Study on Quality Decisions in Supply Chain considering the Lagged Time and Retailers Competition

The lagged time on goodwill is a common phenomenon in the process of quality improvement, which plays an important role in making quality strategy of supply chain. With increasing public attention to quality, supply chain quality management has become a research focus in recent years. This paper probes into the lagged time of quality on goodwill under the competitive environment of retailers and constructs a lagged differential equation of quality on goodwill based on the Nerlove–Arrow model. The results indicate that the optimal goodwill and quality are higher under centralized decision-making than under decentralized decision-making; however, whether or not the profit of the entire supply chain is higher under centralized decision-making depends on the span of the lagged time. Under decentralized decision-making, the lagged time of product quality on goodwill is favorable to retailers but unfavorable to manufacturers and vice versa. Therefore, when competition is low, a supply chain tends to adopt centralized decision-making. When competition is intense, it is appropriate for a supply chain to adopt decentralized decision-making. In conclusion, this paper analyzes the effects of the lagged time on the optimal quality level and supply chain profit as well as the effect of the competition coefficient on research findings concerning supply chain profit under centralized and decentralized decision-making to verify the relevant conclusions of this paper.