利用信息扩散确定广告活动的最佳持续时间

Determining the Optimal Duration of an Advertising Campaign Based on Diffusion of Information

根据建立的数学模型的信息在社会群体中的扩散情况,可以用来确定广告活动的最佳持续时间。作为一项准备,信息的扩散被优化了。令人惊讶的是,信息扩散的最佳时间与特定人群无关。设计了所建立模型的一个假想算例,并利用电子表格工具求解。首先通过蒙特卡罗模拟得到了扩散系数,而不是通过经典的微分方程求解得到。所建立的模型以总利润为目标函数,分别对无约束优化模型以及整数非线性规划模型进行求解。一场广告活动的最佳持续时间取决于扩散系数、人口规模、单位时间内的广告成本、单位价格以及贴现率。贴现曲线与目标函数的增长率曲线相交的点的值就是广告活动的最佳持续时间。结果还发现随着贴现率的增加,最佳持续时间缩短。

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 by 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.