,
Backlogs=FALSE)
{
inventory_level<-NULL
period<-NULL
L = leadtime
Q = Quantity
inventory_level<-NULL
period<-NULL
ComputeNBDoverR <- function(x, mu_R, sigm_R){
if(sigm_R^2 <= mu_R){
sigm_R<- 1.05 * sqrt(mu_R)
}
z <- (sigm_R ^ 2) / mu_R
if (z > 1){
P0 <- (1 / z) ^ (mu_R / (z - 1))
if (x == 0){
PX <- P0
} else {
PX <- P0
for (i in 1:x){
PX = (((mu_R / (z - 1)) + i - 1) / i) * ((z - 1) / z) * PX
}
}
}
return(PX)}
if(recalculate_windows==FALSE & recalculate !=FALSE){
mean = c(rep(NA,length(demand)+1))
sd= c(rep(NA,length(demand)+1))
max= c(rep(NA,length(demand)+1))
min= c(rep(NA,length(demand)+1))
mean[1]<- demand[1]
sd[1]<- sd(demand)
for (i in 2: length(mean)){
mean[i]= mean(demand[1:i],na.rm=TRUE)
sd[i]= sd(demand[1:i],na.rm=TRUE)
if(distribution== 'normal'){
max[i] = round((mean[i] * (leadtime)) + ((sd[i] * sqrt(leadtime)) *
qnorm(service_level)), digits = 0)
} else if (distribution== 'poisson') {
max[i] = qpois(service_level,mean[i]*(leadtime))
} else if( distribution== 'gamma'){
dl= mean[i]*(leadtime)
sigmadl= sd[i] * sqrt(leadtime)
alpha= dl ^2 / sigmadl^2
beta <- dl / sigmadl^2
max[i]<- round(qgamma(service_level,alpha,beta))
} else if (distribution== 'nbinom'){
dl= mean[i]*(leadtime)
sigmadl= sd[i] * sqrt(leadtime)
x <- 0
supp <- ComputeNBDoverR(x, dl, sigmadl)
while (supp < service_level){
x <- x + 1
supp <- supp + ComputeNBDoverR(x, dl, sigmadl)
}
max[i]<- x
}
}
min <- max
min[1]= max[2]
} else if ( recalculate_windows !=FALSE & recalculate != FALSE) {
mean = c(rep(NA,length(demand)+1))
sd= c(rep(NA,length(demand)+1))
max= c(rep(NA,length(demand)+1))
min= c(rep(NA,length(demand)+1))
mean[1]<- demand[1]
sd[1]<- sd(demand)
for (i in 2: length(mean)){
mean[i]= mean(demand[max((i- recalculate_windows),1):(i-1)],na.rm=TRUE)
sd[i]= ifelse(is.na(sd(demand[max((i- recalculate_windows),1):(i-1)],na.rm=TRUE)),sd[i-1],sd(demand[max((i- recalculate_windows),1):(i-1)],na.rm=TRUE))
if(distribution== 'normal'){
max[i] = round((mean[i] * (leadtime)) + ((sd[i] * sqrt(leadtime)) *
qnorm(service_level)), digits = 0)
} else if (distribution== 'poisson') {
max[i] = qpois(service_level,mean[i]*(leadtime))
} else if( distribution== 'gamma'){
dl= mean[i]*(leadtime)
sigmadl= sd[i] * sqrt(leadtime)
alpha= dl ^2 / sigmadl^2
beta <- dl / sigmadl^2
max[i]<- round(qgamma(service_level,alpha,beta))
} else if (distribution== 'nbinom'){
dl= mean[i]*(leadtime)
sigmadl= sd[i] * sqrt(leadtime)
x <- 0
supp <- ComputeNBDoverR(x, dl, sigmadl)
while (supp < service_level){
x <- x + 1
supp <- supp + ComputeNBDoverR(x, dl, sigmadl)
}
max[i]<- x
}
}
min[1]= max[2]
for (i in 2: length(max)){
min[i]<- ifelse(i %% recalculate_windows !=0,min[i-1],max[i])
}
}
N= length(demand)
if(mean[1]== FALSE & recalculate==FALSE){
mean= mean(demand)
} else if (mean[1]!= FALSE & recalculate==FALSE) {
mean=mean
}
if(sd[1]== FALSE & recalculate==FALSE){
sd= sd(demand)
} else if (sd[1]!= FALSE & recalculate==FALSE) {
sd =sd
}
if (min[1] != FALSE& recalculate==FALSE){
min= min
min = rep(min, N + 1)
} else if(distribution== 'normal'& recalculate==FALSE){
min = round((mean * (leadtime)) + ((sd * sqrt(leadtime)) *
qnorm(service_level)), digits = 0)
