Abstract: In recent years, the delayed launch of updated products has become one of product operation strategies in many enterprises. At present, researches on the timing of launching updated products are mainly based on the Bass model which assumes homogeneous users without considering specific social networks, and without optimizing initial seed selection. Based on the social influence maximization model, this paper considers the optimization of launching time and seed selection for updated products: in a social network with the existence of old products, products spread their influence in the form of diffusion model , and the old products would stop the spread when the updated products were launched, and how to choose the stage   and the   seeds for launching new products maximizes the sum of the profits from both the old and the updated products. In the diffusion model  , if the influence of a user from the neighbors of the purchased product exceeds a certain threshold, the user remains active and influences his/her inactive neighbors, and the diffusion stops when there is no new active user. In this paper, an integer programming model was established for the timing and seed optimization of product diffusion, and a multi-stage greedy algorithm was designed to solve large-scale instances. The computational experiments show that this algorithm has a higher solution efficiency than the traditional greedy algorithm, and a better solution quality than the degree discount algorithm and the random algorithm. Meanwhile, simulations in a real network exhibit that when the profit of the updated product is small, the number of seeds is small, and the planning stage restrictions are larger, the delayed launching time will easily make the manufacturer obtain a higher profit and market effect.

Key words: social network analysis, influence maximization, updated products, updated product, launch timing

摘要： 近年来，更新产品的延期投放成为许多企业的产品运营策略。目前关于产品投放时机的研究主要基于Bass模型，假定同质用户，没有考虑具体的社会网络，也没有优化初始的投放种子选择。基于社会影响力最大化模型的更新产品投放时机和种子优化问题：在一个已存在旧产品的社会网络 中，产品以扩散模型 的形式传播其影响力，但更新产品投放时旧产品停止扩散，如何选择投放阶段 和 个更新产品的种子使得新旧产品利润之和最大化。在本文的扩散模型中，如果用户来自已购买产品的邻居影响力超过某一确定阈值，则该用户保持激活并影响其未激活邻居，当未有新的激活用户时停止扩散。本文建立了更新产品扩散的投放时机和种子优化问题的整数规划模型，设计了求解大规模问题的多阶段贪婪算法。计算实验显示，相比传统贪婪算法，该算法具有更高的求解效率，相比度数下降算法、随机算法，该算法具有更好的求解质量。同时在一个真实网络中进行扩散模拟，发现：更新产品利润小、种子数量少、计划阶段限制大时，延期投放容易使厂商获得更高的利润和市场效果。

关键词: 社会网络分析, 影响力最大化问题, 更新产品, 投放时机