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.
KeywordsProduct diffusion Potential consumer Birth and death process Product sampling
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- 1.Bass FM (1969) A new product growth model for consumer durables. Management Science 15:215–227Google Scholar
- 2.Hu Z, Xie R, Xu J (2012) Impact of product sampling for diffusion. Systems Engineering Theory and Practic 20(6):167–175 (In Chinese)Google Scholar
- 3.Hu Z (2005) Sampling for diffusion of new product. Systems Engineering Theory and Practic (3):97–100 (In Chinese)Google Scholar
- 4.Hu Z (2006) Incorporating price in optimal product sampling for diffusion. International Journal of Management Science and Engineering Management 1(2):119–136Google Scholar
- 5.Lammers BH (1991) The effect of free samples on the immediate consumer purchase. Consumer Marketing 8(2):31–37Google Scholar
- 6.Heiman HB, Mcwilliams B, Shen Z et al (2001) Learning and forgetting: Modeling optimal product sampling over time. Management Science 47(4):532–546Google Scholar
- 7.Jain DC, Mahajan V, Muller E (1995) An approach for determining optimal product sampling for the diffusion of a new product. Journal of Product Innovation Management 12(4):124–135Google Scholar
- 8.Mahajan V, Peterson RA (1985) Models for innovation diffusion. CA Sage Publication Inc, Beverly HillGoogle Scholar
- 9.Lu Y, Ku Y, Lin H (2003) 7th Pacific Asia Conference on Imformation Systems. 10–13 July, Adelaide, South AustraliaGoogle Scholar
- 10.Rai R, Samaddar ST (1998) How to anticipate the internet’s global diffusion. Communications of the ACM 41(10):97–106Google Scholar
- 11.Meade N, Islam T (2006) Modelling and forecasting the diffusion of innovation-a 25-year review. International Journal of forecasting 22(3):519–545Google Scholar
- 12.Ho TH, SAVIN S, Terwiesch C (2002) Managing demand and sales dynamics in new product diffusion under supply constraint. Managing Science 48(2):187–206Google Scholar