Abstract: Aiming at the presence of showrooming and delay phenomenon in the dual-channel supply chain,the dynamic dual-channel supply chain model was constructed.By using Pontryagin maximum principle and differential game theory,the optimal strategies and profit were derived under centralized,decentralized and cost-sharing patterns respectively.The result showed that the advertising and service investment of manufacturer and retailer should be increased when the showrooming parameter increasing and the marginal profit of online channel was higher than that of offline channel under the centralized scenario,conversely should be decreased.But the service investment of retailer should be reduced and the ratio of service cost shared by manufacturer should be increased with the increasing of showrooming parameter when showrooming parameter increasing in the decentralized and cost-sharing scenarios;with the increasing of delay time,the investment in advertising and service of manufacturer and retailer should be decreased respectively;cost-sharing strategy would not enhance the manufacturer's investment but could enhance the service investment decided by retailer.Within certain conditions,the service level incentivized by cost-sharing was higher than that under decentralized scenario.Moreover,according to the numerical analysis,the cost-sharing decision could make the profits of both manufacturer and retailer higher than those under centralized pattern and when the delay time of service strategy satisfies specific condition,the total profit of supply chain under cost-sharing pattern was higher than the total profit of centralized supply chain.

Key words: dual-channel supply chain, showrooming, time delay, cost-sharing, differential game

摘要： 针对双渠道供应链中的展厅和延时现象,构建了动态双渠道供应链模型。利用庞特里亚金极大值原理,分别求解了制造商和零售商在集中、分散以及成本分担决策模式下的最优策略和最优利润。研究发现;①在集中决策模式下,展厅效应系数增大时,若线上渠道的边际利润高于线下渠道的边际利润,则制造商和零售商应增加其广告和服务投入,反之则应该减少。而在分散和成本分担决策模式下,当展厅效应系数增大时,零售商应减少其服务投入,而制造商应增加其广告投入并增加其成本分担比例。②3种模式下,当延时时间增大时,制造商和零售商都应减少其广告和服务投入。但随着广告策略延时时间的增加,制造商应增加其成本分担比例,而服务策略的延时时间对成本分担策略无影响。③在特定情况下,成本分担激励下的服务策略会高于集中决策模式下的水平。另外,根据数值分析可知,成本分担策略能提高双方在分散决策模式下的利润,实现帕累托改进,且当服务策略延时时间满足一定条件时,成本分担模式下供应链总利润高于集中模式下供应链的总利润。

关键词: 双渠道供应链, 展厅现象, 延时现象, 成本分担, 微分对策