Richard F. Deckro
In this paper, an effort is made to build a model capturing non-linear relationship between frequency and reach. The objective function is having number of exposure, dollar invested in each media and, cost per insertion as variables. Besides using exact nonlinear relationship, quantity discount can also be included in the model.
Vadyar, Sridhar V., "Media Allocation Model" (1992). Engineering and Technology Management Student Projects. 736.