中文摘要：

本文基于互补产品扩散模型，在考虑价格策略以及重复购买与批量购买的消费者行为下，建立了免费商品赠送对互补产品扩散影响的优化模型群。通过模拟计算，分析结果表明免费商品的赠送对互补产品的扩散有促进作用，同时赠送互补产品优于仅赠送其中一种产品。在产品引入前进行免费商品赠送的边际效应要高于在其他时期赠送，形成“首期赠送效应”。当消费者有批量购买行为时，企业值得赠送更多的免费商品来提高消费者对产品的了解程度，以获得更高的利润。在对首期赠送水平的参数灵敏度分析后，给出了扩散过程中各个参数选取对于赠样水平的影响趋势与范围。在此基础上，为企业在实际促销决策中给出了具体的应用步骤。

英文摘要：

Considering the pricing strategies and the consumer behaviors of repeat purchase and multiple-u- nit purchase, an optimal model group of product sampling of complementary products based on the diffu- sion model of complementary products is established. With the numerical simulation, the results show that the sampling can advance the diffusion of complementary products, and sending the free samples of both complementary products is better than just sending one of them. Also, sampling at the initial period is much better than other periods, which forms ＂a promotional phenomenon of sampling at time zero＂. In the case of the consumers having the demand of multiple-unit purchase, the firm deserves to send more free samples to make the product known wider in order to enhance the sales profit. Moreover, the sensitive a- nalysis in the optimal sampling period shows the trend and extent of the effect of the parameters on the sampling levels. Finally, how to apply the results in the reality is also shown.