Abstract: Considering the lagged effect of quality on goodwill,the lagged differential equation of quality on goodwill was constructed based on Nerlove-Arrow model to study the dynamic product quality and service quality level under decentralized decision and centralized decision respectively.The results indicated that the optimal product goodwill,product quality and service quality were higher in centralized decision than that in decentralized decision,yet whether the entire supply chain profit was higher in centralized decision depended on the relationship between two different types of lagged time.Under decentralized decision-making,the product quality lagged effect on goodwill was beneficial to retailers but unfavorable to manufacturers,while the service quality lagged effect on goodwill was unfavorable to retailers and beneficial to manufacturers.The effects of two different types of lagged time on the optimal quality level and profit of supply chain under centralized and decentralized conditions were analyzed to verify the relevant conclusions.

Key words: quality, goodwill, lagged effect, differential game, supply chains

摘要： 考虑质量对商誉影响的延迟效应,基于Nerlove-Arrow模型构建质量对商誉影响的延迟微分方程,研究分散式决策和集中式决策情形下的产品质量水平和服务质量水平决策问题。研究发现,对于产品商誉、产品质量水平和服务质量水平而言,集中式决策获得的最优值高于分散式决策,两种决策情形下供应链利润的高低取决于产品质量延迟时间和服务质量延迟时间之间的关系;分散决策下,产品质量延迟效应对零售商有利而对制造商不利,服务质量延迟效应对零售商不利而对制造商有利。通过分析集中和分散情形下产品质量和服务质量延迟时间对供应链最优质量水平及利润的影响,验证了相关结论。

关键词: 质量, 商誉, 延迟效应, 微分博弈, 供应链