Determining the optimal duration of an advertising campaign using diffusion of information

This study developed a mathematical model to determine the optimal duration of an advertising campaign based on diffusion of information in a social group. As a preparation, diffusion of information is optimized. It is surprising that optimal time for information diffusion is independent of population size. A hypothetical example for the developed model is solved using spreadsheets. The diffusion coefficient is first obtained via Monte Carlo simulation rather than classical differential equation solution. Then, the developed model, which has an objective of total profit, is solved as both an unconstrained optimization and an integer nonlinear programming model. The optimal timing depends on diffusion coefficient, population size, ad cost per time unit, unit price and discount rate. Optimal timing is a time point that the discount line and the growth rate curve of the objective function intersect. As the discount rate increases, optimal time decreases.