min = rep(min, N + 1)
} else if (distribution== 'poisson' & recalculate==FALSE){
min = qpois(service_level,mean*(leadtime))
min = rep(min, N + 1)
} else if (distribution== 'gamma' & recalculate==FALSE){
dl= mean*(leadtime)
sigmadl= sd * sqrt(leadtime)
alpha= dl ^2 / sigmadl^2
beta <- dl / sigmadl^2
min <- round(qgamma(service_level,alpha,beta))
min = rep(min, N + 1)
} else if (distribution== 'nbinom' & recalculate==FALSE){
dl= mean*(leadtime)
sigmadl= sd * sqrt(leadtime)
x <- 0
supp <- ComputeNBDoverR(x, dl, sigmadl)
while (supp < service_level){
x <- x + 1
supp <- supp + ComputeNBDoverR(x, dl, sigmadl)
}
min<- round(x)
min = rep(min, N + 1)
}
saftey_stock= min- (mean*(leadtime))
classfication <- function(demand){
intervals <- function(x){
y<-c()
k<-1
counter<-0
for (tmp in (1:length(x))){
if(x[tmp]==0){
counter<-counter+1
}else{
k<-k+1
y[k]<-counter
counter<-1
}
}
y<-y[y>0]
y[is.na(y)]<-1
y
}
demand1 <- function(x){
y<-x[x!=0]
y
}
D <- demand1(demand)
ADI <- mean(intervals(demand))
CV2 <- (sd(D)/mean(D))^2
if (ADI > (4/3)){
if (CV2 > 0.5){
Type <- "Lumpy"
}else{
Type <- "Intermittent"
}
}else{
if (CV2 > 0.5){
Type <- "Erratic"
}else{
Type <- "Smooth"
}
}
return(data.frame('Type'=Type))
}
demand_class= classfication(demand)
L= leadtime
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)
order[1] = 0
demand <- c(0, demand)
if(initial_inventory_level==FALSE){
IP[1] = I[1] = min[1]
} else {
IP[1] = I[1] = initial_inventory_level
}
if(Backlogs != TRUE){
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[t])
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[t])
IP[t] = IP[t - 1] + order[t] - sales[t]
recieved[t] <- order[t - L]
}
} else {
backlogs = rep(NA, N + 1)
comu_backlogs = rep(NA, N + 1)
expected=rep(NA, N + 1)
order[1] = 0
sales[1] <- 0
expected[1]<- 0
backlogs[1]<- 0
comu_backlogs[1]<-0
for (t in 2:(L)) {
sales[t] <- min(demand[t], I[t - 1])
I[t] <- ifelse(I[t-1]-demand[t]- comu_backlogs[t-1]>0,I[t-1]-
demand[t]-comu_backlogs[t-1],0)
order[t] <- Q * (IP[t - 1] <= min[t])
expected[t]<- expected[t-1]+ order[t-1]
backlogs[t]<- ifelse(I[t-1]< demand[t],abs(I[t-1]-demand[t]),0)
comu_backlogs[t]<- ifelse(backlogs[t]>I[t-1] | backlogs[t]>0,comu_backlogs[t-1]+backlogs[t],0)
IP[t] <- I[t]+ expected[t]- comu_backlogs[t]
}
for (t in ((L+1):N)) {
sales[t] <- min(demand[t], I[t - 1])
recieved[t] <- order[t - L]
I[t] <- ifelse(I[t-1]-demand[t]+recieved[t]- comu_backlogs[t-1]>0,I[t-1]-
demand[t]+recieved[t]-comu_backlogs[t-1],0)
order[t] <- Q * (IP[t - 1] <= min[t])
expected[t]<- expected[t-1]+ order[t-1]- recieved[t]
backlogs[t]<- ifelse(I[t-1]< demand[t],abs(I[t-1]-demand[t]),0)
comu_backlogs[t]<- ifelse(backlogs[t]>I[t-1] | backlogs[t]>0,comu_backlogs[t-1]+backlogs[t],0)
IP[t] <- I[t]+ expected[t]- comu_backlogs[t]
}
}
if(Backlogs != TRUE){
data <- data.frame('period' = seq(1:(N + 1)), demand = demand,
sales = sales, 'inventory_level' = I, inventory_position = IP,
min = min, order = order, recieved = recieved)
data$lost_order <- data$demand - data$sales
} else {
data <- data.frame('period' = seq(1:(N + 1)), demand = demand,
sales = sales, 'inventory_level' = I, inventory_position = IP,
