minimize. ECH

subject to. ATS1 > 200

and         ATS2 < 8

Ech.Xbar <- function(x, lambda=0.01, delta=0.5, C0=NULL, C1=NULL, Yr=200,
                     W=150, a=1, b=0.2, e=0.275, T0=5.5, T1=3.5, T2=8, d1=1, d2=0) {

  n <- x[1]; h <- x[2], k <- x[3];
  delta.std<-delta*sqrt(n)
  ARL1 <- 1/(2 * pnorm(-L))
  ARL2 <- 1/(1 – (pnorm(L - delta.std) - pnorm(-L - delta.std)))
  ATS1 <- h*ARL1   # **constraint 1**
  ATS2 <- h*ARL2   # **constraint 2**
  s <- exp(-lambda*h)/(1-exp(-lambda*h))
  tau <- (1-(1+lambda*h)*exp(-lambda*h))/(lambda*(1-exp(-lambda*h)))
  ET <- 1/lambda+(1-d1)*s*T0/ARL1 + h*(ARL2)-tau + e*n+T1+T2
  EC <-C0/lambda+C1*(A2+( e*n+d1*T1+d2*T2))
       +(a+b*n)*s+(a+b*n)*(ARL2+( e*n+d1*T1+d2*T2)/h)
       +s*Yr/ARL1 + W
  ECH <- EC/ET
  return(ECH)
}

library(GenSA)

out <- GenSA(lower = c(0,0,1), upper = c(5,5,30), fn = Ech.Xbar, C0=100, C1=250,
control=list(max.call=200000))
out[c("value","par","counts")]

ATS1.2 <- function(n,h,k, lambda=0.01, delta=0.5, C0=NULL, C1=NULL, Yr=200,
                   W=150, a=1, b=0.2, e=0.275, T0=5.5, T1=3.5, T2=8, d1=1, d2=0) {
  delta.std<-delta*sqrt(n)
  ARL1 <- 1/(2 * pnorm(-k))
  ARL2 <- 1/(1 - (pnorm(k - delta.std) - pnorm(-k - delta.std)))
  ATS1 <- h*ARL1   # constraint 1
  ATS2 <- h*ARL2   # constraint 2
  return(c(ATS1, ATS2))
}

ATS1.2(out$par[1], out$par[2], out$par[3], C0=100, C1=250)