Forum: help

Optimization in R [ Reply ]
By: Rodrigo Rodriguez on 2017-06-06 00:00

Dear R-users,

I hope this message finds you well.
I am using nlminb command to solve an following optimization problem:

#----------------------------------------------------------

# Known quantities
a <- 100
b <- 0.5
Ce <- 0.2
d <- 0.01
p <- 5
k1 <- 10
k2 <- 5
MinSales <- 0
MaxSales <- 1500
TMax <- 50

# Function to optimize
Profit <- function(x){

if(length(x) != TMax) stop("Length of x must be equal to TMax")

Sales <- 0; cont <- 1
repeat{
Sales <- c(Sales, (a * x[cont] + d * sum(Sales)) * b * exp(- Ce * p))
if(cont > TMax) break
if(sum(Sales) > MaxSales) break
cont <- cont + 1
}
Sales <- Sales[-c(1, length(Sales))]
if(cont - 1 < TMax)
for(i in cont:TMax){
x[i] <- 0
Sales <- c(Sales, 0)
}

sum(p * Sales - (k1 * x + k2/2 * x^2))

}
MinusProfit <- function(x) -Profit(x)

MaxProfit <- nlminb(start = rep(0, TMax),
objective = MinusProfit,
lower = rep(0, TMax))

#----------------------------------------------------------

The Profit function allows the user to implement a diffusion model (i.e., the Sales vector) evaluated in t, with t in {0, 1, ..., TMax} and Sales(0) = 0. The vector Sales depends on the decision variables (x in Profit function) and this vector is constrained such that the cumulative sales cannot be higher than MaxSales. If t* is the time when the cumulative sales reach MaxSales, then Sales(t) = 0 for all t in {t* + 1, ..., TMax}. The decision variables form a vector of length TMax that represent advertising rates at times 0, 1, 2, ..., TMax - 1.

I was wondering if you could tell me how to incorporate the following additional constraint into this optimization problem to find the advertising rates: the advertising rate must be zero for all t in {t*, t*+1, ..., TMax - 1}, where t* was mentioned before. I will appreciate any suggestion.

Thank you.