min = min, order = order, recieved = recieved,comu_backlogs=comu_backlogs)
data$lost_order <- data$demand - data$sales
}
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, average_inventory_level = mean(data$inventory_level, na.rm = TRUE),total_orders= length(which(data$order > 0)),ordering_cost = length(which(data$order > 0)) * ordering_cost,
total_lost_sales = sum(data$lost_order, na.rm = TRUE), average_ordering_quantity= mean(order[order>0],na.rm = TRUE),ordering_interval= paste0(round(length(demand)/length(which(data$order > 0)),2),'_periods'),
Item_fill_rate = 1 - (sum(data$lost_order, na.rm = TRUE)/sum(demand[1:(length(demand) - 1)])),
cycle_service_level = 1 -(length(which(data$lost_order > 0))/(length(demand) - 1)), saftey_stock = mean(saftey_stock,na.rm = TRUE),
average_sales= mean(sales,na.rm = TRUE))
metrics$"average_flow_time(throughput)"= metrics$average_inventory_level/metrics$average_sales
metrics$demand_class<- demand_class$Type
if(plot== TRUE){
suppressWarnings(
print(plotly::ggplotly(data[is.na(data[,c('sales','demand','order')])==FALSE,] %>% ggplot(aes(x= period,y= demand,color="demand"))+geom_line()+
geom_line(aes(y=sales,color="sales"))+
geom_point(aes(y=inventory_level,color="inventory level"))+
theme_minimal()+geom_line(aes(y=order,color="order"))+ggtitle("Min Q policy")))
)
}
return(list(simu_data = data, metrics = metrics))
}
sim_min_Q(demand = rpois(90,7),leadtime = 5,service_level = 0.95,Quantity = 80,
distribution = 'gamma')
demand = rpois(90,7)
leadtime = 5
service_level = 0.95
uantity = 80
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#' sim_min_Q
#'
#' 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 an 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 or a poisson distribution, also min can be set manually.
#' Q (fixed quantity) is ordered whenever inventory position reaches min
#' @param demand A vector of demand in N time periods.
#' @param mean average demand in N time periods.default is FALSE and is automatically calculated. otherwise set manually.
#' @param sd standard deviation in N time periods.default is FALSE and is automatically calculated. otherwise set manually.
#' @param leadtime lead time from order to arrival
#' @param service_level cycle service level requested
#' @param initial_inventory_level integer,Default is False and simulation starts with min as inventory level
#' @param min integer,Default is False and min is calculated based on mean,demand and leadtime unless set manually
#' @param Quantity Fixed order quantity to be ordered at min
#' @param shortage_cost numeric,Default is FALSE shortage cost per unit of sales lost
#' @param inventory_cost numeric,Default is FALSE inventory cost per unit.
#' @param ordering_cost numeric,Default is FALSE ordering cost for every time an order is made.
#' @param distribution distribution to calculate safety stock based on demand distribution, current choices are 'normal'
#' 'poisson','gamma' and negative binomial 'nbinom'
#' @param recalculate Logical, if true the mean and sd is recalculated every period from first period to t,default is FALSE .
