Modeling Sales of Multigeneration Technology Products in the Presence of Frequent Repeat Purchases: A Fractional Calculus-Based Approach
针对现有模型忽略代内重复购买的不足，提出了一个基于分数阶微积分的多代销售模型，能更准确预测技术产品各代的销售轨迹，并用于优化市场进入时机。
Frequently releasing a new product generation has become a common practice to sustain sales over time, thus accurately forecasting the sales trajectory of each product generation plays a vital role in the short-, medium-, and long-term planning of a firm. Classic multigeneration diffusion models do not incorporate within-generation repeat purchases, making them unusable for product lines with high rates of such purchases. Concentrating on technology products, we develop a multigeneration sales model to fill this void. We demonstrate that the new model can be used for predictive and prescriptive analytics. Our empirical results show that the new model estimates and forecasts sales more accurately than a state-of-the-art benchmark model that does not account for within-generation repeat purchases, underscoring the importance of incorporating repeat purchases. Furthermore, we use two different versions of our model to examine market entry timing under two main strategies, that is, (i) a phase-out transition strategy in which firms continue to sell the old generation after the release of the new generation, and (ii) a total transition strategy in which firms discontinue the old generation after the introduction of the new generation. Our results indicate that the repeat purchases rate determines whether it is optimal to expedite or delay the new product launch, underscoring the importance of incorporating repeat purchases in market entry strategies.