Abstract: The multiple-unit adoptions are quite common in the purchasing process of nondurables. Based on the Bass model, this paper develops a new diffusion model involving free product samples and considering the multiple-unit adoptions as a diffusion process; then, the paper introduces the repeat purchase and pricing strategies to build an optimal model group. The simulation analysis of free samples under two types of purchase styles and the sensitive analysis of some key parameters in the model group indicate that like the case of individual purchase, free samples can accelerate the diffusion process when there are multiple-unit adoptions; moreover, to achieve a higher profit, it deserves the firm to send more free samples than ones in the case of only individual purchase. Also, the more multiple units purchased, the more free samples should be sent, even sent to every consumer, which can make more consumers to know the product. Furthermore, the benefit of sampling at time zero is larger than sampling at any other periods, which forms “A promotional phenomenon of sampling at time zero”. Finally, the paper shows the trend and extent of the impact of the parameters on the sampling level.

Key words: new product, product sampling, product diffusion, multiple-unit ownership, simulation

摘要： 在非耐用品的购买过程中,批量购买的消费行为较为普遍。本文基于Bass模型,将批量购买看作一个扩散过程,建立批量购买下含免费商品的产品扩散模型;然后在扩散模型中引入重复购买和价格策略等因素的影响,构建了优化模型群。对不同购买方式下的免费商品赠送进行仿真分析,同时对模型中重要参数进行优化后分析,计算分析表明:和单量购买情形一致,当存在批量购买时,免费商品的赠送同样会加快产品的扩散速度,但值得赠送更多的免费商品以达到利润最大化。消费者的批量购买量越大,就越有必要赠送更多的免费商品来让消费者了解该产品,甚至对每个消费者发放免费商品。同时,通过对赠送时期的对比分析,发现只有在产品引入初期赠送最佳,形成了“首期赠送效应”。最后,给出了参数对免费商品赠送水平的影响范围与趋势。

关键词: 新产品, 免费商品, 产品扩散, 批量购买, 仿真