#' @param recalculate_windows integer, the min mean and sd windows to recalculate , for example if it is set to 4 mean and sd
#' is calculated from t to t-4,,default is FALSE, if TRUE, recalculate has to be TRUE Also.
#' @param plot Logical, Default is False, if true a plot is generated
#' @param Backlogs Logical, Default is False, if true inventory level accounts for previous lost orders
#' is calculated from t to t-4,,default is FALSE .
#' @importFrom plotly ggplotly
#' @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
#' @importFrom stats qgamma
#' @return a list of two date frames, the simulation and the metrics.
#' @author "haytham omar email: <haytham@rescaleanalytics.com>"
#' @export
#' @examples
#'sim_min_Q(demand = rpois(90,7),leadtime = 5,service_level = 0.95,Quantity = 80,
#'recalculate = TRUE,distribution = 'normal',recalculate_windows = 5,Backlogs=FALSE)
sim_min_Q<- function (demand, mean=FALSE, sd=FALSE, leadtime, service_level, initial_inventory_level = FALSE, min= FALSE,
Quantity, shortage_cost = FALSE, inventory_cost = FALSE,
ordering_cost = FALSE,distribution= 'normal',recalculate=FALSE,recalculate_windows=FALSE,plot=FALSE,
Backlogs=FALSE)
{
inventory_level<-NULL
period<-NULL
L = leadtime
Q = Quantity
inventory_level<-NULL
period<-NULL
ComputeNBDoverR <- function(x, mu_R, sigm_R){
if(sigm_R^2 <= mu_R){
sigm_R<- 1.05 * sqrt(mu_R)
}
z <- (sigm_R ^ 2) / mu_R
if (z > 1){
P0 <- (1 / z) ^ (mu_R / (z - 1))
if (x == 0){
PX <- P0
} else {
PX <- P0
for (i in 1:x){
PX = (((mu_R / (z - 1)) + i - 1) / i) * ((z - 1) / z) * PX
}
}
}
return(PX)}
if(recalculate_windows==FALSE & recalculate !=FALSE){
mean = c(rep(NA,length(demand)+1))
sd= c(rep(NA,length(demand)+1))
max= c(rep(NA,length(demand)+1))
min= c(rep(NA,length(demand)+1))
mean[1]<- demand[1]
sd[1]<- sd(demand)
for (i in 2: length(mean)){
mean[i]= mean(demand[1:i],na.rm=TRUE)
sd[i]= sd(demand[1:i],na.rm=TRUE)
if(distribution== 'normal'){
max[i] = round((mean[i] * (leadtime)) + ((sd[i] * sqrt(leadtime)) *
qnorm(service_level)), digits = 0)
} else if (distribution== 'poisson') {
max[i] = qpois(service_level,mean[i]*(leadtime))
} else if( distribution== 'gamma'){
dl= mean[i]*(leadtime)
sigmadl= sd[i] * sqrt(leadtime)
alpha= dl ^2 / sigmadl^2
beta <- dl / sigmadl^2
max[i]<- round(qgamma(service_level,alpha,beta))
} else if (distribution== 'nbinom'){
dl= mean[i]*(leadtime)
sigmadl= sd[i] * sqrt(leadtime)
x <- 0
supp <- ComputeNBDoverR(x, dl, sigmadl)
while (supp < service_level){
x <- x + 1
supp <- supp + ComputeNBDoverR(x, dl, sigmadl)
}
max[i]<- x
}
}
min <- max
min[1]= max[2]
} else if ( recalculate_windows !=FALSE & recalculate != FALSE) {
mean = c(rep(NA,length(demand)+1))
sd= c(rep(NA,length(demand)+1))
max= c(rep(NA,length(demand)+1))
min= c(rep(NA,length(demand)+1))
mean[1]<- demand[1]
sd[1]<- sd(demand)
for (i in 2: length(mean)){
mean[i]= mean(demand[max((i- recalculate_windows),1):(i-1)],na.rm=TRUE)
sd[i]= ifelse(is.na(sd(demand[max((i- recalculate_windows),1):(i-1)],na.rm=TRUE)),sd[i-1],sd(demand[max((i- recalculate_windows),1):(i-1)],na.rm=TRUE))
