R/revenue_max.R

In inventorize: Inventory Analytics, Pricing and Markdowns

#' revenue_max
#'
#' maxmizing revenue based on chage in price and elasticity.
#'
#'#' This function is helpful to determine the elasticity of a product with effect to price change, the figure could be negative as the change is price is negative.
#' it translates as for each unit percentage  decrease in price , this much is ecpected precentage of  increase of sales. condition must be that Price in period one was more than proce
#' in period 2 and sales in period two was more than sales in period 1.  a proposed optimum  price is given to period 3 which is future period to maxmize revenue.
#'
#' @param  salesP1, integer, unit sales in period 1.
#' @param salesP2 integer unit sales in period 2.
#' @param priceP1 numeric,  average price of sku in period 1.
#'
#' @param  priceP2 average price of sku in period 2.
#'
#' @param na.rm logical with a default of TRUE
#' @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 qpois
#' @importFrom stats sd
#' @return the elasticity ratio in unit sales, the -ve number represents the increase in sales for each decrease of unit currency.
#' @author "haytham omar  email: <haytham@rescaleanalytics.com>"
#' @export
#' @examples
#' revenue_max(salesP1=50,salesP2=100,priceP1=6,priceP2=4)




revenue_max<- function(salesP1,salesP2,priceP1,priceP2,na.rm=TRUE){


  revenueP3<- function(discount,elasticity,salesP1,salesP2,priceP1,priceP2){
  revenueP1<- salesP1*priceP1
  revenueP2<- salesP2*priceP2
  newprice<- priceP2*(1+discount)
  change<- newprice-priceP2
  salesP3<- salesP2*(1+elasticity*discount)
  x<-salesP3*newprice
  return(x)
  }

 elasticity<- ((salesP2-salesP1)/salesP1)/((priceP2-priceP1)/priceP1)
opt<-optimize(revenueP3,c(-2,2),tol = 0.0001,maximum = TRUE,elasticity=elasticity,salesP1=salesP1,salesP2=salesP2,priceP1=priceP1,priceP2=priceP2)
revenueP1<- salesP1*priceP1
revenueP2<- salesP2*priceP2
proposed_discount<-opt$maximum
projected_revenue<-opt$objective
newprice<-priceP2*(1+proposed_discount)
changeinprice<-newprice-priceP2
salesP3<- salesP2*(1+elasticity*proposed_discount)
revenue_max<-data.frame(salesP1=salesP1,salesP2=salesP2,priceP1=priceP1,priceP2=priceP2,revenuep1=revenueP1,revenuep2=revenueP2,elasticity=elasticity,proposed_discount=proposed_discount,changeinprice=changeinprice,newprice=newprice,
                        change_in_sales=salesP3-salesP2,salesP3=salesP3,revenueP3=projected_revenue)
return(revenue_max)
}