Birth and Death: Modeling Optimal Product Sampling Over Time for Nondurables

To confirm the idea of sampling over time under the framework of Bass model, this paper builds a diffusion model based on the idea of birth and death process, systems dynamics. The basic results show that the model can include the results of previous models as a special case or reduced case. It is assumed that the total amount of potential consumers remain unchanged, and the effect of repeat purchase is consider, so as to build the Optimization model group. The analysis showed that product diffusion entered a stable period in the late and the amount of diffusion is maintained at a certain level. As part of potential customers don’t purchase the product, the amount of diffusion must be less than the total potential customers’ purchases and the diffusion continues as long as the product exist in the market. No matter the change of potential customer is static or dynamic, sampling promotes the diffusion and the best time to carry out the activity is first period. If sampling rate is limited, and the limit value is reduced to a certain extent, it will appear continuous sampling. With the reduction of the limit value, the sampling rate decreases, which causes the reduction of the amount of final product diffusion, eventually lead NPV of enterprise lower.