if(distribution== 'normal'){
max[i] = round((mean[i] * (leadtime)) + ((sd[i] * sqrt(leadtime)) *
qnorm(service_level)), digits = 0)
} else if (distribution== 'poisson') {
max[i] = qpois(service_level,mean[i]*(leadtime))
} else if( distribution== 'gamma'){
dl= mean[i]*(leadtime)
sigmadl= sd[i] * sqrt(leadtime)
alpha= dl ^2 / sigmadl^2
beta <- dl / sigmadl^2
max[i]<- round(qgamma(service_level,alpha,beta))
} else if (distribution== 'nbinom'){
dl= mean[i]*(leadtime)
sigmadl= sd[i] * sqrt(leadtime)
x <- 0
supp <- ComputeNBDoverR(x, dl, sigmadl)
while (supp < service_level){
x <- x + 1
supp <- supp + ComputeNBDoverR(x, dl, sigmadl)
}
max[i]<- x
}
}
min[1]= max[2]
for (i in 2: length(max)){
min[i]<- ifelse(i %% recalculate_windows !=0,min[i-1],max[i])
}
}
N= length(demand)
if(mean[1]== FALSE & recalculate==FALSE){
mean= mean(demand)
} else if (mean[1]!= FALSE & recalculate==FALSE) {
mean=mean
}
if(sd[1]== FALSE & recalculate==FALSE){
sd= sd(demand)
} else if (sd[1]!= FALSE & recalculate==FALSE) {
sd =sd
}
if (min[1] != FALSE& recalculate==FALSE){
min= min
min = rep(min, N + 1)
} else if(distribution== 'normal'& recalculate==FALSE){
min = round((mean * (leadtime)) + ((sd * sqrt(leadtime)) *
qnorm(service_level)), digits = 0)
min = rep(min, N + 1)
} else if (distribution== 'poisson' & recalculate==FALSE){
min = qpois(service_level,mean*(leadtime))
min = rep(min, N + 1)
} else if (distribution== 'gamma' & recalculate==FALSE){
dl= mean*(leadtime)
sigmadl= sd * sqrt(leadtime)
alpha= dl ^2 / sigmadl^2
beta <- dl / sigmadl^2
min <- round(qgamma(service_level,alpha,beta))
min = rep(min, N + 1)
} else if (distribution== 'nbinom' & recalculate==FALSE){
dl= mean*(leadtime)
sigmadl= sd * sqrt(leadtime)
x <- 0
supp <- ComputeNBDoverR(x, dl, sigmadl)
while (supp < service_level){
x <- x + 1
supp <- supp + ComputeNBDoverR(x, dl, sigmadl)
}
min<- round(x)
min = rep(min, N + 1)
}
saftey_stock= min- (mean*(leadtime))
classfication <- function(demand){
intervals <- function(x){
y<-c()
k<-1
counter<-0
for (tmp in (1:length(x))){
if(x[tmp]==0){
counter<-counter+1
}else{
k<-k+1
y[k]<-counter
counter<-1
}
}
y<-y[y>0]
y[is.na(y)]<-1
y
}
demand1 <- function(x){
y<-x[x!=0]
y
}
D <- demand1(demand)
ADI <- mean(intervals(demand))
CV2 <- (sd(D)/mean(D))^2
if (ADI > (4/3)){
if (CV2 > 0.5){
Type <- "Lumpy"
}else{
Type <- "Intermittent"
}
}else{
if (CV2 > 0.5){
Type <- "Erratic"
}else{
Type <- "Smooth"
}
}
return(data.frame('Type'=Type))
}
demand_class= classfication(demand)
L= leadtime
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)
order[1] = 0
demand <- c(0, demand)
if(initial_inventory_level==FALSE){
IP[1] = I[1] = min[1]
} else {
IP[1] = I[1] = initial_inventory_level
}
if(Backlogs != TRUE){
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[t])
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[t])
IP[t] = IP[t - 1] + order[t] - sales[t]
recieved[t] <- order[t - L]
}
} else {
backlogs = rep(NA, N + 1)
comu_backlogs = rep(NA, N + 1)
