ELMSO.fixed {ELMSO}

Fixed ELMSO Function (fixed advertising costs, no cost curve)

Description

This function allows you to allocate budget to a set of websites when cost is fixed at each website based on a matrix of pageviews for those sites.

Usage

ELMSO.fixed(z, CPM, tau = NULL, step = 0.05, size = 100,
  tol = 10^-3, iters = 200)

Arguments

z

An n by p matrix of pageviews

CPM

A p-dimensional vector of the (fixed) CPM values at each website

tau

A p-dimensional vector of total pageviews (in thousands) for each website. Defaults to the total pageviews in the matrix for each website (i.e., assumes z matrix represents all website pageviews) divided by 1000.

step

A value to control the step size of the lambda grid (distance between budget points). Default is 0.05.

size

A value to control the number of lambda values tried (number of budget points). Default is 100.

tol

A value to control the convergence tolerance of the coordinate descent procedure. Default is 10^-3.

iters

A value to control the number of iterations until algorithm should exit if convergence tolerance is not reached. Default is 200.

Value

spend: a matrix of total spend by website at each budget

budget: a vector of budget values

lambda: a vector of lambda values

References

Courtney Paulson, Lan Luo, and Gareth M. James (2018) Efficient Large-Scale Internet Media Selection Optimization for Online Display Advertising. Journal of Marketing Research: August 2018, Vol. 55, No. 4, pp. 489-506.

Examples

z=matrix(round(abs(rnorm(5000,0,0.7))),1000,5)
CPM.fixed=c(3,4,5,6,7)
tau.values=rep(100,5) #Note tau here is in thousands of pageviews

allocation=ELMSO.fixed(z=z,CPM=CPM.fixed,tau=tau.values)
allocation$spend
allocation$budget
allocation$lambda