require(ZINO)

library(gamlss)
library(markovchain)

sample <- 30 # DPUT sample initial in each different scenario
prop <- runif(1, 0, 1) # Proportion of zeros in the sample of DPUT in each scenario
x.zino <- rZINO(n = sample, mu = 12, sigma = 1, nu = prop) # random sample ZINO
state <- ifelse(x.zino == 0, "zero", "nonzero") # State definition
T <- markovchainFit(data = state, confidencelevel = 0.95)$estimate@transitionMatrix # Transition matrix
G <- rmarkovchain(
  n = 200,
  object = new("markovchain", transitionMatrix = T)
) # Generate simulated state DPUT
A <- replace(G, G == "nonzero", rNO(200, 12, 1)) # replace non-zero values for simulated values normal
k <- as.numeric(replace(A, A == "zero", 0)) # replace zeros and make numeric, DPUT
# considering lead time=2
remDLT <- matrix(k, nrow = 2) # Group DPUTs during the defined lead time
DLT <- remDLT[1, ] + remDLT[2, ] # Jitter lead time demand (LTD)
nudlt <- 1 - length(subset(DLT, DLT > 0)) / length(DLT) # Proportion of zeros in the jitter of LTD in each scenario