expected=rep(NA, N + 1)
order[1] = 0
sales[1] <- 0
expected[1]<- 0
backlogs[1]<- 0
comu_backlogs[1]<-0
for (t in 2:(L)) {
sales[t] <- min(demand[t], I[t - 1])
I[t] <- ifelse(I[t-1]-demand[t]- comu_backlogs[t-1]>0,I[t-1]-
demand[t]-comu_backlogs[t-1],0)
order[t] <- Q * (IP[t - 1] <= min[t])
expected[t]<- expected[t-1]+ order[t-1]
backlogs[t]<- ifelse(I[t-1]< demand[t],abs(I[t-1]-demand[t]),0)
comu_backlogs[t]<- ifelse(backlogs[t]>I[t-1] | backlogs[t]>0,comu_backlogs[t-1]+backlogs[t],0)
IP[t] <- I[t]+ expected[t]- comu_backlogs[t]
}
for (t in ((L+1):N)) {
sales[t] <- min(demand[t], I[t - 1])
recieved[t] <- order[t - L]
I[t] <- ifelse(I[t-1]-demand[t]+recieved[t]- comu_backlogs[t-1]>0,I[t-1]-
demand[t]+recieved[t]-comu_backlogs[t-1],0)
order[t] <- Q * (IP[t - 1] <= min[t])
expected[t]<- expected[t-1]+ order[t-1]- recieved[t]
backlogs[t]<- ifelse(I[t-1]< demand[t],abs(I[t-1]-demand[t]),0)
comu_backlogs[t]<- ifelse(backlogs[t]>I[t-1] | backlogs[t]>0,comu_backlogs[t-1]+backlogs[t],0)
IP[t] <- I[t]+ expected[t]- comu_backlogs[t]
}
}
if(Backlogs != TRUE){
data <- data.frame('period' = seq(1:(N + 1)), demand = demand,
sales = sales, 'inventory_level' = I, inventory_position = IP,
min = min, order = order, recieved = recieved)
data$lost_order <- data$demand - data$sales
} else {
data <- data.frame('period' = seq(1:(N + 1)), demand = demand,
sales = sales, 'inventory_level' = I, inventory_position = IP,
min = min, order = order, recieved = recieved,comu_backlogs=comu_backlogs)
data$lost_order <- data$demand - data$sales
}
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, average_inventory_level = mean(data$inventory_level, na.rm = TRUE),total_orders= length(which(data$order > 0)),ordering_cost = length(which(data$order > 0)) * ordering_cost,
total_lost_sales = sum(data$lost_order, na.rm = TRUE), average_ordering_quantity= mean(order[order>0],na.rm = TRUE),ordering_interval= paste0(round(length(demand)/length(which(data$order > 0)),2),'_periods'),
Item_fill_rate = 1 - (sum(data$lost_order, na.rm = TRUE)/sum(demand[1:(length(demand) - 1)])),
cycle_service_level = 1 -(length(which(data$lost_order > 0))/(length(demand) - 1)), saftey_stock = mean(saftey_stock,na.rm = TRUE),
average_sales= mean(sales,na.rm = TRUE))
metrics$"average_flow_time(throughput)"= metrics$average_inventory_level/metrics$average_sales
metrics$demand_class<- demand_class$Type
if(plot== TRUE){
suppressWarnings(
print(plotly::ggplotly(data[is.na(data[,c('sales','demand','order')])==FALSE,] %>% ggplot(aes(x= period,y= demand,color="demand"))+geom_line()+
geom_line(aes(y=sales,color="sales"))+
geom_point(aes(y=inventory_level,color="inventory level"))+
theme_minimal()+geom_line(aes(y=order,color="order"))+ggtitle("Min Q policy")))
)
}
return(list(simu_data = data, metrics = metrics))
}
sim_min_Q(demand = rpois(90,7),leadtime = 5,service_level = 0.95,Quantity = 80,
distribution = 'gamma')
demand = rpois(90,7)
leadtime = 5
service_level = 0.95
uantity = 80
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